Testing for Upper Outliers in Gamma Sample

The problem of multiple upper outlier detection in gamma sample is considered. Balasooriya and Gadag (1994 Balasooriya , U. , Gadag , V. ( 1994 ). Tests for upper outliers in the two-parameter exponential distribution . J. Statist. Computat. Simul. 50 : 249 – 259 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) proposed a location and scale invariant test based on the test statistic Z _k for testing the k upper outliers in two-parameter exponential sample. In this article, the test statistic is extended for gamma sample and the null distribution of the statistic is obtained. A simulation study is carried out to compare the performance of the tests and is found that the test based on Z _k is more powerful than the test based on the test statistic proposed by Jabbari Nooghabi et al. (2010 Jabbari Nooghabi , M. , Jabbari Nooghabi , H. , Nasiri , P. ( 2010 ). Detecting outliers in gamma distribution . Commun. Statist. Theor. Meth. 39 : 698 – 706 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]).     

On some tests for independence in nonnormal situations: neyman'S C(A)test

A study is made of Neyman's C(a) test for testing independence in nonnormal situations. It is shown that it performs very well both in terms of the level of significance and the powereven for smallvalues of the samplesize. Also, in the case of the bivariate Polsson distribution, itis shown that Fisher's z and Student's t transforms of the sample correlation coefficient are good competitors for Neyman's procedure.

     

Development of Adaptive Group Sequential Procedure for Changing Sample Size

In this study, we propose a group sequential procedure that allows the change of necessary sample size at intermediary stage in sequential test. In the procedure, we formulate the conditional power to judge the necessity of the change of sample size in decision rules. Furthermore, we present an integral formula of the power of the test and show how to change the necessary sample size by using the power of the test. In simulation studies, we investigate the characteristics of the change of sample size and the pattern of decision across all stages based on generated normal random numbers.     

Data driven smooth test for paired populations

In this paper we propose a smooth test of comparison of two distribution functions. This test adapts to the classical two-sample problem as well as that of paired populations, including discrete distributions. A simulation study and an application to real data show its good performances.     

Analysis of binary data in the randomized complete block design

The technique proposed by Shah and Claypool (1984) is extended here for the randomized complete block design with one binary observation per cell. In addition, it provides an al- ternative derivation of the distribution of Cochran's Q sta- tistic which is straightforward.     

The Multiple Outlier Problem in Time Series Analysis

In this paper we consider the multiple outlier problem in time series analysis. The underlying undisturbed time series is assumed to be an autoregressive process. The location of the suspicious values is supposed to be known. We introduce conditional least squares estimators for the parameters. The estimates are shown to be strongly consistent. Using similar arguments as in the theory of linear models, we get a test statistic for the general linear hypothesis. Its asymptotic distribution is derived.     

Distribution of the Activity Time in Network Analysis: A Critical Revisit with a Gamma Alternative

Network analysis is an important technique for project management. However, the current literature is biased toward beta distribution for modeling activity times. In this article, we have critically examined the role of beta distribution. It has been shown that beta distribution plays no specific role. Further, the method for calculating the chance of project completion must be revised. We have accordingly suggested an alternative modeling in terms of gamma distribution and proposed how to calculate the chance of project completion by taking into consideration both critical and noncritical paths. For demonstration purposes, we have considered a small project.     

An Efficient Method to Generate Data and Compute Exact P-Values in Goodness-of-Fit Testing

In this article, we use a characterization of the set of sample counts that do not match with the null hypothesis of the test of goodness of fit. Two direct applications arise: first, to instantaneously generate data sets whose corresponding asymptotic P-values belong to a certain pre-defined range; and second, to compute exact P-values for this test in an efficient way. We present both issues before illustrating them by analyzing a couple of data sets. Method's efficiency is also assessed by means of simulations. We focus on Pearson's X ² statistic but the case of likelihood-ratio statistic is also discussed.     

