Ching-Kang Ing

National Tsing Hua University | NTHU · Institute of Statistics

Although existing literature on high-dimensional regression models is rich, the vast majority of studies have focused on independent and homogeneous error terms. In this article, we consider the problem of selecting high-dimensional regression models with heteroscedastic and time series errors, which have broad applications in economics, quantitati...

Principal component analysis (PCA) is the most commonly used statistical procedure for dimension reduction. An important issue for applying PCA is to determine the rank, which is the number of dominant eigenvalues of the covariance matrix. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) are among the most widely used...

We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. To prevent OGA from overfitting, we introduce a high-dimensional Akaike's information criter...

Consider finite parametric time series models. “I have n observations and k models, which model should I choose on the basis of the data alone” is a frequently asked question in many practical situations. This poses the key problem of selecting a model from a collection of candidate models, none of which is necessarily the true data generating proc...

We introduce a fast stepwise regression method, called the orthogonal greedy algorithm (OGA), that selects input variables to enter a p-dimensional linear regression model (with p n, the sample size) sequentially so that the selected variable at each step minimizes the residual sum squares. We derive the convergence rate of OGA and develop a consis...

We establish a negative moment bound for the sample autocovariance matrix of a stationary process driven by conditional heteroscedastic errors. This moment bound enables us to asymptotically express the mean squared prediction error (MSPE) of the least squares predictor as the sum of three terms related to model complexity, model misspecification,...

We consider model selection for linear mixed‐effects models with clustered structure, where conditional Kullback‐Leibler (CKL) loss is applied to measure the efficiency of the selection. We estimate the CKL loss by substituting the empirical best linear unbiased predictors (EBLUPs) into random effects with model parameters estimated by maximum like...

This paper studies an important sequential decision making problem known as the multi-armed stochastic bandit problem with covariates. Under a linear bandit framework with high-dimensional covariates, we propose a general multi-stage arm allocation algorithm that integrates both arm elimination and randomized assignment strategies. By employing a c...

Principal component analysis (PCA) is a commonly used statistical tool for dimension reduction. An important issue in PCA is to determine the rank, which is the number of dominant eigenvalues of the covariance matrix. Among information-based criteria, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are the two mo...

Estimating the orders of the autoregressive fractionally integrated moving average (ARFIMA) model has been a long-standing problem in time series analysis. This paper tackles this challenge by establishing the consistency of the Bayesian information criterion (BIC) for ARFIMA models with independent errors. Since the memory parameter of the model c...

We consider a linear mixed-effects model with a clustered structure, where the parameters are estimated using maximum likelihood (ML) based on possibly unbalanced data. Inference with this model is typically done based on asymptotic theory, assuming that the number of clusters tends to infinity with the sample size. However, when the number of clus...

The framework of model-X knockoffs provides a flexible tool for exact finite-sample false discovery rate (FDR) control in variable selection. It also completely bypasses the use of conventional p-values, making it especially appealing in high-dimensional nonlinear models. Existing works have focused on the setting of independent and identically dis...

The concepts of Industry 4.1 for achieving Zero-Defect (ZD) manufacturing were disclosed in IEEE Robotics and Automation Letters in January 2016. ZD of all the deliverables can be achieved by discarding the defective products via a real-time and online total inspection technology, such as Automatic Virtual Metrology (AVM). Further, the Key-variab...

We consider a linear mixed-effects model with a clustered structure, where the parameters are estimated using maximum likelihood (ML) based on possibly unbalanced data. Inference with this model is typically done based on asymptotic theory, assuming that the number of clusters tends to infinity with the sample size. However, when the number of clus...

We are interested in constructing confidence intervals for the autoregressive (AR) coefficient of a first‐order AR model with i.i.d. positive errors via an extreme value estimate (EVE). We assume that the error distribution has a density function fε(x) behaving like as x→0, where b1,0 and α0 are unknown positive constants. These specifications impl...

Prediction has long been a vibrant topic in modern probability and statistics. In addition to finding optimal forecasts and for model selection, it is argued in this paper that the prediction principle can also be used to analyze critical phenomena, in particular, in stationary and unstable time series. Although the notion of nearly unstable models...

