Some inference results in several symmetric multivariate exponential models

In this paper, we consider multivariate exponential models with identical marginals. We obtain MLEs of the parameters and large sample tests for mutual independence of k components in the multivariate exponential models proposed by Weinman (1966), Marshall-Olkin (1967) and Block (1975).     

More flexible sequential and non-sequential designs in long-term clinical trial

In this paper, we describe decision making procedures as they exist in most clinical trials,review some recently suggested approaches to monitoring and clarify how these methods allow greater flexibility in monitoring and explicit specification of data monitoring methods in the protocol.     

Nonparametric estimation of the survival distribution in censored data

Two nonparametric estimators o f the survival distributionare discussed. The estimators were proposed by Kaplan and Meier (1958) and Breslow (1972) and are applicable when dealing with censored data. It is known that they are asymptotically unbiased and uniformly strongly consistent, and when properly normalized that they converge weakly to the same Gaussian process. In this paper, the properties of the estimators are carefully inspected in small or moderate samples. The Breslow estimator, a shrinkage version of the Kaplan-Meier, nearly always has the smaller mean square error (MSE) whenever the truesurvival probabilityis at least 0.20, but has considerably larger MSE than the Kaplan-Meier estimator when the survivalprobability is near zero.     

On Energy Policy Models

Many energy models cannot be relied upon in forecasting or policy analysis. The quality of the data is often poor, and the theoretical underpinnings tend to be inadequate. These points are illustrated by example.     

A Nonstochastic Interpretation of Reported Significance Levels

Tests of significance are often made in situations where the standard assumptions underlying the probability calculations do not hold. As a result, the reported significance levels become difficult to interpret. This article sketches an alternative interpretation of a reported significance level, valid in considerable generality. This level locates the given data set within the spectrum of other data sets derived from the given one by an appropriate class of transformations. If the null hypothesis being tested holds, the derived data sets should be equivalent to the original one. Thus, a small reported significance level indicates an unusual data set. This development parallels that of randomization tests, but there is a crucial technical difference: our approach involves permuting observed residuals; the classical randomization approach involves permuting unobservable, or perhaps nonexistent, stochastic disturbance terms.     

A Case Study in Nonresponse: Plaintiff vs. California State Board of Equalization

In any sample survey, nonresponse bias is a potential issue. Even with a moderately high nonresponse rate, however, covariates can sometimes be used to show that the nonresponse bias is likely to be small. This note presents such an argument, which was used by the winning side in a tax case.     

A Bootstrap Stationarity Test for Predictive Regression Invalidity

In order for predictive regression tests to deliver asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that any predictability in the variable of interest is purely attributable to the predictors under test. Violation of this assumption by the omission of relevant persistent predictors renders the predictive regression invalid, and potentially also spurious, as both the finite sample and asymptotic size of the predictability tests can be significantly inflated. In response, we propose a predictive regression invalidity test based on a stationarity testing approach. To allow for an unknown degree of persistence in the putative predictors, and for heteroscedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We demonstrate the asymptotic validity of the proposed bootstrap test by proving that the limit distribution of the bootstrap statistic, conditional on the data, is the same as the limit null distribution of the statistic computed on the original data, conditional on the predictor. This corrects a long-standing error in the bootstrap literature whereby it is incorrectly argued that for strongly persistent regressors and test statistics akin to ours the validity of the fixed regressor bootstrap obtains through equivalence to an unconditional limit distribution. Our bootstrap results are therefore of interest in their own right and are likely to have applications beyond the present context. An illustration is given by reexamining the results relating to U.S. stock returns data in Campbell and Yogo (2006 Campbell, J. Y. and Yogo, M. (2006), “Efficient Tests of Stock Return Predictability,” Journal of Financial Economics, 81, 27–60.[Crossref], [Web of Science ®] , [Google Scholar]). Supplementary materials for this article are available online.     

An introduction to survival models: in honor of Ross Prentice

I review some key ideas and models in survival analysis with emphasis on modeling the effects of covariates on survival times. I focus on the proportional hazards model of Cox (J R Stat Soc B 34:187–220, 1972), its extensions and alternatives, including the accelerated life model. I briefly describe some models for competing risks data, multiple and repeated event-time data and multivariate survival data.     

Modifications of the Empirical Likelihood Interval Estimation with Improved Coverage Probabilities

The empirical likelihood (EL) technique has been well addressed in both the theoretical and applied literature in the context of powerful nonparametric statistical methods for testing and interval estimations. A nonparametric version of Wilks theorem (Wilks, 1938 Wilks , S. S. ( 1938 ). The large-sample distribution of the likelihood ratio for testing composite hypotheses . Annals of Mathematical Statistics 9 : 60 – 62 .[Crossref] , [Google Scholar]) can usually provide an asymptotic evaluation of the Type I error of EL ratio-type tests. In this article, we examine the performance of this asymptotic result when the EL is based on finite samples that are from various distributions. In the context of the Type I error control, we show that the classical EL procedure and the Student's t-test have asymptotically a similar structure. Thus, we conclude that modifications of t-type tests can be adopted to improve the EL ratio test. We propose the application of the Chen (1995 Chen , L. ( 1995 ). Testing the mean of skewed distributions . Journal of the American Statistical Association 90 : 767 – 772 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) t-test modification to the EL ratio test. We display that the Chen approach leads to a location change of observed data whereas the classical Bartlett method is known to be a scale correction of the data distribution. Finally, we modify the EL ratio test via both the Chen and Bartlett corrections. We support our argument with theoretical proofs as well as a Monte Carlo study. A real data example studies the proposed approach in practice.