David Ruppert

• PhD, Michigan State University, Statistics, 1977
• Cornell University

Background Myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS) is a complex, heterogenous disease characterized by unexplained persistent fatigue and other features including cognitive impairment, myalgias, post-exertional malaise, and immune system dysfunction. Cytokines are present in plasma and encapsulated in extracellular vesicles (EVs...

We develop a generalized partially additive model to build a single semiparametric risk scoring system for physical activity across multiple populations. A score comprised of distinct and objective physical activity measures is a new concept that offers challenges due to the nonlinear relationship between physical behaviors and various health outco...

Sample splitting is widely used in statistical applications, including classically in classification and more recently for inference post model selection. Motivating by problems in the study of diet, physical activity, and health, we consider a new application of sample splitting. Physical activity researchers wanted to create a scoring system to q...

Suppose there are two unknown parameters, each parameter is the solution to an estimating equation, and the estimating equation of one parameter depends on the other parameter. The parameters can be jointly estimated by "stacking" their estimating equations and solving for both parameters simultaneously. Asymptotic confidence intervals are readily...

We now focus on models for the joint effect of two continuous predictor variables. Additive models are convenient, but there is no reason to assume that they are always adequate. In the general bivariate models studied in this chapter, the joint effect of the two variables is a smooth, but otherwise unrestricted, function of these variables. Theref...

Chapters 2– 5 deal with the most fundamental semiparametric regression topics and implementation in R. There are numerous other topics but, of course, not all of them can be covered in a single book. Instead we cover a selection of additional topics in this final chapter that we feel are worthy of some mention. These concern robust and quantile reg...

The models fit in Chap. 2 have two limitations. First, the conditional distribution of the response, given the predictors, is assumed to be Gaussian. Second, only a single predictor is allowed to have a smooth nonlinear effect—the other predictors are modeled linearly. The first limitation is addressed by using generalized linear models (GLMs), whi...

Grouped data arise in several diverse contexts in statistical design and analysis. Examples include medical studies in which patients are followed over time and measurements on them recorded repeatedly, educational studies in which students grouped into classrooms and schools are scored on examinations, and sample surveys in which the respondents t...

In this chapter, we study nonparametric regression with a single continuous predictor. This problem is often called scatterplot smoothing. Our emphasis is on the use of penalized splines. We also show that a penalized spline model can be represented as a linear mixed model, which allows us to fit penalized splines using linear mixed model software.

We propose a copula-based approach for analyzing functional data with correlated multiple functional outcomes exhibiting heterogeneous shape characteristics. To accommodate the possibly large number of parameters due to having several functional outcomes, parameter estimation is performed in two steps: first, the parameters for the marginal distrib...

Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS) is a disease of enigmatic origin with no established cure. Its constellation of symptoms has silently ruined the lives of millions of people around the world. A plethora of hypotheses have been vainly investigated over the past few decades, so that the biological basis of this debilitating...

Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA (PCA+ICA), which could remove important information. The problem is that interesting independent components (ICs) co...

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself, as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function....

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon the global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we allow the local scale parameter...

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon a global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence among the local...

This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is suitable for more complicated data structures. However, its estimation inherits the difficulties and complexitie...

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with non-negligible measurement error. The latent process is dynamically modeled as a functional autoregression (F...

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. W...

Estimating spatiotemporal models for multi-subject fMRI is computationally challenging. We propose a mixed model for localization studies with spatial random effects and time-series errors. We develop method-of-moment estimators that leverage population and spatial information and are scalable to massive datasets. In simulations, subject-specific e...

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with non-negligible measurement error. The latent process is dynamically modeled as a functional autoregression (F...

Given uncertainty in the input model and parameters of a stochastic simulation study, the goal of the study often becomes the estimation of a conditional expectation. The conditional expectation is expected performance conditioned on the selected model and parameters. The density of this conditional expectation describes precisely, and concisely, t...

Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS) remains a continuum spectrum disease without biomarkers or simple objective tests, and therefore relies on a diagnosis from a set of symptoms to link the assortment of brain and body disorders to ME/CFS. Although recent studies show various affected pathways, the underlying basis of ME/CFS...

Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA (PCA+ICA), which could remove important information. The problem is that interesting independent components (ICs) co...

