A new test for the extreme value distribution

In this paper a test statistic which is a modification of the W statistic for testing the goodness of fit for the two paremeter extreme value (smallest element) distribution is proposed. The test statistic Is obtained as the ratio of two linear estimates of the scale parameter. It Is shown that the suggested statistic is computationally simple and has good power properties. Percentage points of the statistic are obtained by performing Monte Carlo experiments. An example is given to illustrate the test procedure.     

Tukey-Type Distributions in the Context of Financial Data

Abstract

In one-parameter (θ) families, we were not aware of explicit hypothesis testing scenarios where maximal invariant statistics failed to distinguish the models. We start with a concrete example (Sec. 2.2) to highlight such a hypothesis testing problem involving markedly different models. In this problem, because of the absence of a nontrivial uniformly most powerful invariant (UMPI) test, we briefly suggest two approaches to test the hypothesis. The first resolution (Sec. 3.1) is frequentist in nature. It utilizes a weight function on the parameter space and compares “average” distributions obtained under the null and alternative models in the sense of Wald (1947 Wald , A. ( 1947 ). Sequential Analysis . New York : Wiley . [Google Scholar] 1950 Wald , A. ( 1950 ). Statistical Decision Functions . New York : Wiley . [Google Scholar]). In contrast, a fully Bayesian resolution (Sec. 3.2) is also included. The note ends with a series of other interesting examples involving one-parameter families where maximal invariant statistics fail to distinguish the hypothesized models. The examples include easy-to-construct families of probability models involving only a single location or scale parameter θ.     

Nonparametric maximum likelihood estimation for artificially truncated absence data

In manpower planning it is cornmoniy tue case tnat employees withuraw from active service for a period of time before returning to take up post at a later date. Such periods of absence are frequently of major concern to employers who are anxious to ensure that employees return as soon as possible. The distribution of duration of such periods of absence are therefore of considerable interest as is the probability that such employees will ever return to active service. In this paper we derive a nonparametric estimator for such a lifetime distribution based on renewal data which are subject to various forms of incompleteness, namely right censoring, left and right truncation, and forward recurrence. Artificial truncation is used to ensure that the data are time homogeneous. A nonparametric maximum likelihood estimator for the lifetime.     

Hypothesis Testing Problems in an Unbalanced Longitudinal Ophthalmology Study

ABSTRACT

The analysis of clustered data in a longitudinal ophthalmology study is complicated by correlations between repeatedly measured visual outcomes of paired eyes in a participant and missing observations due to the loss of follow-up. In the present article we consider hypothesis testing problems in an ophthalmology study, where eligible eyes are randomized to two treatments (when two eyes of a participant are eligible, the paired eyes are assigned to different treatments), and vision function outcomes are repeatedly measured over time. A large sample-based nonparametric test statistic and a nonparametric Bootstrap test analog are proposed for testing an interaction effect of two factors and testing an effect of a eye-specific factor within a level of the other person-specific factor on visual function outcomes. Both test statistics allow for missing observations, correlations between repeatedly measured outcomes on individual eyes, and correlations between repeatedly measured outcomes on both eyes of each participant. A simulation study shows that these proposed test statistics maintain nominal significance levels approximately and comparable powers to each other, as well as higher powers than the naive test statistic ignoring correlations between repeated bilateral measurements of both eyes in the same person. For illustration, we apply the proposed test statistics to the changes of visual field defect score in the Advanced Glaucoma Intervention Study.     

Survival Estimation with Missing Censoring Times for the Generalized Koziol–Green Model

ABSTRACT

When analyzing time-to-event data, there are various situations in which right censoring times for unfailed units are missing. In that context, by taking a supplementary sample of a convenient percentage of unfailed units, we propose a semi-parametric method for estimating a survival function under the natural extension of the Koziol–Green model to double random censoring. Some large sample properties of this estimator are derived. We prove uniform strong consistency and asymptotic weak convergence to a Gaussian process. A simulation study is also presented in order to analyze the behavior of the proposed estimator.     

Goodness-of-Fit Tests for Multivariate Distributions

We propose three new statistics, Z _p , C _p , and R _p for testing a p-variate (p ≥ 2) normal distribution and compare them with the prominent test statistics. We show that C _p is overall most powerful and is effective against skew, long-tailed as well as short-tailed symmetric alternatives. We show that Z _p and R _p are most powerful against skew and long-tailed alternatives, respectively. The Z _p and R _p statistics can also be used for testing an assumed p-variate nonnormal distribution.     

Binary Regression with Stochastic Covariates

In binary regression the risk factor X has been treated in the literature as a non-stochastic variable. In most situations, however, X is stochastic. We present solutions applicable to such situations. We show that our solutions are more precise than those obtained by treating X as non-stochastic when, in fact, it is stochastic.     

Optimal allocation of time points for the random effects model

In this article the problem of the optimal selection and allocation of time points in repeated measures experiments is considered. D‐ optimal designs for linear regression models with a random intercept and first order auto‐regressive serial correlations are computed numerically and compared with designs having equally spaced time points. When the order of the polynomial is known and the serial correlations are not too small, the comparison shows that for any fixed number of repeated measures, a design with equally spaced time points is almost as efficient as the D‐ optimal design. When, however, there is no prior knowledge about the order of the underlying polynomial, the best choice in terms of efficiency is a D‐ optimal design for the highest possible relevant order of the polynomial. A design with equally‐spaced time points is the second best choice     

Modeling service-time distributions for queueing network simulation

Shapes of service-time distributions in queueing network models have a great impact on the distribution of system response-times. It is essential for the analysis of response-time distribution that the modeled service-time distributions have the correct shape. Tradionally modeling of service-time distributions is based on a parametric approach by assuming a specific distribution and estimating its parameters. We introduce an alternative approach based on the principles of exploratory data analysis and nonparametric data modeling. The proposed method applies nonlinear data transformation and resistant curve fitting. The method can be used in cases, where the available data is a complete sample, a histogram, or the mean and a set of 5-10 quantiles. The reported results indicate that the proposed method is able to approximate the distribution of measured service times so that accurate estimates for quantiles of the response-time distribution are obtained     

MULTIVARIATE TESTS OF NORMAL MEAN VECTORS WITH RESTRICTED ALTERNATIVES

ABSTRACT

In this paper, we consider tests for the hypothesis that the mean vector is zero against one-sided alternatives when the observation vectors are independently and identically distributed as normal with unknown covariance matrix. The exact null-distribution of the tests is derived. The tests generalize the centre-direction test proposed by Tang et al.[1] Tang, D.-I., Gnecco, C. and Geller, N. 1989. An Approximate Likelihood Ratio Test for a Normal Mean Vector with Nonnegative Components with Application to Clinical Trials. Biometrika, 76: 577–583. [Crossref], [Web of Science ®] , [Google Scholar] for known covariance. In addition, the modification is order- and scale-invariant. Power comparisons with some other tests are presented. It can be shown that the null distribution of the test statistic holds for data arising from any elliptical distribution, not just the normal distribution.