Testing of Suspected Observations in an Exponential Sample With Unknown Origin

The problem of multiple upper outliers in two-parameter exponential sample is considered. A test statistic is proposed to identify the outliers at the upper end of the sample. The null distribution of the test statistic is obtained and the critical values are found. The performance of the test is also compared with the earlier work.     

Testing for multiple upper and lower outliers in an exponential sample

Due to wide applicability and simplicity, the exponential distribution is the most commonly used distribution in reliability engineering and other life testing experiments. In this paper a test statistic for testing upper and lower outliers simultaneously in an exponential sample is proposed. However, the distribution of test statistic under the alternative is rather intricate, the null distribution is derived and critical values are obtained. A simulation study is also carried out to compare the performance of test and is found that the test based on this statistic is more powerful than the other two selected tests.     

A Flexible Nonparametric Test for Ordered and Umbrella Alternatives

A flexible and robust test for the ordered and umbrella alternatives is proposed in this paper. A two-step procedure is presented to make the proposed test be easily applicable. Type I error and power of the given approach are thoroughly investigated by extensive Monte Carlo studies.     

Masking and swamping effects on tests for multiple outliers in normal sample

A study of some commonly used multiple outlier tests in case of normal samples is presented. When the number of outliers in the sample is unknown, two phenomena, namely, the masking and the swamping effect can occur. The performance of the tests is studied using the measures of masking and swamping effects proposed by Bendre and Kale (1985) and Bendre (1985). The effects are illustrated in case of the Murphy test, Tietjen—Moore test and Dixon test. A small simulation study is carried out to indicate these effects.     

Multiple outlier test for upper outliers in an exponential sample

In this paper, a test statistic for testing upper outliers with a slippage alternative, in an exponential sample is proposed. No tables for critical values are required as they can be calculated easily for any sample size. A simulation study is also carried out to compare the performance of the test with the maximum likelihood ratio test and other existing tests.     

Testing for Unit Root Against Stationarity Using the Likelihood Ratio Test

In a first-order autoregressive model with drift, we derive the likelihood ratio test for a unit root against the stationary alternative. We also derive the test in a state space model with trend. Finite sample and asymptotic critical values are obtained by Monte Carlo simulations. A simulation study investigates the power performance of the likelihood ratio test and we also examine how a bias correction of the test affects the results.     

A statistical measure of internal consistency

A test for homogeneity of several populations against the simple tree alternative is proposed when the observations in various groups are subject to the same pattern of random right-censorship. The test is a generalization of the one proposed by Slivka (1970) which is useful when testing time is expensive so that an early termination of an experiment is desirable. The power of the test is examined in a simulation study.     

On the Power of Bootstrapped Specification Tests

Abstract

Decisions based on econometric model estimates may not have the expected effect if the model is misspecified. Thus, specification tests should precede any analysis. Bierens' specification test is consistent and has optimality properties against some local alternatives. A shortcoming is that the test statistic is not distribution free, even asymptotically. This makes the test unfeasible. There have been many suggestions to circumvent this problem, including the use of upper bounds for the critical values. However, these suggestions lead to tests that lose power and optimality against local alternatives. In this paper we show that bootstrap methods allow us to recover power and optimality of Bierens' original test. Bootstrap also provides reliable p-values, which have a central role in Fisher's theory of hypothesis testing. The paper also includes a discussion of the properties of the bootstrap Nonlinear Least Squares Estimator under local alternatives.     

Rank tests for the k-sample problem with restricted alternatives

An asymptotically maximin most powerful rank test among somewhere asymptotically most powerful linear rank tests with scores generating function cf> is derived for each of the simple order alternative, the simple loop alternative and the simple tree alternative in the k-sample problem. The comparisons of the tests obtained with the rank analogues of the Bartholomew's xv tests are made in terms of local asymptotic relative efficiency. It is found that our tests are better than the rank analogues of the xk tests. Furthermore, the asymptotic equivalence of the ranking by the pooled sample to the ranking in pairs are discuss¬ed and the tests which are asymptotically equivalent to ours are given.     

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).     

