Noncentral Convergence of Wald's Large-Sample Test Statistic in Exponential Families

Noncentral Convergence of Multiple

Fix ν > 0, denote by G(ν/2) a Gamma random variable with parameter ν/2 and let n ≥ 2 be a fixed even integer. Consider a sequence {F k } k≥1 of square integrable random variables belonging to the nth Wiener chaos of a given Gaussian process and with variance converging to 2ν. As k → ∞, we prove that F k converges in distribution to 2G(ν/2) − ν if and only if E(F 4 k) − 12E(F 3 k) → 12ν 2 − 48ν.

Convergence of the Monte Carlo Em for Curved Exponential Families

SUMMARY The Monte Carlo Expectation Maximization (MCEM) algorithm (Wei and Tanner (1991)), a stochas-tic version of EM, is a versatile tool for inference in incomplete data models, especially when used in combination with MCMC simulation methods. Examples of applications include, among many others: regression with missing values (Wei and Tanner (1991)), time-series analysis (Chan and Ledolter (...

ANALYSIS OF COVARIANCE BASED ON FUZZY TEST STATISTIC

One-way analysis of covariance is a popular and common statisticalmethod, wherein the equality of the means of several random variables whichhave a linear relationship with a random mathematical variable, is tested. Inthis study, a method is presented to improve the one-way analysis of covari-ance when there is an uncertainty in accepting the statistical hypotheses. Themethod deals with a fuzzy...

Estimation Sampling Sampling Estimation Sampling Test Statistic Test Statistic

In this paper, we introduce a Goodness-of-Fit test for the Multivariate Exponential Power (MEP) distribution, a multivariate extension of the Generalized Gaussian, which has recently gained considerable interest as a model for wavelet coefficients in the context of color image retrieval and spread-spectrum watermarking. We present a size and power study of this test and show Goodness-of-Fit res...

Exponential families