We present a method to simultaneously model the dust far-infrared spectral energy distribution (SED) and the total infrared − carbon monoxide (CO) integrated intensity (SIR−ICO) relationship. The modelling employs a hierarchical Bayesian (HB) technique to estimate the dust surface density, temperature (Teff), and spectral index at each pixel from t...

We present a method to simultaneously model the dust far-infrared spectral energy distribution (SED) and the total infrared $-$ carbon monoxide (CO) integrated intensity $(S_{\rm IR}-I_{\rm CO})$ relationship. The modelling employs a hierarchical Bayesian (HB) technique to estimate the dust surface density, temperature ($T_{\rm eff}$), and spectral...

Linear mixed-effects models are a powerful tool for modelling longitudinal data and are widely used in practice. For a given set of covariates in a linear mixed-effects model, selecting the covariance structure of random effects is an important problem. In this paper, we develop a joint likelihood-based selection criterion. Our criterion is the app...

To model heteroscedasticity in a broad class of additive partial linear models, we allow the variance function to be an additive partial linear model as well and the parameters in the variance function to be different from those in the mean function. We develop a two-step estimation procedure, where in the first step initial estimates of the parame...

Regression is one of the most widely used of all statistical methods. For univariate regression, the available data are one response variable and p predictor variables, all measured on each of n observations. We let Y denote the response variable and \(X_{1},\ldots,X_{p}\) be the predictor or explanatory variables.KeywordsPredictor VariableOrthogon...

The CAPM (capital asset pricing model) has a variety of uses. It provides a theoretical justification for the widespread practice of passive investing by holding index funds. The CAPM can provide estimates of expected rates of return on individual investments and can establish “fair” rates of return on invested capital in regulated firms or in firm...

Finding a single set of estimates for the parameters in a statistical model is not enough. An assessment of the uncertainty in these estimates is also needed. Standard errors and confidence intervals are common methods for expressing uncertainty. In the past, it was sometimes difficult, if not impossible, to assess uncertainty, especially for compl...

The financial world has always been risky, and financial innovations such as the development of derivatives markets and the packaging of mortgages have now made risk management more important than ever, but also more difficult.

This book is about the statistical analysis of financial markets data such as equity prices, foreign exchange rates, and interest rates. These quantities vary randomly thereby causing financial risk as well as the opportunity for profit. Figures 4.1, 4.2, and 4.3 show, respectively, time series plots of daily log returns on the S&P 500 index, daily...

As seen in earlier chapters, financial market data often exhibits volatility clustering, where time series show periods of high volatility and periods of low volatility; see, for example, Fig. 14.1. In fact, with economic and financial data, time-varying volatility is more common than constant volatility, and accurate modeling of time-varying volat...

Suppose one could find a stock whose price (or log-price) series was stationary and therefore mean-reverting. This would be a wonderful investment opportunity. Whenever the price was below the mean, one could buy the stock and realize a profit when the price returned to the mean. Similarly, one could realize profits by selling short whenever the pr...

How should we invest our wealth? Portfolio theory provides an answer to this question based upon two principles: we want to maximize the expected return; and we want to minimize the risk, which we define in this chapter to be the standard deviation of the return, though we may ultimately be concerned with the probabilities of large losses. These go...

Copulas are a popular framework for both defining multivariate distributions and modeling multivariate data. A copula characterizes the dependence—and only the dependence—between the components of a multivariate distribution; they can be combined with any set of univariate marginal distributions to form a full joint distribution. Consequently, the...

The goal of investing is, of course, to make a profit. The revenue from investing, or the loss in the case of negative revenue, depends upon both the change in prices and the amounts of the assets being held. Investors are interested in revenues that are high relative to the size of the initial investments. Returns measure this, because returns on...

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline the...

This article has no abstract.

In high dimensions, the classical Hotelling's $T^2$ test tends to have low power or becomes undefined due to singularity of the sample covariance matrix. In this paper, this problem is overcome by projecting the data matrix onto lower dimensional subspaces through multiplication by random matrices. We propose RAPTT (RAndom Projection T-Test), an ex...

The Seychelles Child Development Study (SCDS) examines the effects of prenatal exposure to methylmercury on the functioning of the central nervous system. The SCDS data include 20 outcomes measured on 9-year old children that can be classified broadly in four outcome classes or "domains": cognition, memory, motor, and social behavior. Previous anal...

