Canadian Journal of Statistics (CAN J STAT)

Publications in this journal

• Article: Parallelism, uniqueness, and large-sample asymptotics for the Dantzig selector.

  Lee Dicker, Xihong Lin
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  ABSTRACT: The Dantzig selector (Candès and Tao, 2007) is a popular ℓ(1)-regularization method for variable selection and estimation in linear regression. We present a very weak geometric condition on the observed predictors which is related to parallelism and, when satisfied, ensures the uniqueness of Dantzig selector estimators. The condition holds with probability 1, if the predictors are drawn from a continuous distribution. We discuss the necessity of this condition for uniqueness and also provide a closely related condition which ensures uniqueness of lasso estimators (Tibshirani, 1996). Large sample asymptotics for the Dantzig selector, i.e. almost sure convergence and the asymptotic distribution, follow directly from our uniqueness results and a continuity argument. The limiting distribution of the Dantzig selector is generally non-normal. Though our asymptotic results require that the number of predictors is fixed (similar to (Knight and Fu, 2000)), our uniqueness results are valid for an arbitrary number of predictors and observations.
  Canadian Journal of Statistics 03/2013; 41(1):23-35.
• Article: Q-learning for estimating optimal dynamic treatment rules from observational data.

  Erica E M Moodie, Bibhas Chakraborty, Michael S Kramer
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  ABSTRACT: The area of dynamic treatment regimes (DTR) aims to make inference about adaptive, multistage decision-making in clinical practice. A DTR is a set of decision rules, one per interval of treatment, where each decision is a function of treatment and covariate history that returns a recommended treatment. Q-learning is a popular method from the reinforcement learning literature that has recently been applied to estimate DTRs. While, in principle, Q-learning can be used for both randomized and observational data, the focus in the literature thus far has been exclusively on the randomized treatment setting. We extend the method to incorporate measured confounding covariates, using direct adjustment and a variety of propensity score approaches. The methods are examined under various settings including non-regular scenarios. We illustrate the methods in examining the effect of breastfeeding on vocabulary testing, based on data from the Promotion of Breastfeeding Intervention Trial.
  Canadian Journal of Statistics 12/2012; 40(4):629-645.
• Article: Variable selection and estimation in generalized linear models with the seamless L 0 penalty.

  Zilin Li, Sijian Wang, Xihong Lin
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  ABSTRACT: In this paper, we propose variable selection and estimation in generalized linear models using the seamless L 0 (SELO) penalized likelihood approach. The SELO penalty is a smooth function that very closely resembles the discontinuous L 0 penalty. We develop an e cient algorithm to fit the model, and show that the SELO-GLM procedure has the oracle property in the presence of a diverging number of variables. We propose a Bayesian Information Criterion (BIC) to select the tuning parameter. We show that under some regularity conditions, the proposed SELO-GLM/BIC procedure consistently selects the true model. We perform simulation studies to evaluate the finite sample performance of the proposed methods. Our simulation studies show that the proposed SELO-GLM procedure has a better finite sample performance than several existing methods, especially when the number of variables is large and the signals are weak. We apply the SELO-GLM to analyze a breast cancer genetic dataset to identify the SNPs that are associated with breast cancer risk.
  Canadian Journal of Statistics 12/2012; 40(4):745-769.
• Article: Multivariate Kendall's tau for change-point detection in copulas

  Jean-François Quessy, Mériem Saïd, Anne-Catherine Favre
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  ABSTRACT: Statistical procedures for the detection of a change in the dependence structure of a series of multivariate observations are studied in this work. The test statistics that are proposed are $L_1$, $L_2$, and $L_\infty$ distances computed from vectors of differences of Kendall's tau; two multivariate extensions of Kendall's measure of association are used. Since the distributions of these statistics under the null hypothesis of no change depend on the unknown underlying copula of the vectors, a procedure based on the multiplier central limit theorem is used for the computation of p-values; the method is shown to be valid both asymptotically and for moderate sample sizes. Alternative versions of the tests that take into account possible breakpoints in the marginal distributions are also investigated. Monte Carlo simulations show that the tests are powerful under many scenarios of change-point. In addition, two estimators of the time of change are proposed and their efficiency is carefully studied. The methodologies are illustrated on simulated series from the Canadian Regional Climate Model.
  Canadian Journal of Statistics 09/2012;
• Article: The effect of misspecification of random effects distributions in clustered data settings with outcome-dependent sampling.

  John M Neuhaus, Charles E McCulloch
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  ABSTRACT: Genetic epidemiologists often gather outcome-dependent samples of family data to measure within-family associations of genetic factors with disease outcomes. Generalized linear mixed models provide effective methods to estimate within-family associations but typically require parametric specification of the random effects distribution. Although misspecification of the random effects distribution often leads to little bias in estimated regression coefficients in standard, prospective clustered data settings, some recent studies suggest that such misspecification will impact parameter estimates from outcome-dependent cluster sampling designs. Using analytic results, simulation studies and fits to example data, this study examines the effect of misspecification of random effects distributions on parameter estimates in clustered data settings with outcome-dependent sampling. We show that the effects are consistent with results from prospective cluster sampling settings. In particular, ascertainment corrected mixed model methods that assume normally distributed random intercepts and conditional likelihood approaches provide accurate estimates of within-family covariate effects even under a misspecified random effects distribution.
  Canadian Journal of Statistics 09/2011; 39(3):488-497.
• Article: Semiparametric transformation models for multivariate panel count data with dependent observation process.

