The limiting power of point optimal autocorrelation tests

This paper considers the point optimal tests for AR(1) errors in the linear regression model. It is shown that these tests have the same limiting power characteristics as the Durbin-Watson test. . The limiting power is zero or one when the regression has no intercept, but lies strictly between these values when an intercept is included.     

Tests for the two-sample problem based on empirical probability measures

Tests are proposed for the equality of two unknown distributions. For empirical probability measures that are defined for samples from the two distributions, the proposed tests are based on the supremum of the absolute differences between the corresponding empirical probabilities, the supremum being taken over all possible events (Borel sets). In contrast, competing EDF tests compare only empirical probabilities of a subclass of Borel sets. The proposed tests are compared for simulated samples to the Kolmogorov-Smirnov, Cramér-von Mises, Kuiper, and Mann-Whitney-Wilcoxon tests     

Structural properties and estimation in m|EK| 1 queue

In this paper we study the distribution of the number of customers served in a busy period in the framework of modified power series distribution introduced by Gupta (197U) and obtain the moments and probability generating function of this distribution. We also study the maximum likelihood estimation of the parameter θand the variance and the asymptotic bias of the MLE are also obtained. The minimum variance unbiased estimate of θ^ris investigated and an estimate of the probabilities is given.     

Bivariate distributions of some ratios of independent noncentral chi-square random variables

The bivariate distributions of three pairs of ratios of in¬dependent noncentral chi-square random variables are considered. These ratios arise in the problem of computing the joint power function of simultaneous F-tests in balanced ANOVA and ANCOVA. The distributions obtained are generalizations to the noncentral case of existing results in the literature. Of particular note is the bivariate noncentral F distribution, which generalizes a special case of Krishnaiah*s (1964,1965) bivariate central F distribution. Explicit formulae for the cdf's of these distribu¬tions are given, along with computational procedures     

On the power of the durbin-watson test under high autocorrelation

In the linear regression model without an intercept, it is known that the limiting power of the Durbin-Watson test (as correlation among errors increases) equals either one or zero, depending on the underlying regressor matrix. This paper considers the limiting power in the model with an intercept, and proves that it will never equal one or zero.     

The two-sample t test versus satterthwaite's approximate f test

A comparison between the two-sample t test and Satterthwaite's approximate F test is made, assuming the choice between these two tests is based on a preliminary test on the variances. Exact formulas for the sizes and powers of the tests are derived. Sizes and powers are then calculated and compared for several situations.     

A method of power assessment for tests comparing several treatments with a control

A method of power assessment for the problem of comparing several treatments with a control is considered. Power assessment is based on the power function of a two-sided hypothesis test that none of the treatment is different from the control. Normally distributed data and binary response data are considered. Minimum power levels are found under certain easily interpretable range conditions on the treatment and control means or success probabilities. Expressions are provided allowing simple computer evaluation of minimum guaranteed power levels, and some illustrative tables of power levels are given.     

New class of location-parameter discrete probability distributions and their characterizations

A new class of location-parameter discrete probability distributions (LDPD) has been defined where the population mean is the location parameter. It has been shown that some single parameter discrete distributions do not belong to this class and all discrete probability distributions belonging to this class can be characterized by their variances only. Expressions are given for the first four central moments and a recurrence formula for higher central moments has been obtained. Eight theorems are given to characterize the various distributions in the LDPD class.     

An efficient sequential design of clinical trials

We propose an efficient group sequential monitoring rule for clinical trials. At each interim analysis both efficacy and futility are evaluated through a specified loss structure together with the predicted power. The proposed design is robust to a wide range of priors, and achieves the specified power with a saving of sample size compared to existing adaptive designs. A method is also proposed to obtain a reduced-bias estimator of treatment difference for the proposed design. The new approaches hold great potential for efficiently selecting a more effective treatment in comparative trials. Operating characteristics are evaluated and compared with other group sequential designs in empirical studies. An example is provided to illustrate the application of the method.     

Rethinking the Univariate Approach to Panel Unit Root Testing: Using Covariates to Resolve the Incidental Trend Problem

In an influential article, Hansen showed that covariate augmentation can lead to substantial power gains when compared to univariate tests. In this article, we ask if this result extends also to the panel data context? The answer turns out to be yes, which is maybe not that surprising. What is surprising, however, is the extent of the power gain, which is shown to more than outweigh the well-known power loss in the presence of incidental trends. That is, the covariates have an order effect on the neighborhood around unity for which local asymptotic power is negligible.