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This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
Often it is not easy to choose between estimators, based on the estimated MSE and bias using simulation studies. Normality in small samples and a variance of the estimator, which is correct and easy to calculate using a single sample, give…
Several performance measures are used to evaluate binary and multiclass classification tasks. But individual observations may often have distinct weights, and none of these measures are sensitive to such varying weights. We propose a new…
Ever since the proof of asymptotic normality of maximum likelihood estimator by Cramer (1946), it has been understood that a basic technique of the Taylor series expansion suffices for asymptotics of $M$-estimators with…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…
Many results that are difficult can be found more easily by using a generalization in the complex plane of Einstein's addition law of parallel velocities. Such a generalization is a natural way to add quantities that are limited to bounded…
We establish a general criterion for the validity of inequalities of the following form: A certain convex combination of the values of a convex function at n points and of its value at a weighted mean of these n points is always greater or…
This paper presents two novel classes of variance estimators with superior properties, in the absence of parametric or semi-parametricassumptions. The first new class of estimator is the Oblozene Chlebizky (OC) variance estimators as a…
We study a simple learning algorithm for binary classification. Instead of predicting with the best hypothesis in the hypothesis class, that is, the hypothesis that minimizes the training error, our algorithm predicts with a weighted…
In many important statistical applications, the number of variables or parameters $p$ is much larger than the number of observations $n$. Suppose then that we have observations $y=X\beta+z$, where $\beta\in\mathbf{R}^p$ is a parameter…
We prove a large deviation principle for a sequence of point processes defined by Gibbs probability measures on a Polish space. This is obtained as a consequence of a more general Laplace principle for the non-normalized Gibbs measures. We…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…
In the framework of a strictly local regular Dirichlet space ${\bf X}$ we introduce the subspaces $PW_{\omega},\>\>\omega>0,$ of Paley-Wiener functions of bandwidth $\omega$. It is shown that every function in $PW_{\omega},\>\>\omega>0,$ is…
We derive two upper bounds for the probability of deviation of a vector-valued Lipschitz function of a collection of random variables from its expected value. The resulting upper bounds can be tighter than bounds obtained by a direct…
In this paper we have proposed a general class of modified regression type estimator in systematic sampling under non-response to estimate the population mean using auxiliary information. The expressions of bias and mean square error (MSE)…
In this work, an extension of two-point Ostrowski's formula for $n$-times differentiable functions is proved. A generalization of Taylor formula is deduced. An identity of Fink type for this extension is provided. Error estimates for the…
We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient…
Let $ \mathcal{B}:=\{f(z)=\sum_{n=0}^{\infty}a_nz^n\; \mbox{with}\; |f(z)|<1\;\mbox{for all}\; z\in\mathbb{D}\} $. The improved version of the classical Bohr's inequality \cite{Bohr-1914} states that if $ f\in\mathcal{B} $, then the…
We study the problem of estimating the average of a Lipschitz continuous function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal…
In this paper, we propose a novel and generic family of multiple importance sampling estimators. We first revisit the celebrated balance heuristic estimator, a widely used Monte Carlo technique for the approximation of intractable…