Testing for a separation between two normal distributions

Three tests are proposed for testing for a specified degree of overlap between two normal distributions, The hypotheses considered are an extension of the Behrens-Fisher problem, A simulation study of the performance of the tests is presented.     

Restricted Estimation in Partially Linear Errors-in-Variables Models

As a compromise between parametric regression and nonparametric regression, partially linear models are frequently used in statistical modelling. This article considers statistical inference for this semiparametric model when the linear covariate is measured with additive error and some additional linear restrictions on the parametric component are assumed to hold. We propose a restricted corrected profile least-squares estimator for the parametric component, and study the asymptotic normality of the estimator. To test hypothesis on the parametric component, we construct a Wald test statistic and obtain its limiting distribution. Some simulation studies are conducted to illustrate our approaches.     

Nonparametric Bayes and empirical Bayes estimation of the population median,with application in finite-population sampling

ABSTRACT

Nonparametric Bayes and empirical Bayes estimators of the population median are provided under Dirichlet process priors. The finite-population sampling is used to estimate the finite-population median under Dirichlet process priors. The asymptotic properties of the estimators are obtained from a frequentist perspective.     

Goodness of fit tests with misclassified data

The most popular goodness of fit test for a multinomial distribution is the chi-square test. But this test is generally biased if observations are subject to misclassification, In this paper we shall discuss how to define a new test procedure when we have double sample data obtained from the true and fallible devices. An adjusted chi-square test based on the imputation method and the likelihood ratio test are considered, Asymptotically, these two procedures are equivalent. However, an example and simulation results show that the former procedure is not only computationally simpler but also more powerful under finite sample situations.     

Maximum likelihood estimation of correlation between maximal oxygen consumption and the 6-min walk test in patients with chronic heart failure

Maximal oxygen consumption (VO₂max) is the standard measurement used to quantify cardiovascular functional capacity and aerobic fitness. Unfortunately, it is a costly, impractical and labour-intensive measure to obtain. The 6-min walk test (6MWT) also assesses cardiopulmonary function, but in contrast to the VO₂max test, it is inexpensive and can be performed almost anywhere. Various medical studies have addressed the correlation between VO₂max and 6MWT in patients with chronic heart failure. Of particular interest, from a medical point of view, is the conditional correlation between the two measures given the individual's height, weight, age and gender. In this paper, we have calculated the maximum likelihood estimate of the conditional correlation in patients with chronic heart failure under the assumption of skew normality. Data were recorded from 98 patients in the Operative Unit of Thoracic Surgery in Bari, Italy. The estimated conditional correlation was found to be much smaller than estimated marginal correlations reported in the medical literature.     

Testing a markov chain for independence

A bootstrap procedure is proposed for testing whether an observed Markov chain is actually an independent process, based on the observed transition probability matrix. The results of simulations showing the power and size of the bootstrap test are presented. The asymptotic distribution of the non-unit eigenvalues is given under the null hypothesis.     

On some tests in manocova model with different dispersion matrices

In this article we have considered the problem of testing linear hypothesis in MANOCOVA model with different dispersion Matrices by two test procedures in the line of Anderson (1963) and fihargava CI971). Also efficiencies of the two tests have often compared.     

Distribution- free test for slope in linear regression model with replications

Some distribution-free methods are suggested in the paper for testing the hypothesis about the slope parameter in a one-sample linear regression model with multiple observations at each level of independent variable. Asymptotic relative efficiencies of these tests are discussed, and the tests are compared with their nonparametric competitors.     

Asymptotic bootstrap validity for finite markov chains

Two methods of bootstrap, viz., standard, and conditional, are presented for estimating the transition probabilities of a finite state Markov chain. Asymptotic validity of the bootstrap estimates are established for both methods. An applica- tion to a bootstrapped statistic for testing independence is briefly discussed together with some simulation results.     

Test procedures in coyariamce analysis assuming a general correlation pattern

The analysis of covariance procedure is considered when the observations in each cell are equicorrelated. A correction procedure is given, A computationally easier conservative test statistic is also given. The conservative test statistic allows one to more readily determine the consequences of ignoring correlations, even slight correlations, in the analysis of covariance procedure. The difference of the corrected test and the conservative test is shown to converge in probability to zero. This conservative test is easy to implement on statistical computer packages, It is shown, that for the general correlation pattern, any test involving the regression coefficients of the covariables is an exact test. An example illustrates the procedure