Searcharxiv⌕ Search

arXiv subjects

A. H. Welsh

Publications and source records attributed to A. H. Welsh.

26 records · Page 2Linked to original sources
arXiv2021

Screening methods for linear errors-in-variables models in high dimensions

Microarray studies, in order to identify genes associated with an outcome of interest, usually produce noisy measurements for a large number of gene expression features from a small number of subjects. One common approach to analyzing such high-dimensional data is to use linear errors-in-variables models; however, current methods for fitting such models are computationally expensive. In this paper, we present two efficient screening procedures, namely corrected penalized marginal screening and corrected sure independence screening, to reduce the number of variables for final model building. Both screening procedures are based on fitting corrected marginal regression models relating the outcome to each contaminated covariate separately, which can be computed efficiently even with a large number of features. Under mild conditions, we show that these procedures achieve screening consistency and reduce the number of features considerably, even when the number of covariates grows exponentially with the sample size. Additionally, if the true covariates are weakly correlated, corrected penalized marginal screening can achieve full variable selection consistency. Through simulation studies and an analysis of gene expression data for bone mineral density of Norwegian women, we demonstrate that the two new screening procedures make estimation of linear errors-in-variables models computationally scalable in high dimensional settings, and improve finite sample estimation and selection performance compared with estimators that do not employ a screening stage.

stat.ME↗
arXiv2021

Sparse Sliced Inverse Regression via Cholesky Matrix Penalization

We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of the central subspace. The new estimators use the Cholesky decomposition of the covariance matrix of the covariates and include a regularization term in the objective function to achieve sparsity in a computationally efficient manner. We establish the theoretical values of the tuning parameters that achieve estimation and variable selection consistency for the central subspace. Furthermore, we propose a new projection information criterion to select the tuning parameter for our proposed estimators and prove that the new criterion facilitates selection consistency. The Cholesky matrix penalization estimator inherits the strength of the Matrix Lasso and the Lasso sliced inverse regression estimator; it has superior performance in numerical studies and can be adapted to other sufficient dimension methods in the literature.

stat.ME↗
arXiv2021

Increasing Cluster Size Asymptotics for Nested Error Regression Models

This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent clusters and the cluster sizes (the number of observations in each cluster) go to infinity. Under very mild conditions, the estimators are shown to be asymptotically normal with an elegantly structured covariance matrix. There are no restrictions on the rate at which the cluster size tends to infinity but it turns out that we need to treat within cluster parameters (i.e. coefficients of unit-level covariates that vary within clusters and the within cluster variance) differently from between cluster parameters (i.e. coefficients of cluster-level covariates that are constant within clusters and the between cluster variance) because they require different normalisations and are asymptotically independent.

math.ST↗
arXiv2018

Bootstrapping F test for testing Random Effects in Linear Mixed Models

Recently Hui et al. (2018) use F tests for testing a subset of random effect, demonstrating its computational simplicity and exactness when the first two moment of the random effects are specified. We extended the investigation of the F test in the following two aspects: firstly, we examined the power of the F test under non-normality of the errors. Secondly, we consider bootstrap counterparts to the F test, which offer improvement for the cases with small cluster size or for the cases with non-normal errors.

stat.ME↗
arXiv2014

Fletcher-Turek Model Averaged Profile Likelihood Confidence Intervals

We evaluate the model averaged profile likelihood confidence intervals proposed by Fletcher and Turek (2011) in a simple situation in which there are two linear regression models over which we average. We obtain exact expressions for the coverage and the scaled expected length of the intervals and use these to compute these quantities in particular situations. We show that the Fletcher-Turek confidence intervals can have coverage well below the nominal coverage and expected length greater than that of the standard confidence interval with coverage equal to the same minimum coverage. In these situations, the Fletcher-Turek confidence intervals are unfortunately not better than the standard confidence interval used after model selection but ignoring the model selection process.

stat.ME↗
arXiv2013

Model Selection in Linear Mixed Models

Linear mixed effects models are highly flexible in handling a broad range of data types and are therefore widely used in applications. A key part in the analysis of data is model selection, which often aims to choose a parsimonious model with other desirable properties from a possibly very large set of candidate statistical models. Over the last 5-10 years the literature on model selection in linear mixed models has grown extremely rapidly. The problem is much more complicated than in linear regression because selection on the covariance structure is not straightforward due to computational issues and boundary problems arising from positive semidefinite constraints on covariance matrices. To obtain a better understanding of the available methods, their properties and the relationships between them, we review a large body of literature on linear mixed model selection. We arrange, implement, discuss and compare model selection methods based on four major approaches: information criteria such as AIC or BIC, shrinkage methods based on penalized loss functions such as LASSO, the Fence procedure and Bayesian techniques.

stat.ME↗
arXiv2007

Robust model selection in generalized linear models

In this paper, we extend to generalized linear models (including logistic and other binary regression models, Poisson regression and gamma regression models) the robust model selection methodology developed by Mueller and Welsh (2005; JASA) for linear regression models. As in Mueller and Welsh (2005), we combine a robust penalized measure of fit to the sample with a robust measure of out of sample predictive ability which is estimated using a post-stratified m-out-of-n bootstrap. A key idea is that the method can be used to compare different estimators (robust and nonrobust) as well as different models. Even when specialized back to linear regression models, the methodology presented in this paper improves on that of Mueller and Welsh (2005). In particular, we use a new bias-adjusted bootstrap estimator which avoids the need to centre the explanatory variables and to include an intercept in every model. We also use more sophisticated arguments than Mueller and Welsh (2005) to establish an essential monotonicity condition.

stat.ME↗