New Lilliefors and Srinivasan tables with applications

Two approaches to the problem of goodness-of-fit with nuisance parameters are presented in this paper, both based on modifications of the Kolmogorov-Smirnov statistics. Improved tables of critical values originally computed by Lilliefors and Srinivasan are presented in the normal and exponential cases. Also given are tables for the uniform case, normal with known mean and normal with known variance. All tables were computed using Monte Carlo simulation with sample size n = 20000.     

Asymptotic risk comparisions of restricted and unrestricted maximum likelihood estimators

Conditions for choosing between restricted and unrestrieted maximum likelihood estimators based on various asymptotic risk oriteria are derived. These conditions involve the non-centrality parameters of classical and specification test statistics, and are generlizations of well known results for the linear regression model.     

Comparing the relative efficiency of three sequential procedures

We consider the sequential procedures developed by Robbins and Siegmund (1974), Louis (1975) and Zoubeidi (1992) for comparing the means of two treatments. We let the procedures have equal power functions and compare their Bayes and minimax risks using the invariance property of their power functions. For each of several formulations of the problem we determine the most relatively efficient procedure and compute its expected total sample size.     

THE BEHAVIOR OF HEGY TESTS FOR QUARTERLY TIME SERIES WITH SEASONAL MEAN SHIFTS

ABSTRACT

This paper studies the behavior of the HEGY statistics for quarterly data, for seasonal autoregressive unit roots, when the analyzed time series is deterministic seasonal stationary but exhibits a change in the seasonal pattern. We analyze also the HEGY test for the nonseasonal unit root. the data generation process being trend stationary too. Our results show that when the break magnitudes are finite, the HEGY test statistics are not asymptotically biased toward the nonrejection of the seasonal and nonseasonal unit root hypotheses. However, the finite sample power properties may be substantially affected, the behavior of the tests depending on the type of the break.     

A new random permutation test in ANOVA models

This paper developed an exact method of random permutations when testing both interaction and main effects in the two-way ANOVA model. The method of this paper can be regarded as a much improved model when compared with those of the previous studies such as Still and White (1981) and ter Braak (1992). We further conducted a simulation experiment in order to check the statistical performance of the proposed method. The proposed method works relatively well for small sample sizes compare with the existing methods. This work was supported by Korea Science and Engineering Foundation Grant (R14-2003-002-0100)     

Analysis of the Bovine Spongiform Encephalopathy Maternal Cohort Study: the Discordant Case–Control Pairs

The progeny of the affected and non-affected dams in the bovine spongiform encephalopathy (BSE) cohort study were paired in terms of their farm of origin and approximate date of birth. This paper presents an exact logistic regression analysis that avoids modelling the differences between the pairs and so analyses only the discordant pairs. There is some evidence that the pairs in which the affected animal was born to the affected dam tend to be those in which the onset of BSE in the affected dam preceded or occurred soon after the calving. This suggests some occurrence of maternal transmission.     

Monte carlo evidence on the robustness of conditional moment tests in tobit and probit models

This paper numerically examines the size robustness of various conditional moment tests in misspecified tobit and probit models. The misspecifications considered include the incorrect exclusion of regressors, ignored heteroskedasticity and false distributional assumptions. An important feature of the experimental design is that it is based on an existing empirical study and is more realistic than many simulation studies. The tests are seen to have mixed performance depending on both the original null hypothesis being tested and type of misspecification encountered.     

Csiszar’s ϕ-divergences for testing the order in a Markov chain

x ₁, ..., x _n+r can be treated as the sample values of a Markov chain of order r or less (chain in which the dependence extends over r+1 consecutive variables only), and consider the problem of testing the hypothesis H ₀ that a chain of order r− 1 will be sufficient on the basis of the tools given by the Statistical Information Theory: _ϕ-Divergences. More precisely, if p _{a 1 ....., a r}: _{a r +1} denotes the transition probability for a r ^th order Markov chain, the hypothesis to be tested is H ₀:p _{a 1 ....., a r}: _{a r +1} = p _{a 2 ....., a r}: _{a r +1}, a _i ∈{1, ..., s}, i = 1, ..., r + 1 The tests given in this paper, for the first time, will have as a particular case the likelihood ratio test and the test based on the chi-squared statistic. Received: August 3, 1998; revised version: November 25, 1999     

Reconsideration of the F-test of the analysis of variance: the semi-bayesian significance test

The usual F-test of the analysis of variance is reconsidered within the Bayesian framework, In terms of predictive distributions, This leads to the notion of semi-Bayesian significance test, so called because it consists in only probabilizing the space of nuisance parameters, thus bringing a general principle for “eliminating” nuisance parameters, or more exactly incorporating information about these parameters. The approach is shown to extend the F-tests, by allowing the testing of hypotheses of non-zero effects.     

Tests of hypotheses based on ranks in the general linear model

A unified approach is developed for testing hypotheses in the general linear model based on the ranks of the residuals. It complements the nonparametric estimation procedures recently reported in the literature. The testing and estimation procedures together provide a robust alternative to least squares. The methods are similar in spirit to least squares so that results are simple to interpret. Hypotheses concerning a subset of specified parameters can be tested, while the remaining parameters are treated as nuisance parameters. Asymptotically, the test statistic is shown to have a chi-square distribution under the null hypothesis. This result is then extended to cover a sequence of contiguous alternatives from which the Pitman efficacy is derived. The general application of the test requires the consistent estimation of a functional of the underlying distribution and one such estimate is furnished.