We consider a stochastic process model with time trend and measurement error. We establish consistency and derive the limiting distributions of the maximum likelihood (ML) estimators of the covariance function parameters under a general asymptotic framework, including both the fixed domain and the increasing domain frameworks, even when the time tr...

Motivated by applications to root-cause identification of faults in multistage manufacturing processes which involve a large number of tools or equipments at each stage, we consider multiple testing in regression models whose outputs represent the quality characteristics of a multistage manufacturing process. Because of the large number of input va...

This work aims at estimating inverse autocovariance matrices of long memory processes admitting a linear representation. A modified Cholesky decomposition is used in conjunction with an increasing order autoregressive model to achieve this goal. The spectral norm consistency of the proposed estimate is established. We then extend this result to lin...

Threshold autoregressive (TAR) model is an important class of nonlinear time series models that possess many desirable features such as asymmetric limit cycles and amplitude dependent frequencies. Statistical inference for TAR model encounters a major difficulty in the estimation of thresholds, however. This paper develops an efficient procedure to...

There is an extensive literature on fixed-size confidence regions for the regression parameters in a linear model with p regressors, attaining a prescribed coverage probability when p is fixed and the size d approaches 0. Motivated by recent developments in regression modeling in response to applications for which p is considerably larger than the...

Consider a regression model with in?nitely many parameters and time series errors. We are interested in choosing weights for averaging across generalized least squares (GLS) estimators obtained from a set of approximating models. However, GLS estimators, depending on the unknown inverse covariance matrix of the errors, are usually infeasible. We th...

Information criteria, such as Akaike's information criterion and Bayesian information criterion are often applied in model selection. However, their asymptotic behaviors for selecting geostatistical regression models have not been well studied, particularly under the fixed domain asymptotic framework with more and more data observed in a bounded fi...

In this paper, we assume that observations are generated by a linear regression model with short- or long-memory dependent errors. We establish inverse moment bounds for -dimensional sample autocovariance matrices based on the least squares residuals (also known as the detrended time series), where , and n is the sample size. These results are then...

Let observations y 1, …, yn be generated from a first-order autoregressive (AR) model with positive errors. In both the stationary and unit root cases, we derive moment bounds and limiting distributions of an extreme value estimator, [Inline formula], of the AR coefficient. These results enable us to provide asymptotic expressions for the mean squa...

A moment bound for the normalized conditional-sum-of-squares (CSS) estimate of a general autoregressive fractionally integrated moving average (ARFIMA) model with an arbitrary unknown memory parameter is derived in this paper. To achieve this goal, a uniform moment bound for the inverse of the normalized objective function is established. An import...

Consider l(q)-hulls, 0 < q <= 1, from a dictionary of M functions in L-P space for 1 < p < cc. Their precise metric entropy orders are derived. Sparse linear approximation bounds are obtained to characterize the number of terms needed to achieve accurate approximation of the best function in a l(q)-hull that is closest to a target function. Further...

non-stationary autoregressions

We show that Akaike’s Information Criterion (AIC) and its variants are asymptotically efficient in integrated autoregressive processes of infinite order (AR(∞)). This result, together with its stationary counterpart established previously in the literature, ensures that AIC can ultimately achieve prediction efficiency in an AR(∞) process, without k...

The article [Sequential Anal. 30, No. 4, 356–399 (2011; Zbl 1228.62096)] by M. Aoshima and K. Yata considers two-stage procedures to construct fixed-size confidence regions and to select variables in high-dimensional models with a bounded number of nonzero parameters. In this discussion, we describe some recent work on alternative variable selectio...

In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher’s information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear) stochastic regression models. The usefulness of these results is illustrated using time series models. In parti...

Assume that observations are generated from nonstationary autoregressive (AR) processes of infinite order. We adopt a finite-order approximation model to predict future observations and obtain an asymptotic expression for the mean-squared prediction error (MSPE) of the least squares predictor. This expression provides the first exact assessment of...

This paper investigates multistep prediction errors for non-stationary autoregressive processes with both model order and true parameters unknown. We give asymptotic expressions for the multistep mean squared prediction errors and accumulated prediction errors of two important methods, plug-in and direct prediction. These expressions not only chara...

Findings from literature showed inconsistent results for applying service quality scale in hospitals. Moreover, hospitalization services are provided by diversified departments and a scale designed to measure the overall hospitalization quality is difficult and capturing special characteristics of different departments is also not an easy task. Thi...

