On Locating and Characterizing Parameter Variation by the Mosumsq Test Statistic

In modelling a system structure it is often important to test the constancy of the structural parameters. If the hypothesis of constant parameters is rejected we wish to characterize the parameter variation. In this paper we examine the usefulness of the MOSUMSQ test statistics for locating and characterizing the parameter variation in linear regression models. The means and the variances of the test statistics are given for non-random parameter variation. The observed path of the MOSUMSQ test statistics provides valuable knowledge about the time of the onset of the parameter change and whether it is instantaneous or gradual.     

Comparison of two independent life tests subject to type II censoring

The problem of comparing two life distributions is considered. It Is assumed that each life test Is stopped after a predetermined number of failures without regard to the number of failures which have occurred in the other life test. A generalized Wilcoxon-rlann-Whitney test is proposed. Small and large sample distributional results are obtained for the test statistic. Under the assumption that the life distributions differ by at most a scale parameter an exact confidence interval for that parameter is obtained. An algorithm for computing the interval is given.     

A modification of the partial sequential probability ratio test

For the problem of discriminating between two simple hypoth¬eses concerning a Koopman - Darmois parameter, a modification of the partial sequential probability ratio test is proposed where instead of drawing only one fixed sample, two fixed samples are drawn and then Wald's SPRT is started. The OC and the ASN func¬tions are derived. Numerical comparisons are made with Wald's and Read's procedures for testing the normal mean with known variance. For some parameter values, the test procedure has a lower ASN than that of Read's procedure.     

A generalization of mosteller's test

A generalization of Mosteller's test for slippage of the location parameter is proposed. The distribution of the test statistic under the null hypothesis is obtained and the power of the test is compared with that of Mosteller's test     

Some Statistical Properties of Efficiency Robust Tests with Applications to Genetic Association Studies

Although efficiency robust tests are preferred for genetic association studies when the genetic model is unknown, their statistical properties have been studied for different study designs separately under special situations. We study some statistical properties of the maximin efficiency robust test and a maximum‐type robust test (MAX3) under a general setting and obtain unified results. The results can also be applied to testing hypothesis with a constrained two‐dimensional parameter space. The results are applied to genetic association studies using case–parents trio data.     

Likelihood ratio test for testing equality of location parameters of two exponential distributions from doubly censored samples

The Likelihood Ratio (LR) test for testing equality of two exponential distributions with common unknown scale parameter is obtained. Samples are assumed to be drawn under a type II doubly censored sampling scheme. Effects of left and right censoring on the power of the test are studied. Further, the performance of the LR test is compared with the Tiku(1981) test.     

Moving truncations barrier-function methos for estimation in three-parameter lognormal models

A method of centres algorithm for maximum likelihood estimation in the three-parameter lognormal model is presented and discussed, The algorithm is a member of the class of moving truncations algorithms for solving nonlinear programming problems and is able to move the numerical search out of the region of the infinite maximum of the conditional likelihood function, thereby permitting convergence to an interior relative maximum of this function. The algorithm also includes an optimality test to locate the primary relative maximum of the likelihood function.     

TESTS FOR EXPONENTIALITY AGAINST GAMMA ALTERNATIVES USING NORMALIZED WAITING TIMES

In this article, we present some tests for Exponentiality against Gamma alternatives by using normalized waiting times. The test is constructed by using a quadratic form. The asymptotic distribution of the proposed test is derived. The power of the test is computed through Monte Carlo simulation and is compared with Linhart (1965) test, Bain and Engelhardt (1975) test and Keating et al. (1990) test.     

A test for gamma DFR alternative

In this article, a test for exponentiality against gamma DFR alternative based on a quadratic form of the logarithmic observations is proposed. The percentage points and the power of the test are computed through Monte-Carlo simulation. The test is seen to perform well as compared to a chi-square test proposed by Bain and Engelhardt(1975).     

Semiparametric score test for varying copula parameter in Markov time series

This article examines a semiparametric test for checking the constancy of serial dependence via copula models for Markov time series. A semiparametric score test is proposed for testing the constancy of the copula parameter against stochastically varying copula parameter. The asymptotic null distribution of the test is established. A semiparametric bootstrap procedure is employed for the estimation of the variance of the proposed score test. Illustrations are given based on simulated series and historic interest rate data.     

Analysis of proportions for clustered binary data in the presence of unequal dispersions

This paper investigates the test procedures for testing the homogeneity of the proportions in the analysis of clustered binary data in the context of unequal dispersions across the treatment groups. We introduce a simple test procedure based on adjusted proportions using a sandwich estimator of the variance of the proportion estimators obtained by the generalized estimating equations approach of Zeger and Liang (1986) [Biometrics 42, 121-130]. We also extend the exiting test procedures of testing the hypothesis of proportions in this context. These test procedures are then compared, by simulations, in terms of size and power. Moreover, we derive the score test for testing the homogeneity of the dispersion parameters among several groups of clustered binary data. An illustrative application of the recommended test procedures is also presented.     

