We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals. AMS 2000 subject classifications: Primary 60K35; secondary 94A17.

Salah satu hal penting dalam analisis statistik adalah prosedur estimasi suatu fungsi padat peluang yang biasa disebut densitas. Ada dua metode pendekatan biasanya digunakan, yaitu parameter terkait dengan asumsi distribusi tertentu dan densitas secara non parametrik. Metode parametrik sering kita jumpai histogram.
 Beberapa kelemahan histogram menjadi acuan untuk dikembangkannya lain kern...

The Stein-Lovász Theorem can be used to get existence results for some combinatorial problems using constructive methods rather than probabilistic methods. In this paper, we discuss applications of the Stein-Lovász Theorem to some combinatorial set systems and arrays, including perfect hash families, separating hash families, splitting systems, covering designs, lotto designs and ∆-free systems...

An approach is presented to get interconnections between the Fisher information matrix of an ARMAX process and a corresponding solution of a Stein equation. The case of algebraic multiplicity greater than one and the case of distinct eigenvalues are addressed. Appropriate links are constructed for these two cases by applying a factorization both for the Fisher information matrix and for a corre...

This note contains supplementary materials to Kernel Mean Estimation via Spectral Filtering. 1 Proof of Theorem 1 (i) Since μ̌λ = μ̂ λ λ+1 = μ̂P λ+1 , we have ‖μ̌λ − μP‖ = ∥∥∥∥ μ̂P λ+ 1 − μP ∥∥∥∥ ≤ ∥∥∥∥ μ̂P λ+ 1 − μP λ+ 1 ∥∥∥∥+ ∥∥∥∥ μP λ+ 1 − μP ∥∥∥∥ ≤ ‖μ̂P − μP‖+ λ‖μP‖. From [1], we have that ‖μ̂P − μP‖ = OP(n) and therefore the result follows. (ii) Define ∆ := EP‖μ̂P − μP‖ = ∫ k(x,x) dP(x)−‖μP‖ 2 n . ...

In this paper, we investigate the minimax properties of Stein block thresholding in any dimension d with a particular emphasis on d = 2. Towards this goal, we consider a frame coefficient space over which minimaxity is proved. The choice of this space is inspired by the characterization provided in [5] of family of smoothness spaces on R d, a subclass of so-called decomposition spaces [28]. The...

the gastric cancer in iran is the fourth in the general population. this study was designed to determine the five-year survival rate of gastric cancer patients, and to assess its associated factors. we analyzed the data using a time-dependent covariates model, and recommend it for analyses of similar data. 281 gastric cancer patients with adenocarcinomatous pathology who had been operated on at...

In various statistical model, such as density estimation and estimation of regression curves or hazard rates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametric statistics is to estimate a monotone density function f on a compact interval. A known estimator for density function of f under the restriction that f is decreasing, is Grenander estimator, ...

We consider admissibility of generalized Bayes estimators the mean a multivariate normal distribution when scale is unknown under quadratic loss. The priors considered put improper invariant prior on while has hierarchical structure conditional scale. This essentially that Maruyama and Strawderman (2021, Biometrika) (MS21) which indexed by hyperparameter $a$. In paper $a$ chosen so this proper ...