Canadian Journal of Statistics-Revue Canadienne De Statistique最新文献

In this article, we propose an automatic structure recovery method for generalized additive models (GAMs) by extending Wu and Stefanski's approach. In a similar vein, the proposed method is based on a local scoring algorithm coupled with local polynomial smoothing, along with a kernel-based variable selection approach. Given a specific degree $��M�$, the goal is to identify predictors contributing polynomially at different degrees up to $��M�$ and predictors that contribute beyond degree $��M�$. By focusing on two GAMs, logistic regression and Poisson regression, we illustrate the performance of the proposed method using Monte Carlo simulation studies and two real data examples.

In this article, we focus on the two-sample location testing problem for high-dimensional data, where the data dimension is potentially much larger than the sample sizes. First, we construct a general class of weighted spatial sign tests for the two-sample location problem, which can include some existing high-dimensional nonparametric tests. Then, in this article, we find a locally most powerful test by choosing the inverse norm weight function, named the two-sample inverse norm sign test (tINST). The proposed test can be viewed as an extension of the inverse norm sign test devised for the one-sample problem. We establish the asymptotic properties of the proposed test, which indicate that it is consistent and has greater power than competing tests that belong to the proposed class of weighted spatial sign tests for two-sample location problems. Finally, a large number of numerical investigations and a practical biomedical example demonstrate the power and robustness advantages of the proposed test.

Identification of a subset of patients who may be sensitive to a specific treatment is an important step towards personalized medicine. We consider the case where the effect of a treatment is assessed by longitudinal measurements, which may be continuous or categorical, such as quality of life scores assessed over the duration of a clinical trial. We assume that multiple baseline covariates, such as age and expression levels of genes, are available, and propose a generalized single-index linear threshold model to identify the treatment-sensitive subset and assess the treatment-by-subset interaction after combining these covariates. Because the model involves an indicator function with unknown parameters, conventional procedures are difficult to apply for inferences of the parameters in the model. We define smoothed generalized estimating equations and propose an inference procedure based on these equations with an efficient spectral algorithm to find their solutions. The proposed procedure is evaluated through simulation studies and an application to the analysis of data from a randomized clinical trial in advanced pancreatic cancer.

Current status data are widely used in epidemiology and public health, where the only observable information is the random inspection time and the event status at inspection. This article presents a unified methodology to analyze such complex data subject to clustering. Given the random clustering effect, the time to event is assumed to follow a semiparametric generalized odds rate (GOR) model. The nonparametric component of the GOR model is approximated via penalized splines, with a set of knot points that increase with the sample size. The within-subject correlation is accounted for by a random (frailty) effect. For estimation, a novel MM algorithm is developed that allows the separation of the parametric and nonparametric components of the model. This separation makes the problem conducive to applying the Newton–Raphson algorithm that quickly returns the roots. The work is accompanied by a complexity analysis of the algorithm, a rigorous asymptotic proof, and the related semiparametric efficiency of the proposed methodology. The finite sample performance of the proposed method is assessed via simulation studies. Furthermore, the proposed methodology is illustrated via real data analysis on periodontal disease studies accompanied by diagnostic checks to identify influential observations.

We consider the design and analysis of multi-factor experiments using fractional factorial and incomplete designs within the potential outcome framework. These designs are particularly useful when limited resources make running a full factorial design infeasible. We connect our design-based methods to standard regression methods. We further motivate the usefulness of these designs in multi-factor observational studies, where certain treatment combinations may be so rare that there are no measured outcomes in the observed data corresponding to them. Therefore, conceptualizing a hypothetical fractional factorial experiment instead of a full factorial experiment allows for appropriate analysis in those settings. We illustrate our approach using biomedical data from the 2003–2004 cycle of the National Health and Nutrition Examination Survey to examine the effects of four common pesticides on body mass index.

In this article, we present a review of important results and statistical applications obtained or generalized by Canadian pioneers and their collaborators, for empirical processes of independent and identically distributed observations, pseudo-observations, and time series. In particular, we consider weak convergence and strong approximations results, as well as tests for model adequacy such as tests of independence, tests of goodness-of-fit, tests of change point, and tests of serial dependence for time series. We also consider applications of empirical processes of interacting particle systems for the approximation of measure-valued processes.

As evidenced by various recent and significant papers within the frequentist literature, along with numerous applications in macroeconomics, genomics, and neuroscience, there continues to be substantial interest in understanding the theoretical estimation properties of high-dimensional vector autoregression (VAR) models. To date, however, while Bayesian VAR (BVAR) models have been developed and studied empirically (primarily in the econometrics literature), there exist very few theoretical investigations of the repeated-sampling properties for BVAR models in the literature, and there exist no generalized fiducial investigations of VAR models. In this direction, we construct methodology via the $��\epsilon �$-admissible subsets (EAS) approach for inference based on a generalized fiducial distribution of relative model probabilities over all sets of active/inactive components (graphs) of the VAR transition matrix. We provide a mathematical proof of pairwise and strong graphical selection consistency for the EAS approach for stable VAR(1) models, and demonstrate empirically that it is an effective strategy in high-dimensional settings.

Genetic association analysis, which evaluates relationships between genetic markers and complex, heritable traits, is the basis of genome-wide association studies. The many association tests that have been developed can generally be classified as prospective versus retrospective, parametric versus nonparametric, and genotype- versus allele-based. While method classifications are useful, it can be confusing and challenging for practitioners to decide on the “optimal” test to use for their data. We go beyond known differences between some popular association tests and provide new results that show analytical connections between tests, for both population- and family-based study designs.

Change point detection for high-dimensional data is an important yet challenging problem for many applications. In this article, we consider multiple change point detection in the context of high-dimensional generalized linear models, allowing the covariate dimension $��p�$ to grow exponentially with the sample size $��n�$. The model considered is general and flexible in the sense that it covers various specific models as special cases. It can automatically account for the underlying data generation mechanism without specifying any prior knowledge about the number of change points. Based on dynamic programming and binary segmentation techniques, two algorithms are proposed to detect multiple change points, allowing the number of change points to grow with $��n�$. To further improve the computational efficiency, a more efficient algorithm designed for the case of a single change point is proposed. We present theoretical properties of our proposed algorithms, including estimation consistency for the number and locations of change points as well as consistency and asymptotic distributions for the underlying regression coefficients. Finally, extensive simulation studies and application to the Alzheimer's Disease Neuroimaging Initiative data further demonstrate the competitive performance of our proposed methods.

We develop a method of classified mixed model prediction based on generalized linear mixed models that incorporate pseudo-prior information to improve prediction accuracy. We establish consistency of the proposed method both in terms of prediction of the true mixed effect of interest and in terms of correctly identifying the potential class corresponding to the new observations if such a class matching one of the training data classes exists. Empirical results, including simulation studies and real-data validation, fully support the theoretical findings.