Comparing Tests of Autoregressive Versus Moving Average Errors in Regression Models Using Bahadur's Asymptotic Relative Efficiency,

The purpose of this paper is to use Bahadur's asymptotic relative efficiency measure to compare the performance of various tests of autoregressive (AR) versus moving average (MA) error processes in regression models. Tests to be examined include non-nested procedures of the models against each other, and classical procedures based upon testing both the AR and MA error processes against the more general autoregressive-moving average model.

The asymptotic relative efficiency and the ratio of sample sizes when testing two different null hypotheses

Composite endpoints, consisting of the union of two or more outcomes, are often used as the primary endpoint in time-to-event randomized clinical trials. Previously, Gómez and Lagakos provided a method to guide the decision between using a composite endpoint instead of one of its components when testing the effect of a treatment in a randomized clinical trial. Consider the problem of testing the null hypotheses of no treatment effect by means of either the single component or the composite endpoint. In this paper we prove that the usual interpretation of the asymptotic relative efficiency as the reciprocal ratio of the sample sizes required for two test procedures, for the same null and alternative hypothesis, and attaining the same power at the same significance level, can be extended to the test procedures considered here for two different null and alternative hypotheses. A simulation to study the relationship between asymptotic relative efficiency and finite sample sizes is carried out.Peer ReviewedPostprint (published version

On the inconsistency of the unrestricted estimator of the information matrix near a unit root

The unrestricted estimator of the information matrix is shown to be inconsistent for an autoregressive process with a root lying in a neighbourhood of unity with radial length proportional or smaller than 1/n, i.e. a root that takes the form rho=1+c/n^alpha, alpha>=1. In this case the information evaluated at rho-hat_n converges to a non-degenerate random variable and contributes to the asymptotic distribution of a Wald test for the null hypothesis of a random walk versus a stable AR(1) alternative. With this newly derived asymptotic distribution the above Wald test is found to improve its performance. A non local criterion of asymptotic relative efficiency based on Bahadur slopes has been employed for the first time to the problem of unit root testing. The Wald test derived in the paper is found to be as efficient as the Dickey Fuller t ratio test and to outperform the non studentised Dickey Fuller test and a Lagrange Multiplier test.Unit root distribution; neighbourhoods of unity; information matrix; inconsistency; Wald test; Bahadur slopes

A Note on Detecting “More IFR-ness” Property of Life Distributions

In this paper, a problem of testing whether one life distribution possesses “more IFR” property than the other is considered.A new test procedure is proposed and the distribution of the test statistic is studied. The performance of the procedure is evaluated in terms of Pitman asymptotic relative efficiency. The consistency property of the test procedure is established. It is observed that the new procedure is better than the existing procedure in the literatur

PROCEDURE FOR DETECTING ‘MORE NBU-NESS’ PROPERTY OF LIFE DISTRIBUTIONS

Testing the hypothesis of no ageing against positive ageing has been considered by many authors in the literature. However, very fewtests procedures for detecting whether a life distribution possesses ‘more positive ageng’ than the other distribution are developed.Hollander, Park and Proschan(1986) proposed a test procedure to detect ‘More NBUness’ property of life distributions. Pandit and Gudaganavar(2009) developeda procedure which is an improvementover the test due to Hollander, Park and Proschan(1986). In this paper, a test is developed to decide whether onelife distribution possesses more ‘new better than used’ (NBU)property than does another life distribution. The asymptotic performance of the test procedure is evaluated interms of Pitman asymptotic relative efficiency. It is found that new test performs betterthan the tests in the literature