Is the Selected Population the Best?—Location and Scale Parameter Cases

We observe X ₁,…,X _k , where X _i has density f(x,θ _i ) possessing monotone likelihood ratio. The best population corresponds to the largest θ _i . We select the population corresponding to the largest X _i . The goal is to attach the best possible p-value to the inference: the selected population has the uniquely largest θ _i . Gutmann and Maymin (1987 Gutmann , S. , Maymin , Z. ( 1987 ). Is the selected population the best? Ann. Statist . 15 : 456 – 461 .[Crossref], [Web of Science ®] , [Google Scholar]) considered the location parameter case and derived the supremum of the error probability by conditioning on S, the index of the largest X _i . Using this conditioning approach, Kannan and Panchapakesan (2009 Kannan , N. , Panchapakesan , S. ( 2009 ). Does the selected normal population have the smallest variance? Amer. J. Math. Management Sci . 29 : To appear . [Google Scholar]) considered the problem for the gamma family. We consider here a unified approach to both the location and scale parameter cases, and obtain the supremum of the error probability without using conditioning.     

Umvu estimation for the cumulative hazard function in a pareto distribution of the first kind

The uniformly minimum variance unbiased estimator of the cumulative hazard function in the Pareto distribution of the first kind is derived. The variance of the estimator is also obtained in an analytic form, and for some cases its values are compared numerically with mean square errors of the maximum likelihood estimator.     

Dependence function for continuous bivariate densities

The notion of cross-product ratio for discrete two-way contingency table is extended to the case of continuous bivariate densities. This results in the “local dependence function” that measues the margin-free dependence between bivariate random variables. Properties and examples of the dependence function are discussed. The bivariate normal density plays a special role since it has constant dependence. Continuous bivariate densities can be constructed by specifying the dependence function along with two marginals in analogy to the construction of two-way contingency tables given marginals and patterns of interaction. The dependence function provides a partial ordering on bivariate dependence.     

Estimation of signal to noise ratio using mahalanobis distance

In this paper, we propose some alternative estimatiors to that given by C. G. Khatri and C. R. Rao (1985), for estimating Signal to Noise ratio. Using Pitman Nearness, Condition for prefering one estimator over the other is estabilished. It is shown numerically that estimators corresponding to Entropy loss function are better more oftern than those corresponding to Squared Error loss.     

Anderson's classification statistic based on a post-stratified training sample

The performance of Anderson's classification statistic based on a post-stratified random sample is examined. It is assumed that the training sample is a random sample from a stratified population consisting of two strata with unknown stratum weights. The sample is first segregated into the two strata by post-stratification. The unknown parameters for each of the two populations are then estimated and used in the construction of the plug-in discriminant. Under this procedure, it is shown that additional estimation of the stratum weight will not seriously affect the performance of Anderson's classification statistic. Furthermore, our discriminant enjoys a much higher efficiency than the procedure based on an unclassified sample from a mixture of normals investigated by Ganesalingam and McLachlan (1978).     

Rank test statistics for umbrella alternatives

This paper proposes an optimal rank test procedure for testing an umbrella alternative when the peak of the umbrella is known. It is referred to as maximin efficient linear rank test. Also when the peak of the umbrella is unknown, a test procedure is proposed and its performance is discussed.     

Comments on specification of household expenditure functions and equivalence scales by nonparametric regression

This paper considers Lagrange Multiplier (LM) and Likelihood Ratio (LR) tests for determining the cointegrating rank of a vector autoregressive system. n order to deal with outliers and possible fat-tailedness of the error process, non-Gaussian likelihoods are used to carry out the estimation. The limiting distributions of the tests based on these non-Gaussian pseudo-)likelihoods are derived. These distributions depend on nuisance parameters. An operational procedure is proposed to perform inference. It appears that the tests based on non-Gaussian pseudo-likelihoods are much more powerful than their Gaussian counterparts if the errors are fat-tailed. Moreover, the operational LM-type test has a better overall performance than the LR-type test. Copyright O 1998 by Marcel Dekker, Inc.     

Tests for Equality of Parameters of Two Exponential Distributions with Common Known Coefficient of Variation

ABSTRACT

This article considers the problem of testing equality of parameters of two exponential distributions having common known coefficient of variation, both under unconditional and conditional setup. Unconditional tests based on BLUE'S and LRT are considered. Using the Conditionality Principle of Fisher, an UMP conditional test for one-sided alternative is derived by conditioning on an ancillary. This test is seen to be uniformly more powerful than unconditional tests in certain given ranges of ancillary. Simulation studies on the power functions of the tests are done for this purpose.     

BARTLETT CORRECTED LIKELIHOOD RATIO TESTS IN LOCATION-SCALE NONLINEAR MODELS

The paper derives Bartlett corrections for improving the chisquare approximation to the likelihood ratio statistics in a class of location-scale family of distributions, which encompasses the elliptical family of distributions and also asymmetric distributions such as the extreme value distributions. We present, in matrix notation, a Bartlett corrected likelihood ratio statistic for testing that a subset of the nonlinear regression coefficients in this class of models equals a given vector of constants. The formulae derived are simple enough to be used analytically to obtain several Bartlett corrections in a variety of important models. We show that these formulae generalize a number of previously published results. We also present simulation results comparing the sizes and powers of the usual likelihood ratio tests and their Bartlett corrected versions when the scale parameter is considered known and when this parameter is uncorrectly specified.