Related papers: A note on Influence diagnostics in nonlinear mixed…
This paper introduces a direct differentiation-based framework that unifies the derivation of influence functions across parametric, nonparametric, and semiparametric models. We show that the Riesz representer of the functional derivative…
Using the LRT statistic, a model R^2 is proposed for the generalized linear mixed model for assessing the association between the correlated outcomes and fixed effects. The R^2 compares the full model to a null model with all fixed effects…
Influence Functions are a standard tool for attributing predictions to training data in a principled manner and are widely used in applications such as data valuation and fairness. In this work, we present realistic incentives to manipulate…
This paper proposes a debiased estimator for causal effects in high-dimensional generalized linear models with binary outcomes and general link functions. The estimator augments a regularized regression plug-in with weights computed from a…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
Given that hierarchical count data in many fields are not Normally-distributed and include random effects, this paper extends the Generalized Linear Mixed Models (GLMMs) into Poisson Mixed-Effect Linear Model (PMELM) and do numerical…
Influence diagnostics such as influence functions and approximate maximum influence perturbations are popular in machine learning and in AI domain applications. Influence diagnostics are powerful statistical tools to identify influential…
To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse…
A dataset has been classified by some unknown classifier into two types of points. What were the most important factors in determining the classification outcome? In this work, we employ an axiomatic approach in order to uniquely…
Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…
The Fisher information matrix summarizes the amount of information in a set of data relative to the quantities of interest. There are many applications of the information matrix in statistical modeling, system identification and parameter…
The selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. Our focus is on the…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the $\delta$, flat…
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…
We present a brief overview of the methods for making statistical inference (testing statistical hypotheses, construction of confidence and/or prediction intervals and regions) about linear functions of the fixed effects and/or about the…
We propose a random-effects approach to missing values for generalized linear mixed model (GLMM) analysis. The method converts a GLMM with missing covariates to another GLMM without missing covariates. The standard GLMM analysis tools for…
The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…
Influence functions provide a principled method to assess the contribution of individual training samples to a specific target. Yet, their high computational costs limit their applications on large-scale models and datasets. Existing…
This paper proposes a unified class of generalized location-scale mixture of multivariate elliptical distributions and studies integral stochastic orderings of random vectors following such distributions. Given a random vector…