A Semiparametric Approach to the One-Way Layout

Abstract

We consider m distributions in which the rst m ƒ 1 are obtained by multiplicative exponential distortions of the mth distribution, which is a reference. The combined data from m samples, one from each distribution, are used in the semiparametric large-sample problem of estimating each distortion and the reference distribution and testing the hypothesis that the distributions are identical. The approach generalizes the classical normal-based one-way analysis of variance in the sense that it obviates the need for a completely speci ed parametric model. An advantage is that the probability density of the reference distribution is estimated from the combined data and not only from the mth sample. A power comparison with the t and F tests and with two nonparametric tests, obtained by means of a simulation, points to the merit of the present approach. The method is applied to rain-rate data from meteorological instruments.

On empirical likelihood for semiparametric two-sample density ratio models

“…We propose to use, instead of the empirical likelihood ratio statistic, its "dual" form (see (2.11)) (to perform a test of the null hypothesis H 0 : Q = P ) which is well defined regardless of the null hypothesis. Simulation results, presented in Section 4 below, show that the observed level of the test based on the statistic (2.11) converges (to the nominal level) better than the observed level of the test proposed by Fokianos et al (2001). Using φ-divergences and "duality" technique, we give an interpretation for the statistic (2.11), the dual form of the empirical likelihood ratio statistic; see (2.21).…”

“…. , Y n 1 are independent, Fokianos et al (2001) present a statistical test, for the null hypothesis H 0 : Q = P or equivalently H 0 : β T = 0, where the test statistic is based on a "constrained" empirical likelihood estimate of the parameter β T (see Qin (1998)) and an empirical estimate of the limit variance. In the case when the semiparametric assumption (1.1) fails, the test commonly used is the non parametric Wilcoxon rank-sum (see e.g Randles and Wolfe (1979) and Hollander and Wolfe (1999)).…”

“…We compare the power function of the ELR test (ELRT), defined in (2.21), with the power function of the two-sample t-test, Wilcoxon rank-sum test and Fokianos et al (2001) test. We recall that Fokianos et al (2001) test statistic is based on a constrained empirical likelihood estimate of the parameter (see Qin (1998)) and an empirical estimate of its limit variance.…”

Innovative Statistical Inference for Anomaly Detection in Hyperspectral Imagery

“…(17) assume that x 0 and x 1 are independent and that, for some x 0 and x 1 , the combined vector t 22 Casella, 1990. …”

“…14 Rosario, 2000. The novelty in this paper is the mathematical means that is proposed to address HSI anomaly detection. The main contribution of this report is threefold: (i) a recently proposed local anomaly detector 15 shall be discussed for the first time using extended details; I shall describe a suitable mathematical model 16,17,18,19,20 that elegantly materializes a combining idea and shall study the model's maximum likelihood method and its asymptotic behavior; I shall design an effective local anomaly detector based on the model's asymptotic behavior, which for convenience shall be named the semiparametric (SemiP) algorithm; (ii) a second anomaly detector shall be proposed to the community, an approximation to the semiparametric (AsemiP) algorithm, which may be used to replace the complicated equations of the first model's solution with simpler equations-yet describing the same phenomenon; I shall state a proposition of the second model and prove its statement. Derivation of the AsemiP algorithm is motivated by the SemiP's output properties, not by the semiparametric model itself-although, its derivation is also based on approximation theorems of mathematical statistics; and (iii) in order to promote the use of models whose mathematics are based on the statistical assumption of independent, identically distributed random samples, an inside/outside window mechanism shall be introduced aimed at transforming local HSI information into independent sample pairs.…”