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1.
The mixed Weibull distribution provides a flexible model to analyze random durations in a possibly heterogeneous population.
To test for homogeneity against unobserved heterogeneity in a Weibull mixture model, a dispersion score test and a goodness-of-fit
test are investigated. The empirical power of these tests is assessed and compared on a broad range of alternatives. It comes
out that the dispersion score test, as it is based on a Weibull-to-exponential transformation, often breaks down. A simple
new procedure is introduced for Weibull mixtures in scale, which combines the dispersion score test and the goodness-of-fit
test. The new test is compared with several known procedures and shown to have a good overall power. To detect mixtures in
shape and scale, a goodness-of-fit test is recommended.
This research has been partially sponsored by a grant of the Deutsche Forschungsgemeinschaft. We thank Lars Haferkamp for
computational assistance and Wilfried Seidel and a referee for their remarks on alternative test procedures. 相似文献
2.
A Class of Pseudolikelihood Ratio Tests for Homogeneity in Exponential Tilt Mixture Models
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Mixture models are commonly used in biomedical research to account for possible heterogeneity in population. In this paper, we consider tests for homogeneity between two groups in the exponential tilt mixture models. A novel pairwise pseudolikelihood approach is proposed to eliminate the unknown nuisance function. We show that the corresponding pseudolikelihood ratio test has an asymptotic distribution as a supremum of two squared Gaussian processes under the null hypothesis. To maintain the appeal of simplicity for conventional likelihood ratio tests, we propose two alternative tests, both shown to have a simple asymptotic distribution of under the null. Simulation studies show that the proposed class of pseudolikelihood ratio tests performs well in controlling type I errors and having competitive powers compared with the current tests. The proposed tests are illustrated by an example of partial differential expression detection using microarray data from prostate cancer patients. 相似文献
3.
Testing for Homogeneity in an Exponential Mixture Model 总被引:3,自引:0,他引:3
This paper studies diagnostic procedures to test for homogeneity against unobserved heterogeneity in an exponential mixture model. The procedures include a dispersion score test, a likelihood ratio test, a moment likelihood approach and several goodness-of-fit tests. The paper compares the empirical power of these tests on a broad range of alternatives and proposes a new test that combines the dispersion score test with a properly chosen goodness-of-fit procedure; its empirical power comes close to the power of the best of the other tests. 相似文献
4.
Using Monte Carlo simulation, we compare the performance of five asymptotic test procedures and a randomized permutation test procedure for testing the homogeneity of odds ratio under the stratified matched-pair design. We note that the weighted-least-square test procedure is liberal, while Pearson's goodness-of-fit (PGF) test procedure with the continuity correction is conservative. We note that PGF without the continuity correction, the conditional likelihood ratio test procedure, and the randomized permutation test procedure can generally perform well with respect to Type I error. We use the data taken from a case–control study regarding the endometrial cancer incidence published elsewhere to illustrate the use of these test procedures. 相似文献
5.
Gregory Gurevich 《统计学通讯:理论与方法》2013,42(16):2841-2862
The problem considered in this study is that of detecting a change in the unknown parameters of known distribution on the basis of a finite sequence of independent observations, assuming that if a change in the parameters of a distribution has occurred then it is unique. We examine various methods that have been suggested for this problem and suggest a uniform approach, based on likelihood ratio analysis. For tests derived this way we present approximations for levels of significance based on asymptotic analyses. The suggested tests meet the needs of specific problems (such as a one-sided alternative), for which general parametric case solutions have not been suggested explicitly before. We also find that rate of convergence of our asymptotics is fast, and provide accurate results for a level of significance of the suggested tests for sample sizes commonly observed in practice. 相似文献
6.
This article presents a note on the modified likelihood ratio test for homogeneity in beta mixture models. Under consistency of the penalized maximum likelihood estimators, the limiting distribution of the test statistic converges to the chi-bar-squared distributions. The statistic degenerates to zero with a weight due to the negative definiteness of a complicated random matrix. The probability that this matrix is negative definite is related to the parameter values under the homogeneity hypothesis. The dependency pattern enables the introduction of an upper bound on the asymptotic null distribution. Simulation study is investigated to verify the accuracy of the results. 相似文献
7.
《统计学通讯:理论与方法》2013,42(11):2147-2155
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. 相似文献
8.
The aim of this article is to discuss homogeneity testing of the exponential distribution. We introduce the exact likelihood ratio test of homogeneity in the subpopulation model, ELR, and the exact likelihood ratio test of homogeneity against the two-components subpopulation alternative, ELR2. The ELR test is asymptotically optimal in the Bahadur sense when the alternative consists of sampling from a fixed number of components. Thus, in some setups the ELR is superior to frequently used tests for exponential homogeneity which are based on the EM algorithm (like the MLRT, ADDS, and D-tests). One important example of superiority of ELR and ELR2 tests is the case of lower contamination. We demonstrate this fact by both theoretical comparisons and simulations. 相似文献
9.