  Ni Li, Do-Hwan Park, Jianguo Sun, Kyungmann Kim
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  ABSTRACT: This article discusses regression analysis of multivariate panel count data in which the observation process may contain relevant information about or be related to the underlying recurrent event processes of interest. Such data occur if a recurrent event study involves several related types of recurrent events and the observation scheme or process may be subject-specific. For the problem, a class of semiparametric transformation models is presented, which provides a great flexibility for modelling the effects of covariates on the recurrent event processes. For estimation of regression parameters, an estimating equation-based inference procedure is developed and the asymptotic properties of the resulting estimates are established. Also the proposed approach is evaluated by simulation studies and applied to the data arising from a skin cancer chemoprevention trial.
  Canadian Journal of Statistics 09/2011; 39(3):458-474.
• Article: Robust penalized logistic regression with truncated loss functions.

  Seo Young Park, Yufeng Liu
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  ABSTRACT: The penalized logistic regression (PLR) is a powerful statistical tool for classification. It has been commonly used in many practical problems. Despite its success, since the loss function of the PLR is unbounded, resulting classifiers can be sensitive to outliers. To build more robust classifiers, we propose the robust PLR (RPLR) which uses truncated logistic loss functions, and suggest three schemes to estimate conditional class probabilities. Connections of the RPLR with some other existing work on robust logistic regression have been discussed. Our theoretical results indicate that the RPLR is Fisher consistent and more robust to outliers. Moreover, we develop estimated generalized approximate cross validation (EGACV) for the tuning parameter selection. Through numerical examples, we demonstrate that truncating the loss function indeed yields better performance in terms of classification accuracy and class probability estimation.
  Canadian Journal of Statistics 06/2011; 39(2):300-323.
• Article: Additive hazards regression with censoring indicators missing at random.

  Xinyuan Song, Liuquan Sun, Xiaoyun Mu, Gregg E Dinse
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  ABSTRACT: In this article, the authors consider a semiparametric additive hazards regression model for right-censored data that allows some censoring indicators to be missing at random. They develop a class of estimating equations and use an inverse probability weighted approach to estimate the regression parameters. Nonparametric smoothing techniques are employed to estimate the probability of non-missingness and the conditional probability of an uncensored observation. The asymptotic properties of the resulting estimators are derived. Simulation studies show that the proposed estimators perform well. They motivate and illustrate their methods with data from a brain cancer clinical trial.
  Canadian Journal of Statistics 09/2010; 38(3):333-351.
• Article: Longitudinal functional principal component modeling via Stochastic Approximation Monte Carlo.

  Josue G Martinez, Faming Liang, Lan Zhou, Raymond J Carroll
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  ABSTRACT: The authors consider the analysis of hierarchical longitudinal functional data based upon a functional principal components approach. In contrast to standard frequentist approaches to selecting the number of principal components, the authors do model averaging using a Bayesian formulation. A relatively straightforward reversible jump Markov Chain Monte Carlo formulation has poor mixing properties and in simulated data often becomes trapped at the wrong number of principal components. In order to overcome this, the authors show how to apply Stochastic Approximation Monte Carlo (SAMC) to this problem, a method that has the potential to explore the entire space and does not become trapped in local extrema. The combination of reversible jump methods and SAMC in hierarchical longitudinal functional data is simplified by a polar coordinate representation of the principal components. The approach is easy to implement and does well in simulated data in determining the distribution of the number of principal components, and in terms of its frequentist estimation properties. Empirical applications are also presented.
  Canadian Journal of Statistics 06/2010; 38(2):256-270.
• Article: Inference after variable selection using restricted permutation methods.

  Rui Wang, Stephen W Lagakos
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  ABSTRACT: When confronted with multiple covariates and a response variable, analysts sometimes apply a variable-selection algorithm to the covariate-response data to identify a subset of covariates potentially associated with the response, and then wish to make inferences about parameters in a model for the marginal association between the selected covariates and the response. If an independent data set were available, the parameters of interest could be estimated by using standard inference methods to fit the postulated marginal model to the independent data set. However, when applied to the same data set used by the variable selector, standard ("naive") methods can lead to distorted inferences. The authors develop testing and interval estimation methods for parameters reflecting the marginal association between the selected covariates and response variable, based on the same data set used for variable selection. They provide theoretical justification for the proposed methods, present results to guide their implementation, and use simulations to assess and compare their performance to a sample-splitting approach. The methods are illustrated with data from a recent AIDS study.
  Canadian Journal of Statistics 12/2009; 37(4):625-644.
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  Available from: ubc.ca

  Article: Conservative Prior Distributions for Variance Parameters in Hierarchical Models

  Shahadut Hossain, Paul Gustafson
  Canadian Journal of Statistics 01/2006; 34(3).
• Article: Higher-order approximations for Pitman estimators and for optimal compromise estimators

  Laura Ventura
  Canadian Journal of Statistics 01/1998; 26:49-55.
• Article: Some aspects of modern population mathematics.

  D R Brillinger
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  ABSTRACT: "The purpose of this paper is to survey a number of the technical tools and models that have found use in the study of human and other populations, and to indicate some problems of current interest. These tools and models are varied: integral equations, nonlinear oscillations, differential geometry, dynamical systems, nonlinear operation, bifurcation theory, semigroup theory, martingale theory, Markov processes, diffusion processes, branching processes, ergodic theory, prediction theory and state-space models. A fairly extensive bibliography is provided. Also an Appendix has been added describing the analysis of a classical entomological data set." (summary in FRE)
  Canadian Journal of Statistics 02/1981; 9(2):173-94.
• Article: Impact of projected population trends on post-secondary education, 1961-2001.

  Z Zsigmond
  Canadian Journal of Statistics 02/1976; 4(2):255-76.