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This work proposes powerful tests using bootstrap methods for the tail index in the family of distribution functions with nondegenerate right tail. It is of interest to test whether the right tail of a distribution function is the same as or heavier than that of the Pareto distribution with index m0 for some m0, vs. alternatively the right tail is lighter. Based on the nonparametric tests of Jureckova and Picek (2001, A class of tests on the tail index, Extreme 4:2, 165–183) that use empirical distribution functions of sample maxima, the proposed bootstrap tests employ two-stage subsamplings: One is subsampling from the sample maxima to be applicable even to the heavy tailed index and the other is subsampling from collections of empirical distributions of the sample maxima. We show the first-order validity of the bootstrap for the nonparametric test and construct bootstrap test statistics. The limiting distribution of the bootstrap test statistics in the null hypothesis is established and the consistency of the bootstrap tests is verified. Applications of the proposed bootstrap tests are given to autoregressive time series models. A simulation study is conducted to see performance of the bootstrap tests and it illustrates that the proposed bootstrap tests outperform the existing ones. Real data of heavy tailed financial stock indices are applied to the proposed bootstrap tests. [ABSTRACT FROM AUTHOR]

We consider the estimation and hypothesis test for single-index model by proposing a profile mean squares relative error estimation method, coupling with a leave-one-component-out method. The asymptotic normality for the PMSRE estimator is studied. For the hypothesis test of the single-index parameter, a restricted estimator under the null hypothesis and test statistics are proposed. The asymptotic properties for the restricted estimator and test statistic are established. Lastly, we make some comparisons between the proposed estimator and the profile least squares estimator and the profile least product relative estimator through the simulation. Our simulation studies indicate that the profile mean squares relative error estimator provides a better alternative under some settings, particularly for multimodal or asymmetric distributions of the error term. [ABSTRACT FROM AUTHOR]

Suppose we have k samples X 1 , 1 , ... , X 1 , n 1 , ... , X k , 1 , ... , X k , n k with different sample sizes n 1 , ... , n k and unknown underlying distribution functions F 1 , ... , F k as observations plus k families of distribution functions { G 1 (· , ϑ) ; ϑ ∈ Θ } , ... , { G k (· , ϑ) ; ϑ ∈ Θ } , each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F 1 , ... , F k) belongs to the parametric family { (G 1 (· , ϑ) , ... , G k (· , ϑ)) ; ϑ ∈ Θ }. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions. [ABSTRACT FROM AUTHOR]

There are many hypothesis testing settings in which one can calculate a "reasonable" test statistic, but in which the null distribution of the statistic is unknown or completely intractable. Fortunately, in many such situations, it is possible to simulate values of the test statistic under the null hypothesis, in which case one can conduct a Monte Carlo test. A difficulty however arises in that Monte Carlo tests, as they are currently structured, are applicable only if ties cannot occur among the values of the test statistics. There is a frequently occurring scenario in which there are lots of ties, namely that in which the null distribution of the test statistic has a (single) point mass. It turns out that one can modify the current form of Monte Carlo tests so as to accommodate such settings. Developing this modification leads to an intriguing identity involving the binomial probability function and its derivatives. In this article, we will briefly explain the modified procedure, discuss simulation studies which demonstrate its efficacy, and provide a proof of the identity referred to above. [ABSTRACT FROM AUTHOR]

This article is concernedwith comparison of a fewrandomvariate generation techniques for the generalized Poisson distribution. An evaluation is conducted on the degree of proximity between the estimates for its two distributional parameters and first four moments, and the specified or computed true population values via commonly accepted accuracy and precision measures in a simulated setting. [ABSTRACT FROM AUTHOR]

We propose a procedure to identify a lowest dose having greater effect than a threshold dose under the assumption of monotonicity of dose mean response in dose response test. So, we use statistics based on contrasts among sample means and apply a group sequential procedure to our procedure to identify effectively the dose. If we can identify the dose at an early step in the sequential test, since we can terminate the procedure with a few observations, the procedure is useful from an economical point of view. In a simulation studies, we compare the superiority among these procedures based on three contrasts. [ABSTRACT FROM AUTHOR]

The Birnbaum–Saunders distribution is a positively skewed distribution that is frequently used for analyzing lifetime data. Regression analysis is widely used in this context when some covariates are involved in the life-test. In this article, we discuss the maximum likelihood estimation of the model parameters and associated inference. We discuss the likelihood-ratio tests for some hypotheses of interest as well as some interval estimation methods. A Monte Carlo simulation study is then carried out to examine the performance of the proposed estimators and the interval estimation methods. Finally, some numerical data analyses are done for illustrating all the inferential methods developed here. [ABSTRACT FROM PUBLISHER]

Test statistics from the class of two-sample linear rank tests are commonly used to compare a treatment group with a control group. Two independent random samples of sizes m and n are drawn from two populations. As a result, N = m + n observations in total are obtained. The aim is to test the null hypothesis of identical distributions. The alternative hypothesis is that the populations are of the same form but with a different measure of central tendency. This article examines mid p-values from the null permutation distributions of tests based on the class of two-sample linear rank statistics. The results obtained indicate that normal approximation-based computations are very close to the permutation simulations, and they provide p-values that are close to the exact mid p-values for all practical purposes. [ABSTRACT FROM AUTHOR]