Related papers: Finite population inference for skewness measures
This paper examines the finite-sample bias of estimators for the Theil and Atkinson indices, as well as for the variance-to-mean ratio (VMR), under the assumption that the population follows a finite mixture of gamma distributions with a…
We consider the problem of estimating the density $g$ of identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$ and $\sigma \epsilon\_i$ is a noise independent of $X\_i$…
Within the framework of smoothing spline ANOVA, we propose a plug-in kernel ridge regression estimator to estimate the derivatives of the underlying multivariate regression function. We first establish an $L_\infty$ convergence rate of the…
Doubly robust estimators combine an inverse probability weighting estimator and a mass imputation estimator. Several doubly robust estimators for estimating the population mean (or prevalence) of an outcome have been proposed for…
We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…
Bootstrap smoothed (bagged) estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. Efron, 2014, derived a widely applicable formula for a delta method approximation to the standard…
We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…
Based on $X \sim N_d(\theta, \sigma^2_X I_d)$, we study the efficiency of predictive densities under $\alpha-$divergence loss $L_{\alpha}$ for estimating the density of $Y \sim N_d(\theta, \sigma^2_Y I_d)$. We identify a large number of…
Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for…
We develop a new approach for quantifying uncertainty in finite populations, by using design distributions to calibrate sensitivity parameters in finite population identified sets. This yields uncertainty intervals that can be interpreted…
Based on $m$-fold integrated empirical measures, we study three new classes of goodness-of-fits tests, generalizing Anderson-Darling, Cram\'er-von Mises, and Watson statistics, respectively, and examine the corresponding limiting stochastic…
Bivariate extreme-value distributions have been used in modeling extremes in environmental sciences and risk management. An important issue is estimating the dependence function, such as the Pickands dependence function. Some estimators for…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
In this paper we examine the properties of the Wilson score interval, used for inferences for an unknown binomial proportion parameter. We examine monotonicity and consistency properties of the interval and we generalise it to give two…
Based on independently distributed $X_1 \sim N_p(\theta_1, \sigma^2_1 I_p)$ and $X_2 \sim N_p(\theta_2, \sigma^2_2 I_p)$, we consider the efficiency of various predictive density estimators for $Y_1 \sim N_p(\theta_1, \sigma^2_Y I_p)$, with…
The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the asymptotic distribution of the respective empirical process. Moreover, it provides a…
This study presents new closed-form estimators for the Dirichlet and the Multivariate Gamma distribution families, whose maximum likelihood estimator cannot be explicitly derived. The methodology builds upon the score-adjusted estimators…
Given a functional central limit (fCLT) for an estimator and a parameter transformation, we construct random processes, called functional delta residuals, which asymptotically have the same covariance structure as the limit process of the…
Skewness is a common occurrence in statistical applications. In recent years, various distribution families have been proposed to model skewed data by introducing unequal scales based on the median or mode. However, we argue that the point…
We develop a non-standard analysis framework for coherent risk measures and their finite-sample analogues, coherent risk estimators, building on recent work of Aichele, Cialenco, Jelito, and Pitera. Coherent risk measures on $L^\infty$ are…