Contiguous Hypotheses Research Articles

Robust inference for nonlinear regression models

A family of weighted estimators of the regression parameter under a nonlinear model is introduced. The proposed weighted estimators are computed through a four-step MM-procedure, and the given approach allows for possible missing responses. Under mild conditions, the proposed estimators turn to be consistent and asymptotically normal. A robust Wald-type test statistic based on this family of estimators is also provided, and its asymptotic distribution is derived under the null and contiguous hypotheses. The local robustness of the proposed procedures is studied via the influence function analysis, and the finite sample behaviour of the estimators and tests is investigated through a Monte Carlo study in different contaminated scenarios. An application to an environmental data set illustrates the procedure.

Goodness-of-fit tests via ϕ-measures of divergence for censored data

Measures of divergence or discrepancy are used extensively in statistics in various fields. In this article, we are focusing on divergence measures that are based on a class of measures known as Csiszar's divergence measures. In particular, we propose a class of goodness-of-fit tests based on Csiszar's class of measures designed for censored survival or reliability data. Further, we derive the asymptotic distribution of the test statistic under simple and composite null hypotheses as well as under contiguous alternative hypotheses. Simulations are furnished and real data are analysed to show the performance of the proposed tests for different ϕ-divergence measures.

Cluster Analysis for Stable Processes

It is known that various financial time series, e.g., daily log returns on a share price, foreign exchange rates, excess bond returns, etc., exhibit heavy-tailed behavior. Recently, discriminant analysis has been applied to financial time series, such as, the problem of credit rating for companies. In this article, we investigate the problem of classifying an α-stable linear process into one of two categories with indices α1 and α2, respectively. We propose some discriminant criteria. It is shown that our discriminant statistics are consistent. The misclassification probabilities are also evaluated under contiguous hypotheses. Some numerical studies for an (AR(1)) process are given.

Preliminary test estimators in intraclass correlation model under unequal family sizes

The intraclass correlation model is well known in the literature of multivariate analysis and it is mainly used in studying familial data. This model is considered in this paper and the interest is focused on the estimation of the intraclass correlation on the basis of familial data from families which are randomly selected from two or more independent populations. The size of the families is considered unequal and the variances of the populations are considered unequal, too. In this statistical framework some preliminary test estimators are presented in a unified way and their asymptotic distribution is obtained. A decision-theoretic approach is developed to compare the estimators by using the asymptotic distributional quadratic risk under the null hypothesis of equality of the intraclass correlations and under contiguous alternative hypotheses, as well. Some interesting relationships are obtained between the estimators considered.

Testing equality restrictions in generalized linear models for multinomial data

Based on φ-divergences an estimator of the generalized linear models for multinomial data under linear restrictions on the parameters is considered. New test statistics, also based on φ-divergences are considered as alternatives to the classical ones for testing a hypothesis about linear restrictions on the parameters. The asymptotic distribution of them is obtained under the null hypothesis as well as under contiguous local hypotheses. An application of the estimators and the tests is illustrated in a numerical example and in simulation studies. contiguous local hypotheses.An application of the estimators and the tests is illustrated in a numerical example and in simulation studies.

Asymptotic distribution and local power of the log-likelihood ratio test for mixtures: bounded and unbounded cases

We consider the log-likelihood ratio test (LRT) for testing the number of components in a mixture of populations in a parametric family. We provide the asymptotic distribution of the LRT statistic under the null hypothesis as well as under contiguous alternatives when the parameter set is bounded. Moreover, for the simple contamination model we prove, under general assumptions, that the asymptotic local power under contiguous hypotheses may be arbitrarily close to the asymptotic level when the set of parameters is large enough. In the particular problem of normal distributions, we prove that, when the unknown mean is not a priori bounded, the asymptotic local power under contiguous hypotheses is equal to the asymptotic level.

An upper bound for the accuracy of the Wiener process approximation of the error probabilities of the sprt

For Wald's SPRT of a simple hypothesis against a simple alternative an upper bound for the differences of the error probabilities and their Wiener process approximations is derived. This upper bound only depends on the first three moments of the log-likelihood ratio and is seen to be especially useful in the case of contiguous hypotheses.

Properties of Bayes Sequential Tests

Consider the problem of sequentially testing composite, contiguous hypotheses where the risk function is a linear combination of the probability of error in the terminal decision and the expected sample size. Assume that the common boundary of the closures of the null and the alternative hypothesis is compact. Observations are independent and identically distributed. We study properties of Bayes tests. One property is the exponential boundedness of the stopping time. Another property is continuity of the risk functions. The continuity property is used to establish complete class theorems as opposed to the essentially complete class theorems in Brown, Cohen and Strawderman.

Discriminative, Informational, Eliciting, and Contiguous Stimuli as Secondary Reinforcers for Human Subjects

128 humans (8 groups of 16 Ss) were used to test the efficacy of operations proposed for establishing a neutral stimulus (SN) as a secondary reinforcer (Sr) by the discriminative, eliciting, informational and contiguous stimulus hypotheses. Phase I was a factorial design composed of 2 levels of consistency of pairing SN with verbal reinforcement (experimental vs control Ss) and 4 treatments (SN presented as a discriminative stimulus vs as a trace vs as a forward vs as a backward conditional stimulus). In Phase II, SN was tested as an Sr in a verbal conditioning paradigm. The analyses showed that all treatments established SN as an Sr for the experimental Ss only, thus supporting the contiguous stimulus hypothesis. It was suggested that an Sr is a confirmational stimulus and that discriminative, eliciting, or informational stimuli be considered secondary motivators insofar as such stimuli control emission of an operant.