Testing for linearity in Markov switching models: a bootstrap approach

Testing for linearity in the context of Markov switching models is complicated because standard regularity conditions for likelihood based inference are violated. In particular, under the null hypothesis of linearity, some parameters are not identified and scores are identically zero. Thus, the asymptotic distribution of the relevant test statistic does not possess the standard χ ²-distribution. A bootstrap resampling scheme to approximate the distribution of the relevant test statistic under the null of linearity is proposed. The procedure is relatively easy to program and computation requirements are reasonable. The performance of the bootstrap-based test is investigated by means of Monte Carlo simulations. Results show that this test works well and outperforms the Hansen test and the Carrasco et al. test.     

Hypothesis tests for linear functional relationships

The analysis of linear functional relationships is considered. Expressions useful for the estimation of both unconstrained and con¬strained parameters are presented. The testing of hypotheses which consist of linear constraints on the parameters is discussed. Wald type and Wilks type test statistics and their asymptotic null dis¬tributions are derived. It appears that these test statistics are not asymptotically equivalent.     

On the efficiency of a testimator for the weibull shape parameter

In estimating the shape parameter of a two-parameter Weibull distribution from a failure-censored sample, a recently popular procedure is to employ a testimator which is a shrinkage estimator based on a preliminary hypothesis test for a guessed value of the parameter. Such an adaptive testimator is a linear compound of the guessed value and a statistic. A new compounding coefficient is numerically shown to yield higher efficiency in many situations compared to some of the existing ones.     

Power properties of the modified CUSUM tests

The CUSUM test has played an important role in theory and applications related to structural change, but its drawback is that it loses power when the break is orthogonal to the mean of the regressors. In this study, we consider two modified CUSUM tests that have been proposed, implicitly or explicitly, in the literature to detect such structural changes and investigate the limiting power properties of these tests under a fixed alternative. We demonstrate that the modified tests are superior to the classic tests in terms of both asymptotic theory and in finite samples when detecting an orthogonal structural shift.     

Residual-based CUSUM of squares test for Poisson integer-valued GARCH models

This study considers the problem of testing for a parameter change in integer-valued time series models in which the conditional density of current observations is assumed to follow a Poisson distribution. As a test, we consider the CUSUM of the squares test based on the residuals from INGARCH models and find that the test converges weakly to the supremum of a Brownian bridge. A simulation study demonstrates its superiority to the residual and standardized residual-based CUSUM tests of Kang and Lee [Parameter change test for Poisson autoregressive models. Scand J Statist. 2014;41:1136–1152] and Lee and Lee [CUSUM tests for general nonlinear inter-valued GARCH models: comparison study. Ann Inst Stat Math. 2019;71:1033–1057.] as well as the CUSUM of squares test based on standardized residuals.     

Partial Round-Robin Comparisons with Perfect Rankings

In teaching the development of uniformly most powerful unbiased (UMPU) tests, one rarely discusses the performance of alternative biased tests. It is shown, through the comparison of two independent Bernoulli proportions, that a biased test (the Z test) can be more powerful than the UMPU test (Fisher's exact test—randomized) in a large region of the alternative parameter space. A more general example is also given.     

Obtaining efficient estimates of park use and testing for the structural adequacy of models

This paper provides an examination of the problem of heteroscedasticity as it relates to estimating park use, although the results can also be applied to a wide variety of flow problems involving traffic, people or commodities. The major issue is that estimates of flows obtained using ordinary least squares, OLS, often yield statistically significant results while still giving rise to large differences between observed and predicted flows (residuals). The paper presents results which show that for the flow estimation problem of concern, more accurate use estimates may be obtained by using generalized least squares, GLS, rather than using OLS. Weights to use in GLS regression are developed taking into account the variance to be expected in origin-destination flows. It is shown that deriving the correct weights, estimates of variances, to use in a regression analysis results in an ‘absolute’ test for the structural appropriateness of the regression model. Tests related to the ‘absolute’ adequacy test are introduced and their use to identify specific structural problems with a model is illustrated.     

On optimal tests for separate hypotheses and conditional probability integral transformations

Consider the problem of testing the composite null hypothesis that a random sample X₁,…,X_n is from a parent which is a member of a particular continuous parametric family of distributions against an alternative that it is from a separate family of distributions. It is shown here that in many cases a uniformly most powerful similar (UMPS) test exists for this problem, and, moreover, that this test is equivalent to a uniformly most powerful invariant (UMPI) test. It is also seen in the method of proof used that the UMPS test statistic Is a function of the statistics U₁,…,U_n?k obtained by the conditional probability integral transformations (CPIT), and thus that no Information Is lost by these transformations, It is also shown that these optimal tests have power that is a nonotone function of the null hypothesis class of distributions, so that, for example, if one additional parameter for the distribution is assumed known, then the power of the test can not lecrease. It Is shown that the statistics U₁, …, U_n?k are independent of the complete sufficient statistic, and that these statistics have important invariance properties. Two examples at given. The UMPS tests for testing the two-parameter uniform family against the two-parameter exponential family, and for testing one truncation parameter distribution against another one are derived.     

A modified likelihood ratio test for the mean direction in the von mises distribution

The likelihood ratio test (LRT) for the mean direction in the von Mises distribution is modified for possessing a common asymptotic distribution both for large sample size and for large concentration parameter. The test statistic of the modified LRT is compared with the F distribution but not with the chi-square distribution usually employed, Good performances of the modified LRT are shown by analytical studies and Monte Carlo simulation studies, A notable advantage of the test is that it takes part in the unified likelihood inference procedures including both the marginal MLE and the marginal LRT for the concentration parameter.