A major research area of Ching-Zong Wei (1949--2004) was time series models and their applications in econometrics and engineering, to which he made many important contributions. A conference on time series and related topics in memory of him was held on December 12--14, 2005, at Academia Sinica in Taipei, where he was Director of the Institute of...

In this article asymptotic expressions for the final prediction error (FPE) and the accumulated prediction error (APE) of the least squares predictor are obtained in regression models with nonstationary regressors. It is shown that the term of order $1/n$ in FPE and the term of order $\log n$ in APE share the same constant, where $n$ is the sample...

Assume that observations are generated from an infinite-order autoregressive [AR($\infty$)] process. Shibata [Ann. Statist. 8 (1980) 147--164] considered the problem of choosing a finite-order AR model, allowing the order to become infinite as the number of observations does in order to obtain a better approximation. He showed that, for the purpose...

We establish a maximal moment inequality for the weighted sum of a sequence of random variables with finite second moments. An extension of the J. Hájek and A. Rény [Acta Math. Acad. Sci. Hung. 6, 281–283 (1956; Zbl 0067.10701)] and Y. S. Chow [Proc. Am. Math. Soc. 11, 107–111 (1960; Zbl 0102.13501)] inequalities is then obtained. When certain seco...

The predictive capability of a modification of Rissanen's accumulated prediction error (APE) criterion, APE$_{\delta_{n}}$,is investigated in infinite-order autoregressive (AR($\infty$)) models. Instead of accumulating squares of sequential prediction errors from the beginning, APE$_{\delta_{n}}$ is obtained by summing these squared errors from sta...

We consider the problem of choosing the optimal (in the sense of mean-squared prediction error) multistep predictor for an autoregressive (AR) process of finite but unknown order. If a working AR model (which is possibly misspecified) is adopted for multistep predictions, then two competing types of multistep predictors (i.e., plug-in and direct pr...

We investigate the predictive ability of the accumulated prediction error (APE) of Rissanen in an infinite-order autoregressive (AR(#)) model. Since there are infinitely many parameters in the model, all finite-order AR models are misspecified. We first show that APE is asymptotically equivalent to Bayesian information criterion (BIC) and is not as...

Zhang and Shaman considered the problem of estimating the conditional mean-squared prediciton error (CMSPE) for a Gaussian autoregressive (AR) process. They used the final prediction error (FPE) of Akaike to estimate CMSPE and proposed that FPE's effectiveness be judged by its asymptotic correlation with CMSPE. However, as pointed out by Kabaila an...

Let observations come from an infinite-order autoregressive (AR) process. For predicting the future of the observed time series (referred to as the same-realization prediction), we use the least-squares predictor obtained by fitting a finite-order AR model. We also allow the order to become infinite as the number of observations does in order to ob...

In this paper, two competing types of multistep predictors, i.e., plug-in and direct predictors, are considered in autoregressive (AR) processes. When a working model AR(k) is used for the h-step prediction with h 1, the plug-in predictor is obtained from repeatedly using the fitted (by least squares) AR(k) model with an unknown future value replac...

An asymptotic expression for the mean-squared prediction error (MSPE) of the least squares predictor is obtained in the random walk model. It is shown that the term of order 1/n in this error, where n is the sample size, is twice as large as the one obtained from the first-order autoregressive (AR(1)) model satisfying the stationary assumption. Mor...

We investigate the predictive ability of the accumulated prediction error (APE) of Rissanen in an infinite-order autoregressive (AR(∞)) model. Since there are infinitely many parameters in the model, all finite-order AR models are misspecified. We first show that APE is asymptotically equivalent to Bayesian information criterion (BIC) and is not as...

This paper considers the order (predictor) selection problem in autoregressive (AR) processes. When the underlying AR model is known to be stationary and of infinite order, Shibata (1980) and Ing and Wei (2005) showed that AIC is asymptotically efficient for independent-and same-realization predictions, respectively. Ing (2007) recently removed the...

This paper investigates multistep prediction errors for nonstationary au- toregressive processes with both model order and true parameters unknown. We give asymptotic expressions for the multistep mean squared prediction errors and accumulated prediction errors of two important methods, plug-in and direct prediction. These expres- sions not only ch...