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Qualifying gene and isoform expression is one of the primary tasks for RNA-Seq experiments. Given a sequence of counts representing numbers of reads mapped to different positions (exons and junctions) of isoforms, methods based on Poisson…
We consider high-dimensional regression with a count response modeled by Poisson or negative binomial generalized linear model (GLM). We propose a penalized maximum likelihood estimator with a properly chosen complexity penalty and…
In this article, we study a robust estimation method for a general class of integer-valued time series models. The conditional distribution of the process belongs to a broad class of distribution and unlike classical autoregressive…
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…
Under complete linkage disequilibrium (LD), robust tests often have greater power than Pearson's chi-square test and trend tests for the analysis of case-control genetic association studies. Robust statistics have been used in…
We are interested in the problem of robust parametric estimation of a density from $n$ i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk…
M-estimators offer simple robust alternatives to the maximum likelihood estimator. Much of the robustness literature, however, has focused on the problems of location, location-scale and regression estimation rather than on estimation of…
Testing the association between a phenotype and many genetic variants from case-control data is essential in genome-wide association study (GWAS). This is a challenging task as many such variants are correlated or non-informative.…
We consider the problem of variable screening in ultra-high dimensional generalized linear models (GLMs) of non-polynomial orders. Since the popular SIS approach is extremely unstable in the presence of contamination and noise, we discuss a…
This article proposes a novel estimator for regression coefficients in clustered data that explicitly accounts for within-cluster dependence. We study the asymptotic properties of the proposed estimator under both finite and infinite…
The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical…
We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a…
Most signal processing and statistical applications heavily rely on specific data distribution models. The Gaussian distributions, although being the most common choice, are inadequate in most real world scenarios as they fail to account…
Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with complex traits, and some variants are shown to be associated with multiple complex traits. Genetic covariance between two traits is defined…
Many modern products exhibit high reliability under normal operating conditions. Conducting life tests under these conditions may result in very few observed failures, insufficient for accurate inferences. Instead, accelerated life tests…
Robust inferential methods based on divergences measures have shown an appealing trade-off between efficiency and robustness in many different statistical models. In this paper, minimum density power divergence estimators (MDPDEs) for the…
We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…
In this paper we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of…
Gaussian process-based latent variable models are flexible and theoretically grounded tools for nonlinear dimension reduction, but generalizing to non-Gaussian data likelihoods within this nonlinear framework is statistically challenging.…
We introduce a density-power weighted variant for the Stein operator, called the $\gamma$-Stein operator. This is a novel class of operators derived from the $\gamma$-divergence, designed to build robust inference methods for unnormalized…