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The standard regression tree method applied to observations within clusters poses both methodological and implementation challenges. Effectively leveraging these data requires methods that account for both individual-level and sample-level…
Rank regression offers robustness to outliers and heavy-tailed response distributions, invariance to monotonic transformations, and improved efficiency under non-Gaussian errors, making it a versatile tool for analyzing complex data. This…
In this work we provide a simple estimation procedure for a general frailty model for analysis of prospective correlated failure times. Rigorous large-sample theory for the proposed estimators of both the regression coefficient vector and…
We present \textit{universal} estimators for the statistical mean, variance, and scale (in particular, the interquartile range) under pure differential privacy. These estimators are universal in the sense that they work on an arbitrary,…
In this paper we have suggested a family of estimators for the population mean when study variable itself is qualitative in nature. Expressions for the bias and mean square error (MSE) of the suggested family have been obtained. An…
INTRODUCTION: Wald's, the likelihood ratio (LR) and Rao's score tests and their corresponding confidence intervals (CIs), are the three most common estimators of parameters of Generalized Linear Models. On finite samples, these estimators…
We propose a novel $\ell_1+\ell_2$-penalty, which we refer to as the Generalized Elastic Net, for regression problems where the feature vectors are indexed by vertices of a given graph and the true signal is believed to be smooth or…
The naive importance sampling estimator, based on samples from a single importance density, can be numerically unstable. Instead, we consider generalized importance sampling estimators where samples from more than one probability…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…
This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…
We propose a class of tests for linear regression on concomitants (induced order statistics). These tests are based on sequential sums of regression residuals. We self-center and self-normalize these sums. The resulting process is called an…
An inference procedure is proposed to provide consistent estimators of parameters in a modal regression model with a covariate prone to measurement error. A score-based diagnostic tool exploiting parametric bootstrap is developed to assess…
Given two populations from which independent binary observations are taken with parameters $p_1$ and $p_2$ respectively, estimators are proposed for the relative risk $p_1/p_2$, the odds ratio $p_1(1-p_2)/(p_2(1-p_1))$ and their logarithms.…
We develop generalized approach to obtaining Edgeworth expansions for $t$-statistics of an arbitrary order using computer algebra and combinatorial algorithms. To incorporate various versions of mean-based statistics, we introduce Adjusted…
This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…
We present herein a scheme by which to accurately evaluate the error exponents of a lossy data compression problem, which characterize average probabilities over a code ensemble of compression failure and success above or below a critical…
The objective of this work is to propose an asymptotic correction method for the estimators of parameters from regression models with covariates subject to classification errors. A correction was developed based on the least squares…
We propose a novel computationally low-cost method for estimating a general predictive measure of generalised Bayesian inference. The proposed method utilises posterior covariance and provides estimators of the Gibbs and the plugin…
The generalized log-gamma (GLG) model is a very flexible family of distributions to analyze datasets in many different areas of science and technology. In this paper, we propose estimators which are simultaneously highly robust and highly…
We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any…