Likelihood ratio test for discordancy with slippage alternatives

A likelihood ratio test for discordancy in the sample is considered with slippage alternatives. It is shown for a wide class of univariate distributions that only the extreme observations in the sample need to be tested for discordancy. This result provides a firmer support to many commonly used discordancy tests that take only extreme observations as candidates. The problem of testing multiple discordant observations is also discussed.     

A family of IDMRL tests with unknown turning point

In this paper we propose a family of tests for exponentiality against the IDMRL alternative. Here we assume that the turning point or the proportion before the turning point is unknown. We derive the asymptotic null distributions of the test statistics and obtain their asymptotic critical values based on Durbin's approximation method. A simulation study is conducted to evaluate the proposed tests.     

Reweighted Smooth Tests of Goodness of Fit

Starting from a smooth test for goodness of fit we develop a method to alter this test to a reweighted smooth test, which has greater power to a certain directional alternative. Whereas the original smooth test gives equal weight to the different directions in the space of alternatives, the reweighted smooth test makes a distinction in importance of the directions. The advantage of this test, as opposed to directional tests, is that the smooth character is largely maintained. We discuss both nested and non nested directional alternatives.     

Comment on “a new statistic for testing suspected outliers”

A new statistic proposed by Tiku (1975) is compared with the Ferguson (1961) and Pearson-Chandra Sekar (1936) statistics. A simulation suggests that the new statistic is not superior to the Pearson-Chandra Sekar statistic when performance is assessed by the power of the test against the Dixon (1950) alternative.     

Precedence tests for equality of two distributions based on early failures of ranked set samples

In this article, two different types of precedence tests, each with two different test statistics, based on ranked set samples for testing the equality of two distributions are discussed. The exact null distributions of proposed test statistics are derived, critical values are tabulated for both set size and number of cycles up to 8, and the exact power functions of these two types of precedence tests under the Lehmann alternative are derived. Then, the power values of these two test procedures and their competitors based on simple random samples and based on ranked set samples are compared under the Lehmann alternative exactly and also under a location-shift alternative by means of Monte Carlo simulations. Finally, the impact of imperfect ranking is discussed and some concluding remarks are presented.     

Detecting a change in variances

The likelihood ratio test for testing for a change in a sequence of variances of normal populations is derived. The alternative hypothesis considered is of a one-sided nature. For the test, the conservativeness of the Sidak bound is shown and the asymptotic version of the Sidak bound is also constructed. These bound are compared with the Bonferroni bound and the Worsley bound, using the Monte Carlo method. Finally Hsu's data of stock market returns is reanalysed, using the test.     

A One-Sided Rank Test for Multivariate Censored Data

An asymptotically distribution-free test is proposed for testing the equality of two multivariate failure distributions against a particular one-sided alternative based on censored observations. This test may be interpreted as a multivariate one-sided Gehan test. The consistency of the test is established. An illustrative example is given.     

On the optimality of rao's statistic

This paper establishes the asymptotic optimality of Rao's

test within a very wide class of tests that Includes the likeli hood ratio test and Wald's test. An expression for the defici¬ency of the tests in this class relative to Rao's test has also been obtained     

On a gmanova model likelihood ratio test criterion

For the generalized MANOVA (GMANOVA) model of Potthoff and Roy (1964), X = BξA + E, Khatri (1966) derives the likelihood ratio test criterion for test-ing the composite double linear null hypothesis CξV = 0, C,V known. This criterion plays an important role in statistics, and several authors have recently studied its further properties. However, Khatri's (1966) de-reviation of the distribution of this criterion is involved. By noting that the GMANOVA model is re-stricted MANOVA model, this paper presents an alter-native simple derivation of the distribution of this criterion. The derivation is based on the generalized Sverdrup's lemma, Kabe (1965).     

A class of exceedance-type statistics for the two-sample problem

We consider here a class of test statistics based on exceeding observations and develop exceedance-type tests for the two-sample hypothesis testing problem. The exact distribution of the statistics are derived under the null hypothesis as well as under the Lehmann alternative, and then a comparative power study is carried out.