By the early 1980s, regression with homoscedastic errors was well understood, but methodology for handling heteroscedastic noise was just being developed. There were two general approaches. In the first, studied by Carroll and Ruppert (1981 [TW-1], 1984 [TW-3]), the response is transformed to homoscedasticity. In the second, studied by Carroll and...

We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to t of F{X(t), t} where F( ·, ·) is an unknown regression function and X(t) is a functional covariate. Rather...

This paper introduces a general framework for testing hypotheses about the structure of the mean function of complex functional processes. Important particular cases of the proposed framework are as follows: (1) testing the null hypothesis that the mean of a functional process is parametric against a general alternative modelled by penalized spline...

We examine differences between independent component analyses (ICAs) arising from different assumptions, measures of dependence, and starting points of the algorithms. ICA is a popular method with diverse applications including artifact removal in electrophysiology data, feature extraction in microarray data, and identifying brain networks in funct...

The paper introduces a new method for flexible spline fitting for copula density estimation. Spline coefficients are penalized to achieve a smooth fit. To weaken the curse of dimensionality, instead of a full tensor spline basis, a reduced tensor product based on so called sparse grids (Notes Numer. Fluid Mech. Multidiscip. Des., 31, 1991, 241-251)...

We propose a procedure for testing the linearity of a scalar-on-function regression relationship. To do so, we use the functional generalized additive model (FGAM), a recently developed extension of the functional linear model. For a functional covariate X(t), the FGAM models the mean response as the integral with respect to t of F{X(t),t} where F...

We propose a new method for regression using a parsimonious and scientifically interpretable representation of functional predictors. Our approach is designed for data that exhibit features such as spikes, dips, and plateaus whose frequency, location, size, and shape varies stochastically across subjects. We propose Bayesian inference of the joint...

We consider regression models for multiple correlated outcomes, where the outcomes are nested in domains. We show that random effect models for this nested situation fit into a standard factor model framework, which leads us to view the modeling options as a spectrum between parsimonious random effect multiple outcomes models and more general conti...

For smoothing covariance functions, we propose two fast algorithms that scale linearly with the number of observations per function. Most available methods and software cannot smooth covariance matrices of dimension $J \times J$ with $J>500$; the recently introduced sandwich smoother is an exception, but it is not adapted to smooth covariance matri...

The functional generalized additive model (FGAM) was recently proposed in McLean et al. (2012) as a more flexible alternative to the common functional linear model (FLM) for regressing a scalar on functional covariates. In this paper, we develop a Bayesian version of FGAM for the case of Gaussian errors with identity link function. Our approach all...

The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and additive errors, which we will call the additive functional model, a generalization of the functional linear model...

Bayesian MCMC calibration and uncertainty analysis for computationally expensive models is implemented using the SOARS (Statistical and Optimization Analysis using Response Surfaces) methodology. SOARS uses a radial basis function interpolator as a surrogate, also known as an emulator or meta-model, for the logarithm of the posterior density. To pr...

The sources of ultra-high energy cosmic rays (UHECRs) are unknown but are likely nearby galaxies. To assess association of UHECRs and candidate sources, we developed a multilevel Bayesian framework. We demonstrate this framework using simple models similar to those in previous studies, but our results suggest a need for more complex models; these a...

The Earth is continuously showered by charged cosmic ray particles, naturally produced atomic nuclei moving with velocity close to the speed of light. Among these are ultra high energy cosmic ray particles with energy exceeding 5x10^19 eV, which is ten million times more energetic than the most energetic particles produced at the Large Hadron Colli...

Bayesian analysis offers a general approach to measurement error that has many advantages—it focuses attention on careful modeling, is widely applicable, and provides efficient estimators. Bayesian analysis is relatively easy using WinBUGS software. We discuss here the paper by Brandon Kelly, and present an example of fitting a quadratic regression...

Bayesian inference using Markov chain Monte Carlo (MCMC) is computationally prohibitive when the posterior density of interest, π, is computationally expensive to evaluate. We develop a derivative-free algorithm GRIMA to accurately approximate π by interpolation over its high-probability density (HPD) region, which is initially unknown. Our local a...

The method of maximum tapered likelihood has been proposed as a way to quickly estimate covariance parameters for stationary Gaussian random fields. We show that under a useful asymptotic regime, maximum tapered likelihood estimators are consistent and asymptotically normal for covariance models in common use. We then formalize the notion of tapere...