In this paper, classical optimum tests for symmetry of two-piece normal distribution is derived. Uniformly most powerful one-sided test for the skewness parameter is obtained when the location and scale parameters are known and is compared with sequential probability ratio test. An ad-hoc test for symmetry and likelihood ratio test for symmetry for large samples, can be found in literature for this distribution. But in this paper, we derive exact likelihood ratio test for symmetry, when location parameter is known. The exact power of the test is evaluated for different sample sizes. 相似文献
10.
The empirical likelihood (EL) technique is a powerful nonparametric method with wide theoretical and practical applications. In this article, we use the EL methodology in order to develop simple and efficient goodness-of-fit tests for normality based on the dependence between moments that characterizes normal distributions. The new empirical likelihood ratio (ELR) tests are exact and are shown to be very powerful decision rules based on small to moderate sample sizes. Asymptotic results related to the Type I error rates of the proposed tests are presented. We present a broad Monte Carlo comparison between different tests for normality, confirming the preference of the proposed method from a power perspective. A real data example is provided. 相似文献
11.
William C. Guenther 《The American statistician》2013,67(2):83-85
Approximate chi-square tests for hypotheses concerning multinomial probabilities are considered in many textbooks. In this article power calculations and sample size based on power are discussed and illustrated for the three most frequently used tests of this type. Available noncentrality parameters and existing tables permit a relatively easy solution of these kinds of problems. 相似文献
12.
D. Firth C. Payne & J. Payne 《Journal of the Royal Statistical Society. Series A, (Statistics in Society)》1999,162(1):111-120
An evaluation is described of two UK Government programmes for the long-term unemployed in Great Britain, Employment Training and Employment Action, using discrete time hazard modelling of event histories. The study design employed a closely matched comparison group and carefully chosen control variables to minimize the effect of selection bias on conclusions. The effect of unobserved heterogeneity is investigated by using some standard random effect model formulations. 相似文献
13.
In this article, we consider several statistical models for censored exponential data. We prove a large deviation result for the maximum likelihood estimators (MLEs) of each model, and a unique result for the posterior distributions which works well for all the cases. Finally, comparing the large deviation rate functions for MLEs and posterior distributions, we show that a typical feature fails for one model; moreover, we illustrate the relation between this fact and a well-known result for curved exponential models. 相似文献
14.
Xiaomi Hu 《Australian & New Zealand Journal of Statistics》2000,42(3):359-365
Likelihood ratio tests about the intensity function are obtained by confining the estimated intensity function of a Poisson process to a sample-dependent, left-continuous step function class. These tests have relatively simple test statistics and their distributions are stochastically maximized when the process is homogeneous. 相似文献
15.
In this article, we consider testing independence among components of random vector in multivariate normal population. For testing independence, we use the modified likelihood ratio test statistic which is improved an approximation to χ2 distribution of the likelihood ratio test statistic. In order to perform simultaneous tests for independence among components of random vector, we use the step-down multiple comparison procedure based on the closed testing procedure proposed by Marcus et al. (1976). Finally, we perform Monte Carlo simulations and present numerical results. 相似文献
16.
《统计学通讯:模拟与计算》2012,41(6):833-851
In linear and nonparametric regression models, the problem of testing for symmetry of the distribution of errors is considered. We propose a test statistic which utilizes the empirical characteristic function of the corresponding residuals. The asymptotic null distribution of the test statistic as well as its behavior under alternatives is investigated. A simulation study compares bootstrap versions of the proposed test to other more standard procedures. 相似文献
17.
In this article, we consider two independent zero-inflated power series distributions and provide likelihood ratio test for equality of inflation parameters of the same. As an illustration, testing equality of inflation parameters of two zero inflated Poisson distributions is provided. Further, simulation study to investigate power of likelihood ratio tests has been carried out. 相似文献
18.
Two methods for testing the equality of variances in straight lines regression with a change point are considered. One is likelihood ratio test and the other is Bayesian confidence interval, based on the highest posterior density for the ratio of variances, using non-informative priors. Methods are applied to the renal transplant data analyzed by Smith and Cook(1980) and Stephens(1994). 相似文献
19.
It is often assumed in situations in which life data from Weibull or extreme-value distributions are involved that data in different samples come from extreme-value distributions with the same scale parameter (equivalently, Weibull distributions with the same shape parameter). This paper proposes a number of tests for homogeneity for extreme-value scale parameters, based on a number of commonly used estimators for these scale parameters. Previous theoretical work and some simulation results provided here indicate that the null distributions of the test statistics proposed are well approximated by the x2 distribution under a wide range of conditions 相似文献
20.
Proportional hazards model(Cox, 1972) is reviewed for the case of grouped data with one continuously measured covariate. This leads to a logit-rank procedure for tied data which is reduced to the test proposed by O’Brien(1978) and studied by O’Quigley and Prentice(1991) in the absence of ties. The proposed test is then applied to a special ranking method in order to study non-monotonic associations. 相似文献