Bimatrix Variate Beta Type IV Distribution: Relation to Wilks's Statistic and Bimatrix Variate Kummer-Beta Type IV Distribution

In this article, the bimatrix variate beta Type IV distribution is derived from independent Wishart distributed matrix variables. We explore specific properties of this distribution which is then used to derive the exact expressions of the densities of the product and ratio of two dependent Wilks's statistics and to define the bimatrix Kummer-beta Type IV distribution.     

Testing linear hypotheses in high-dimensional regressions

For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative hypothesis requires complex analytic approximations, and more importantly, these distributional approximations are feasible only for moderate dimension of the dependent variable, say p≤20. On the other hand, assuming that the data dimension p as well as the number q of regression variables are fixed while the sample size n grows, several asymptotic approximations are proposed in the literature for Wilk's Λ including the widely used chi-square approximation. In this paper, we consider necessary modifications to Wilk's test in a high-dimensional context, specifically assuming a high data dimension p and a large sample size n. Based on recent random matrix theory, the correction we propose to Wilk's test is asymptotically Gaussian under the null hypothesis and simulations demonstrate that the corrected LRT has very satisfactory size and power, surely in the large p and large n context, but also for moderately large data dimensions such as p=30 or p=50. As a byproduct, we give a reason explaining why the standard chi-square approximation fails for high-dimensional data. We also introduce a new procedure for the classical multiple sample significance test in multivariate analysis of variance which is valid for high-dimensional data.     

An Adjustment to the Bartlett's Test for Small Sample Size

The Bartlett's test (1937) for equality of variances is based on the χ² distribution approximation. This approximation deteriorates either when the sample size is small (particularly < 4) or when the population number is large. According to a simulation investigation, we find a similar varying trend for the mean differences between empirical distributions of Bartlett's statistics and their χ² approximations. By using the mean differences to represent the distribution departures, a simple adjustment approach on the Bartlett's statistic is proposed on the basis of equal mean principle. The performance before and after adjustment is extensively investigated under equal and unequal sample sizes, with number of populations varying from 3 to 100. Compared with the traditional Bartlett's statistic, the adjusted statistic is distributed more closely to χ² distribution, for homogeneity samples from normal populations. The type I error is well controlled and the power is a little higher after adjustment. In conclusion, the adjustment has good control on the type I error and higher power, and thus is recommended for small samples and large population number when underlying distribution is normal.     

Multi - sample test of equal gamma distribution scale parameters in presence of unknown common shape parameter

Shiue and Bain proposed an approximate F statistic for testing equality of two gamma distribution scale parameters in presence of a common and unknown shape parameter. By generalizing Shiue and Bain's statistic we develop a new statistic for testing equality of L >= 2 gamma distribution scale parameters. We derive the distribution of the new statistic ESP for L = 2 and equal sample size situation. For other situations distribution of ESP is not known and test based on the ESP statistic has to be performed by using simulated critical values. We also derive a C(α) statistic CML and develop a likelihood ratio statistic, LR, two modified likelihood ratio statistics M and MLB and a quadratic statistic Q. The distribution of each of the statistics CML, LR, M, MLB and Q is asymptotically chi-square with L - 1 degrees of freedom. We then conducted a monte-carlo simulation study to compare the perfor- mance of the statistics ESP, LR, M, MLB, CML and Q in terms of size and power. The statistics LR, M, MLB and Q are in general liberal and do not show power advantage over other statistics. The statistic CML, based on its asymptotic chi-square distribution, in general, holds nominal level well. It is most powerful or nearly most powerful in most situations and is simple to use. Hence, we recommend the statistic CML for use in general. For better power the statistic ESP, based on its empirical distribution, is recommended for the special situation for which there is evidence in the data that λ₁ < … < λ_L and n₁ < … < n_L, where λ₁ …, λ_L are the scale parameters and n₁,…, n_L are the sample sizes.     

On Charlier polynomials in testing Poissonity

This article discusses applications of Charlier polynomials when checking how well classic Poisson model fits the data. We show that smooth components pertaining to the polynomials can be effectively used in preliminary analysis of data at hand and we propose and discuss some tests based on them. Our extensive simulations shed new light on power behavior of the best tests in the area.     

