Related papers: Basic properties of generalized $\psi$-estimators
In this article, we have proposed a generalized class of estimators, exponential class of estimators based on adaption of Sharma and Singh (2015) and Solanki and Singh (2013) and simple difference estimator for estimating unknown population…
The least trimmed squares (LTS) estimator is popular in location, regression, machine learning, and AI literature. Despite the empirical version of least trimmed squares (LTS) being repeatedly studied in the literature, the population…
We present two new estimators for estimating the entropy of absolutely continuous random variables. Some properties of them are considered, specifically consistency of the first is proved. The introduced estimators are compared with the…
We develop an asymptotic theory of adversarial estimators ('A-estimators'). They generalize maximum-likelihood-type estimators ('M-estimators') as their average objective is maximized by some parameters and minimized by others. This class…
Certain monotonicity properties of the Poisson approximation to the binomial distribution are established. As a natural application of these results, exact (rather than approximate) tests of hypotheses on an unknown value of the parameter…
For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type…
Traditional statistical mechanics is constrained by the binary paradigms of identical/distinguishable and bosonic/fermionic particle statistics, leading to a fundamental logical gap in describing systems with partial distinguishability. We…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
This paper discusses asymptotic theory for penalized spline estimators in generalized additive models. The purpose of this paper is to establish the asymptotic bias and variance as well as the asymptotic normality of the penalized spline…
Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…
We generalize the na\"ive estimator of a Poisson regression model with measurement errors as discussed in Kukush et al. [1]. The explanatory variable is not always normally distributed as they assume. In this study, we assume that the…
The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…
In this article, we review and discuss different aspects of stability and genericity of some properties of space-times which occur in various contexts in the General Theory of Relativity. We also give argument supporting the conclusion that…
Let $(x_{i}, y_{i})_{i=1,\dots,n}$ denote independent samples from a general mixture distribution $\sum_{c\in\mathcal{C}}\rho_{c}P_{c}^{x}$, and consider the hypothesis class of generalized linear models $\hat{y} = F(\Theta^{\top}x)$. In…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
Sparsity of representations of signals has been shown to be a key concept of fundamental importance in fields such as blind source separation, compression, sampling and signal analysis. The aim of this paper is to compare several…
There is a difficulty in finding an estimate of variance of the profile likelihood estimator in the joint model of longitudinal and survival data. We solve the difficulty by introducing the ``statistical generalized derivative''. The…
This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…
We discuss properties of certain generalization of Power Means proposed in 1971 by Carlson, Meany and Nelson. For any fixed parameter (k,s,q) and vector (v_1,...,v_n) they take the q-th power means of all possible k-tuples…
In this paper we consider the axiomatic characterization of information and certainty measures in a unified way. We present the general axiomatic system which captures the common properties of a large number of the measures previously…