1. Introduction and Motivation. 2. One-Dimensional Estimators. 3. One-Dimensional Tests. 4. Multidimensional Estimators. 5. Estimation of Covariance Matrices and Multivariate Location. 6. Linear Models: Robust Estimation. 7. Linear Models: Robust Testing. 8. Complements and Outlook. References. Index.

This report studies local asymptotics of P-splines with $p$th degree B-splines and a $m$th order difference penalty. Earlier work with $p$ and $m$ restricted is extended to the general case. Asymptotically, penalized splines are kernel estimators with equivalent kernels depending on $m$, but not on $p$. A central limit theorem provides simple expre...

We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent G...

Economic and financial time series typically exhibit time-varying conditional (given the past) standard deviations and correlations. The conditional standard deviation is also called the volatility. Higher volatilities increase the risk of assets and higher conditional correlations cause an increased risk in portfolios. Therefore, models of time-va...

Economic time series often exhibit strong seasonal variation. For example, an investor in mortgage-backed securities might be interested in predicting future housing starts, and these are usually much lower in the winter months compared to the rest of the year. Figure 10.1(a) is a time series plot of the logarithms of quarterly urban housing starts...

Bayesian statistics is based up a philosophy different from that of other methods of statistical inference. In Bayesian statistics all unknowns, and in particular unknown parameters, are considered to be random variables and their probability distributions specify our beliefs about their likely values. Estimation, model selection, and uncertainty...

A time series is a sequence of observations in chronological order, for example, daily log returns on a stock or monthly values of the Consumer Price Index (CPI). A common simplifying assumption is that the data are equally spaced with a discrete-time observation index; however, this may only hold approximately. For example, daily log returns on a...

As seen in Chap. 4, usually the marginal distributions of financial time series are not well fit by normal distributions. Fortunately, there are a number of suitable alternative models, such as t-distributions, generalized error distributions, and skewed versions of t- and generalized error distributions. All of these will be introduced in this cha...

When residual analysis shows that the residuals are correlated, then one of the key assumptions of the linear model does not hold, and tests and confidence intervals based on this assumption are invalid and cannot be trusted. Fortunately, there is a solution to this problem: Replace the assumption of independent noise by the weaker assumption that...

Often we are not interested merely in a single random variable but rather in the joint behavior of several random variables, for example, returns on several assets and a market index. Multivariate distributions describe such joint behavior. This chapter is an introduction to the use of multivariate distributions for modeling financial markets data.

Corporations finance their operations by selling stock and bonds. Owning a share of stock means partial ownership of the company. Stockholders share in both the profits and losses of the company. Owning a bond is different. When you buy a bond you are loaning money to the corporation, though bonds, unlike loans, are tradeable. The corporation is ob...

High-dimensional data can be challenging to analyze. They are difficult to visualize, need extensive computer resources, and often require special statistical methodology. Fortunately, in many practical applications, high-dimensional data have most of their variation in a lower-dimensional space that can be found using dimension reduction technique...

Cointegration analysis is a technique that is frequently applied in econometrics. In finance it can be used to find trading strategies based on meanreversion.

This book is about the statistical analysis of financial markets data such as equity prices, foreign exchange rates, and interest rates. These quantities vary random thereby causing financial risk as well as the opportunity for profit.

The CAPM (capital asset pricing model) has a variety of uses. It provides a theoretical justification for the widespread practice of passive investing by holding index funds. The CAPM can provide estimates of expected rates of return on individual investments and can establish \fair" rates of return on invested capital in regulated firms or in firm...

As seen in earlier chapters, financial markets data often exhibit volatility clustering, where time series show periods of high volatility and periods of low volatility; see, for example, Figure 18.1. In fact, with economic and financial data, time-varying volatility is more common than constant volatility, and accurate modeling of time-varying vol...

Regression is one of the most widely used of all statistical methods. For uni- variate regression, the available data are one response variable and p predictor variables, all measured on each of n observations.

Markov chain Monte Carlo (MCMC) is nowadays a standard approach to numerical computation of integrals of the posterior density π of the parameter vector η. Unfortunately, Bayesian inference using MCMC is computationally intractable when the posterior density π is expensive to evaluate. In many such problems, it is possible to identify a minimal sub...

A model including an age-structure, a stochastic egg-recruitment relationship, density-dependent juvenile growth, age-dependent fishing mortality, and fecundity dependent upon size as well as age was used to investigate three types of harvesting strategies: constant yearly catch policies, constant fishing mortality rate policies, and "egg escapemen...