A Comparative Study of Some Modified Chi-Squared Tests

Some recent results in the theory and applications of modified chi-squared goodness-of-fit tests are briefly discussed. It seems that for the first time power of modified chi-squared type tests for the logistic and three-parameter Weibull distributions based on moment type estimators is studied. Power of different modified tests against some alternatives for equiprobable fixed or random grouping intervals, and for Neyman–Pearson classes is investigated. It is shown that power of test statistic essentially depends on the quantity of Fisher's sample information this statistic uses. Some recommendations on implementing modified chi-squared type tests are given.     

The Cucconi Test for Location-scale Alternatives in Application to Asymmetric Hydrological Variables

To identify location-scale trends, which environmental data often exhibit, location-scale tests have to be addressed. The aim of this article was to estimate size and power of the Cucconi rank-based test when applied to various skewed distributions, typical in hydrology. Results of the Monte Carlo simulation revealed great power for series with low coefficient of variation, time of change close to the middle, not very heavy tail, and with length of at least 60. Comparison to the Lepage test discovered larger usefulness of the Cucconi test for short series and change close to the middle. Several practical applications were presented.     

How to test hypotheses if you must

Drug development is not the only industrial‐scientific enterprise subject to government regulations. In some fields of ecology and environmental sciences, the application of statistical methods is also regulated by ordinance. Over the past 20years, ecologists and environmental scientists have argued against an unthinking application of null hypothesis significance tests. More recently, Canadian ecologists have suggested a new approach to significance testing, taking account of the costs of both type I and type II errors. In this paper, we investigate the implications of this for testing in drug development and demonstrate that its adoption leads directly to the likelihood principle and Bayesian approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

Multiple Decision Procedures for Inference in Regression Models

We consider testing of the significance of the coefficients in the linear model. Unlike in the classical approach, there is no alternative hypothesis to accept when the null hypothesis is rejected. When there is a substantial deviation from the null hypothesis, we reject the null hypothesis and identify based on data alternative hypotheses associated with the independent variables or the levels that contributed most towards the deviation from the null hypothesis.     

Fisher information in censored samples from Downton's bivariate exponential distribution

We develop a simple approach to finding the Fisher information matrix (FIM) for a single pair of order statistic and its concomitant, and Type II right, left, and doubly censored samples from an arbitrary bivariate distribution. We use it to determine explicit expressions for the FIM for the three parameters of Downton's bivariate exponential distribution for single pairs and Type II censored samples. We evaluate the FIM in censored samples for finite sample sizes and determine its limiting form as the sample size increases. We discuss implications of our findings to inference and experimental design using small and large censored samples and for ranked-set samples from this distribution.     

On the test of liu and chow's procedure for assessing equivalence in variability of bioavailability

Similar to Schuirmann's two one-sided tests procedure for assessment of bioequivalence in average bioavailability (Schuirmann,), Liu and Chow proposed a two one-sided tests procedure for assessment of equivalence of variability of bioavailability. Their procedure is derived based on the correlation between crossover differences and subject totals. In this paper, we examined the performance of their test procedure in terms of its test size and power for various situations where the intersubject variability and the intrasubject variability of the test drug product are relatively larger, similar, and smaller than that of the intrasubject variability of the reference drug product.     

On a new goodness‐of‐fit process for families of copulas

A goodness‐of‐fit procedure is proposed for parametric families of copulas. The new test statistics are functionals of an empirical process based on the theoretical and sample versions of Spearman's dependence function. Conditions under which this empirical process converges weakly are seen to hold for many families including the Gaussian, Frank, and generalized Farlie–Gumbel–Morgenstern systems of distributions, as well as the models with singular components described by Durante [Durante ( 2007 ) Comptes Rendus Mathématique. Académie des Sciences. Paris, 344, 195–198]. Thanks to a parametric bootstrap method that allows to compute valid P‐values, it is shown empirically that tests based on Cramér–von Mises distances keep their size under the null hypothesis. Simulations attesting the power of the newly proposed tests, comparisons with competing procedures and complete analyses of real hydrological and financial data sets are presented. The Canadian Journal of Statistics 37: 80‐101; 2009 © 2009 Statistical Society of Canada