Asymptotic Power Of Tests Research Articles

On the asymptotic properties of a certain class of goodness-of-fit tests associated with multinomial distributions

The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the class of power divergence statistics, in particular, on the chi-square and log-likelihood ratio statistics. The main issue of the article is to study the asymptotic properties of tests at the concept of an intermediate setting, when the asymptotic power of tests are bounded away from zero and one, while sequences of alternatives converge to the hypothesis, but not too fast.

On the Asymptotic Power of Tests of Fit under Local Alternatives in Autoregression

We consider a stationary AR(p) model. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of empirical distribution function is defined and the tests of Kolmogorov’s and ω2 type are constructed for testing hypotheses on the distribution of innovations. We obtain the asymptotic power of these tests under local alternatives.

Performance of tests of association in misspecified generalized linear models

We examine the effects of modelling errors, such as underfitting and overfitting, on the asymptotic power of tests of association between an explanatory variable x and an outcome in the setting of generalized linear models. The regression function for x is approximated by a polynomial or another simple function, and a chi-square statistic is used to test whether the coefficients of the approximation are simultaneously equal to zero. Adding terms to the approximation increases asymptotic power if and only if the fit of the model increases by a certain quantifiable amount. Although a high degree of freedom approximation offers robustness to the shape of the unknown regression function, a low degree of freedom approximation can yield much higher asymptotic power even when the approximation is very poor. In practice, it is useful to compute the power of competing test statistics across the range of alternatives that are plausible a priori. This approach is illustrated through an application in epidemiology.

On the Asymptotic Power of Tests for ComparingKCorrelated Proportions

Abstract The limit distribution of Cochran's Q statistic for testing the equality of k proportions in matched samples is obtained for sequences of Pitman alternatives. Comparison of the asymptotic power of the test based on the Q statistic with that of the test based on Wald's statistic for the same asymptotic level shows that neither test is uniformly better than the other. We study by simulation a modified Q test using an estimated critical value obtained from a Satterthwaite-type approximation for cases when the proportions to be compared are near one-half and k = 4. The operating characteristics agree closely with estimated values in samples of 50 and 100, while the agreement with the Wald statistics was occasionally poor.

On the Asymptotic Power of Tests for Comparing K Correlated Proportions

On the Asymptotic Power of Tests for Comparing K Correlated Proportions

Local Asymptotic Power and Efficiency of Tests of Kolmogorov-Smirnov Type

This paper is devoted to some problems related to asymptotic power and efficiency of tests of Kolmogorov-Smirnov type. The results are derived by means of the theory of stochastic processes. The concepts of local asymptotic power and local asymptotic efficiency of tests are introduced according to [7]. Section 4 contains the evaluation of the local asymptotic power of one-sided tests of Kolmogorov-Smirnov type and of Renyi's one-sided test. The asymptotic power of these tests may be expressed by series expansion. Some theoretical results related to terms of the series are given and used for approximations and bounds of the asymptotic power. The paper is an excerpt from the author's dissertation written with the guidance of Professor Jaroslav Hajek.

Corrigenda: Asymptotic Power of Tests of Linear Hypothesis Using the Probit and Logit Transformations.

Corrigenda: Asymptotic Power of Tests of Linear Hypothesis Using the Probit and Logit Transformations.

Asymptotic Power of Tests of Linear Hypotheses Using the Probit and Logit Transformations

Abstract The statistic for testing the fit of a linear model, or the statistic for testing a linear hypothesis under the model, when using probits or logits, has a central χ2-distribution for large samples if the null hypothesis is true. If it is not true, the test statistic has, asymptotically, a non-central χ2-distribution with a non-centrality parameter that depends on the alternative hypothesis, the model, and the transformation. Non-Centrality parameters associated with tests of the two types of hypotheses are derived, and the non-centrality parameters of some tests of interest in bioassay when the response is quantal are derived as special cases. Possible applications are discussed and several numerical examples are given.