Maximum likelihood estimation of the bimodal failure rate for censored and tied observations

DIMITROV, RACHEV and YAKOVLEV ( 1985 ) have obtained the isotonic maximum likelihood estimator for the bimodal failure rate function. The authors considered only the complete failure time data. The generalization of this estimator for the case of censored and tied observations is now proposed.     

Positive False Discovery Rate Estimate in Step-Wise Variable Selection

Selecting predictors to optimize the outcome prediction is an important statistical method. However, it usually ignores the false positives in the selected predictors. In this article, we advocate a conventional stepwise forward variable selection method based on the predicted residual sum of squares, and develop a positive false discovery rate (pFDR) estimate for the selected predictor subset, and a local pFDR estimate to prioritize the selected predictors. This pFDR estimate takes account of the existence of non null predictors, and is proved to be asymptotically conservative. In addition, we propose two views of a variable selection process: an overall and an individual test. An interesting feature of the overall test is that its power of selecting non null predictors increases with the proportion of non null predictors among all candidate predictors. Data analysis is illustrated with an example, in which genetic and clinical predictors were selected to predict the cholesterol level change after four months of tamoxifen treatment, and pFDR was estimated. Our method's performance is evaluated through statistical simulations.     

Robust Correlation Structure for Multivariate Failure Time Data

When incomplete repeated failure times are collected from a large number of independent individuals, interest is focused primarily on the consistent and efficient estimation of the effects of the associated covariates on the failure times. Since repeated failure times are likely to be correlated, it is important to exploit the correlation structure of the failure data in order to obtain such consistent and efficient estimates. However, it may be difficult to specify an appropriate correlation structure for a real life data set. We propose a robust correlation structure that can be used irrespective of the true correlation structure. This structure is used in constructing an estimating equation for the hazard ratio parameter, under the assumption that the number of repeated failure times for an individual is random. The consistency and efficiency of the estimates is examined through a simulation study, where we consider failure times that marginally follow an exponential distribution and a Poisson distribution is assumed for the random number of repeated failure times. We conclude by using the proposed method to analyze a bladder cancer dataset.     

Identification of Influential Cases in Kernel Fisher Discriminant Analysis

We study the influence of a single data case on the results of a statistical analysis. This problem has been addressed in several articles for linear discriminant analysis (LDA). Kernel Fisher discriminant analysis (KFDA) is a kernel based extension of LDA. In this article, we study the effect of atypical data points on KFDA and develop criteria for identification of cases having a detrimental effect on the classification performance of the KFDA classifier. We find that the criteria are successful in identifying cases whose omission from the training data prior to obtaining the KFDA classifier results in reduced error rates.     

A Distribution-Free Control Chart Based on Order Statistics

In this article, we introduce a new distribution-free Shewhart-type control chart that takes into account the location of a single order statistic of the test sample (such as the median) as well as the number of observations in that test sample that lie between the control limits. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of the chart is that, due to its nonparametric nature, the false alarm rate and in-control run length distribution are the same for all continuous process distributions, and so will be naturally robust. Tables are provided for the implementation of the chart for some typical ARL values and false alarm rates. The empirical study carried out reveals that the new chart is preferable from a robustness point of view in comparison to a classical Shewhart-type chart and also the nonparametric chart of Chakraborti et al. (2004 Chakraborti , S. , van der Laan , P. , van de Wiel , M. A. ( 2004 ). A class of distribution-free control charts . J. Roy. Statist. Soc. Ser. C-Appl. Statist. 53 ( 3 ): 443 – 462 .[Web of Science ®] , [Google Scholar]).     

Reliability Properties of Systems with Two Exchangeable Log-Logistic Components

In this article, we study the reliability properties of systems under bivariate log-logistic model which comes out from a particular stress-strength analysis. For this model, we obtain basic reliability characteristics of series and parallel systems and investigate their properties. We also derive distribution and moments of cold standby system under the abovementioned exchangeable model.     

A New Generalized Exponential Geometric Distribution

In this article, another version of the generalized exponential geometric distribution different to that of Silva et al. (2010 Silva , R. B. , Barreto-Souza , W. , Cordeiro , G. M. ( 2010 ). A new distribution with decreasing, increasing and upside-down bathtub failure rate. Computat. Statist. Data Anal. 54: 935–944 . [Google Scholar]) is proposed. This new three-parameter lifetime distribution with decreasing, increasing, and bathtub failure rate function is created by compounding the generalized exponential distribution of Gupta and Kundu (1999 Gupta , R. D. , Kundu , D. ( 1999 ). Generalized exponential distributions . Austral. NZ J. Statist. 41 ( 2 ): 173 – 188 .[Crossref], [Web of Science ®] , [Google Scholar]) with a geometric distribution. Some basic distributional properties, moment-generating function, rth moment, and Rényi entropy of the new distribution are studied. The model parameters are estimated by the maximum likelihood method and the asymptotic distribution of estimators is discussed. Finally, an application of the new distribution is illustrated using the two real data sets.     

Convergence Rate of Wavelet Expansions of Gaussian Random Processes

This article characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.     

Bonferroni-type Plug-in Procedure Controlling Generalized Familywise Error Rate

Consider the multiple hypotheses testing problem controlling the generalized familywise error rate k-FWER, the probability of at least k false rejections. We propose a plug-in procedure based on the estimation of the number of true null hypotheses. Under the independence assumption of the p-values corresponding to the true null hypotheses, we first introduce the least favorable configuration (LFC) of k-FWER for Bonferroni-type plug-in procedure, then we construct a plug-in k-FWER-controlled procedure based on LFC. For dependent p-values, we establish the asymptotic k-FWER control under some mild conditions. Simulation studies suggest great improvement over generalized Bonferroni test and generalized Holm test.