The following biological components concerning the population dynamics of Atlantic menhaden (Brevoortia tyrannus) were investigated: growth, natural mortality, migration, fishing mortality, and recruitment. We found that a hypothesis of density-dependent growth is strongly supported by the data and that the dependence of growth on abundance appears...

Many things can, and often do, go wrong when data are analyzed. There may be data that were entered incorrectly, one might not be analyzing the data set one thinks, the variables may have been mislabeled, and so forth. In Example 10.5, presented shortly, one of the weekly time series of interest rates began with 371 weeks of zeros, indicating missi...

As discussed in Chap. 9, regression analysis estimates the conditional expectation of a response given predictor variables. The conditional expectation is called the regression function and is the best predictor of the response based upon the predictor variables, because it minimizes the expected squared prediction error. There are three types of r...

How should we invest our wealth? Portfolio theory provides an answer to this question based upon two principles: we want to maximize the expected return; and we want to minimize the risk, which we define in this chapter to be the standard deviation of the return, though we may ultimately be concerned with the probabilities of large losses.

Copulas are a popular method for modeling multivariate distributions. A copula models the dependence|and only the dependence|between the variates in a multivariate distribution and can be combined with any set of univariate distributions for the marginal distributions. Consequently, the use of copulas allows us to take advantage of the wide variety...

Finding a single set of estimates for the parameters in a statistical model is not enough. An assessment of the uncertainty in these estimates is also needed. Standard errors and confidence intervals are common methods for expressing uncertainty. In the past, it was sometimes difficult, if not impossible, to assess uncertainty, especially for compl...

The financial world has always been risky, and financial innovations such as the development of derivatives markets and the packaging of mortgages have now made risk management more important than ever but also more difficult.

Markov chain Monte Carlo (MCMC) is nowadays a standard approach to numerical computation of integrals of the posterior density π of the parameter vector η. Unfortunately, Bayesian inference using MCMC is computationally intractable when the posterior density π is expensive to evaluate. In many such problems, it is possible to identify a minimal sub...

This paper performs an asymptotic analysis of penalized spline estimators. We compare P-splines and splines with a penalty of the type used with smoothing splines. The asymptotic rates of the supremum norm of the difference between these two estimators over compact subsets of the interior and over the entire interval are established. It is shown th...

We propose a fast penalized spline method for bivariate smoothing. Univariate P-spline smoothers (Eilers and Marx, 1996) are applied simultaneously along both coordinates. The new smoother has a sandwich form which suggested the name "sandwich smoother" to a referee. The sandwich smoother has a tensor product structure that simplifies an asymptotic...

This book is about the analysis of financial markets data. After this brief introductory chapter, we turn immediately in Chapters 2 and 3 to the sources of the data, returns on equities and prices and yields on bonds. Chapter 4 develops methods for informal, often graphical, analysis of data. More formal methods based on statistical inference, that...

Frailty models derived from the proportional hazards regression model are frequently used to analyze clustered right-censored survival data. We propose a semiparametric Bayesian methodology for this purpose, modeling both the unknown baseline hazard and density of the random effects using mixtures of B-splines. The posterior distributions for all r...

Contenido: 1) Introducción; 2) Retorno de la inversión; 3) Valores de renta fija; 4) Exploración de análisis de datos; 5) Modelos de distribuciones univariantes; 6) Reuestreo; 7) Modelos estadísticos multivariables; 8) Cópulas;9) Modelos de series de tiempo: bases; 10) Modelos de series de tiempo: otros temas; 11) Teoría de portafolio; 12) Regresió...

This paper addresses asymptotic properties of general penalized spline estimators with an arbitrary B-spline degree and an arbitrary order difference penalty. The estimator is approximated by a solution of a linear differential equation subject to suitable boundary conditions. It is shown that, in certain sense, the penalized smoothing corresponds...

This paper presents application of a new computationally efficient method SOARS for statistically rigorous assessment of uncertainty in parameters and model output when the model is calibrated to field data. The SOARS method is general and is here applied to watershed problems The innovative aspect of this procedure is that an optimization method i...

This paper considers generalized partially linear models. We propose empirical likelihood-based statistics to construct confidence regions for the parametric and non-parametric components. The resulting statistics are shown to be asymptotically chi-square distributed. Finite-sample performance of the proposed statistics is assessed by simulation ex...