Hasil untuk "math.ST"

Dietmar Ferger

We consider M-estimators and derive supremal-inequalities of exponential-or polynomial type according as a boundedness- or a moment-condition is fulfilled. This enables us to derive rates of r-complete convergence and also to show r-qick convergence in the sense of Strasser.

Pengtao Li, Hanchao Wang

Catoni proposed a robust M-estimator and gave the deviation inequality for one fixed test function. The present paper is devoted to the uniform concentration inequality for a family of test functions. As an application, we consider empirical risk minimization for heavy-tailed losses.

William Leeb

Recently, Chen, Li and Zhang established conditions characterizing asymptotic identifiability of latent factors in confirmatory factor analysis. We give an elementary proof showing that a similar characterization holds non-asymptotically, and prove a related result for identifiability of factor loadings.

Christian M. Hafner, Oliver B. Linton, Haihan Tang

Supplementary Material for "Estimation of a Multiplicative Correlation Structure in the Large Dimensional Case"

Laura Dumitrescu, Ioana Schiopu-Kratina

In this article we study the existence and strong consistency of GEE estimators, when the generalized estimating functions are martingales with random coefficients. Furthermore, we characterize estimating functions which are asymptotically optimal.

Tingting Li, Zuoxiang Peng

In this paper, convergence for moments of powered normal extremes is considered under an optimal choice of normalizing constants. It is shown that the rates of convergence for normalized powered normal extremes depend on the power index. However, the dependence disappears for higher-order expansions of moments.

Yuhao Liu, Jan Vrbik

Computing moments of various parameter estimators related to an autoregressive model of Statistics, one needs to evaluate several expressions of the type mentioned in the title of this article. We proceed to derive the corresponding formulas.

Michel Valadier

A real random variable admits median(s) and quantiles. These values minimize convex functions on $\mathbb R$. We show by "Convex Analysis" arguments that the function to be minimized is very natural. The relationship with some notions about functions of bounded variation developed by J.J.~Moreau is emphasized.

Jean-Marc Bardet, Ciprian A. Tudor

The purpose of this paper is to estimate the self-similarity index of the Rosenblatt process by using the Whittle estimator. Via chaos expansion into multiple stochastic integrals, we establish a non-central limit theorem satisfied by this estimator. We illustrate our results by numerical simulations.

Shurong Zheng, Zhidong Bai, Jianfeng Yao

This paper proposes a CLT for linear spectral statistics of random matrix $S^{-1}T$ for a general non-negative definite and {\bf non-random} Hermitian matrix $T$.

Xiaolin Gong, Shuzhen Yang

This paper introduces a new distribution to improve tail risk modeling. Based on the classical normal distribution, we define a new distribution by a series of heat equations. Then, we use market data to verify our model.

Abram M. Kagan, Yaakov Malinovsky

It is proved that the average length of standard confidence intervals for parameters of gamma and normal distributions monotonically decrease with the sample size. The proofs are based on fine properties of the classical gamma function.

Natalia Stepanova

The problem of estimation of analytic density function using L_p minimax risk is considered. A kernel-type estimator of an unknown density function is proposed and the upper bound on its limiting local minimax risk is established. Our result is consistent with a conjecture of Guerre and Tsybakov (1998) and augments previous work in this area.

Soumik Pal

This note proves a weak type of the sharpness principle as conjectured by Gneiting, Balabdaoui, and Raftery in 2007 in connection with probabilistic forecasting subject to calibration constraints. A strong version of such a principle still awaits a proper formulation.

Matthieu Lerasle

We build penalized least-squares estimators using the slope heuristic and resampling penalties. We prove oracle inequalities for the selected estimator with leading constant asymptotically equal to 1. We compare the practical performances of these methods in a short simulation study.

Xinjia Chen

In this paper, we derive an explicit sample size formula based a mixed criterion of absolute and relative errors for estimating means of Poisson random variables.

Xiao-Li Meng

Discussion of ``One-step sparse estimates in nonconcave penalized likelihood models'' [arXiv:0808.1012]

Teo Sharia

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general statistical model and study convergence.

Dorota M. Dabrowska

Conditional quantiles provide a natural tool for reporting results from regression analyses based on semiparametric transformation models. We consider their estimation and construction of confidence sets in the presence of censoring.

Anatoliy Malyarenko

We derive a series expansion for the multiparameter fractional Brownian motion. The derived expansion is proven to be rate optimal.