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This paper focuses on exploring the sparsity of the inverse covariance matrix $\bSigma^{-1}$, or the precision matrix. We form blocks of parameters based on each off-diagonal band of the Cholesky factor from its modified Cholesky…
The modified Cholesky decomposition is commonly used for precision matrix estimation given a specified order of random variables. However, the order of variables is often not available or cannot be pre-determined. In this work, we propose…
Nonlinear Mixed effects models are hidden variables models that are widely used in many fields such as pharmacometrics. In such models, the distribution characteristics of hidden variables can be specified by including several parameters…
Boosting techniques from the field of statistical learning have grown to be a popular tool for estimating and selecting predictor effects in various regression models and can roughly be separated in two general approaches, namely gradient…
In this article, an efficient numerical method for computing both the matrix exponential and a finite horizon controllability Gramian in Cholesky-factored form is proposed. The method is applicable to general dense matrices of moderate size…
CholeskyQR is a simple and fast QR decomposition via Cholesky decomposition, while it has been considered highly sensitive to the condition number. In this paper, we provide a randomized preconditioner framework for CholeskyQR algorithm.…
Mixed-effect models are very popular for analyzing data with a hierarchical structure, e.g. repeated observations within subjects in a longitudinal design, patients nested within centers in a multicenter design. However, recently, due to…
Estimating large covariance matrices has been a longstanding important problem in many applications and has attracted increased attention over several decades. This paper deals with two methods based on pre-existing works to impose sparsity…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…
The Cholesky decomposition plays an important role in finding the inverse of the correlation matrices. As it is a fast and numerically stable for linear system solving, inversion, and factorization compared to singular valued decomposition…
Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…
A mixture of multivariate Poisson-log normal factor analyzers is introduced by imposing constraints on the covariance matrix, which resulted in flexible models for clustering purposes. In particular, a class of eight parsimonious mixture…
In this paper, we present Insertus.jl, the Julia package that can help the user generate a randomization sequence of a given length for a multi-arm trial with a pre-specified target allocation ratio and assess the operating characteristics…
Maximum likelihood (ML) estimation is widely used in statistics. The h-likelihood has been proposed as an extension of Fisher's likelihood to statistical models including unobserved latent variables of recent interest. Its advantage is that…
Linear Mixed-Effects (LME) models are a fundamental tool for modeling correlated data, including cohort studies, longitudinal data analysis, and meta-analysis. Design and analysis of variable selection methods for LMEs is more difficult…
The sparsity-restricted maximum likelihood estimator (SMLE) has received considerable attention for feature screening in ultrahigh-dimensional regression. SMLE is a computationally convenient method that naturally incorporates the joint…
This paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models. We propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed…
Motivated by genome-wide association studies, we consider a standard linear model with one additional random effect in situations where many predictors have been collected on the same subjects and each predictor is analyzed separately.…
LLM-as-judge evaluation has become standard practice for open-ended model assessment; however, judges exhibit systematic biases that cannot be averaged out by increasing the number of scenarios or generations. These biases are often similar…
Covariance estimation for high-dimensional datasets is a fundamental problem in modern day statistics with numerous applications. In these high dimensional datasets, the number of variables p is typically larger than the sample size n. A…