Akaike Information Criterion for Selecting Variables in the Nested Error Regression Model

The Akaike Information Criterion (AIC) is developed for selecting the variables of the nested error regression model where an unobservable random effect is present. Using the idea of decomposing the likelihood into two parts of “within” and “between” analysis of variance, we derive the AIC when the number of groups is large and the ratio of the variances of the random effects and the random errors is an unknown parameter. The proposed AIC is compared, using simulation, with Mallows' C _p , Akaike's AIC, and Sugiura's exact AIC. Based on the rates of selecting the true model, it is shown that the proposed AIC performs better.     

A General Model of Random Variation

A statistical distribution of a random variable is uniquely represented by its normal-based quantile function. For a symmetrical distribution it is S-shaped (for negative kurtosis) and inverted S-shaped (otherwise). As skewness departs from zero, the quantile function gradually transforms into a monotone convex function (positive skewness) or concave function (otherwise). Recently, a new general modeling platform has been introduced, response modeling methodology, which delivers good representation to monotone convex relationships due to its unique “continuous monotone convexity” property. In this article, this property is exploited to model the normal-based quantile function, and explored using a set of 27 distributions.     

An extension of the multivariate Chebyshev's inequality to a random vector with a singular covariance matrix

ABSTRACT

We extend Chebyshev's inequality to a random vector with a singular covariance matrix. Then we consider the case of a multivariate normal distribution for this generalization.     

ML and Bayes estimation in a two-phase tandem queue with a second optional service and random feedback

ABSTRACT

In this article, we consider a two-phase tandem queueing model with a second optional service and random feedback. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability α, feedback to the tail of the first queue with probability β if the service is not successful and leaves the system with probability 1 ? α ? β. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.     

Semiparametric quasi-likelihood estimation with missing data

Abstract

This article develops quasi-likelihood estimation for generalized varying coefficient partially linear models when the response is not always observable. This article considers two estimation methods and shows that under the assumption of selection on the observables the resulting estimators are asymptotically normal. As an application of these results this article proposes a new estimator for the average treatment effect parameter. A simulation study illustrates the finite sample properties of the proposed estimators.     

The Product-Limit Estimate as an Inverse-Probability-Weighted Average

Abstract

For randomly censored data, (Satten, G. A., Datta S. (2001 Satten, G. A. and Datta, S. 2001. The Kaplan–Meier estimator as an inverse-probability-of-censoring weighted average. Amer. Statist. Ass., 55: 207–210. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The Kaplan–Meier estimator as an inverse-probability-of-censoring weighted average. Amer. Statist. Ass. 55:207–210) showed that the Kaplan–Meier estimator (product-limit estimator (PLE)) can be expressed as an inverse-probability-weighted average. In this article, we consider the other two PLEs: the truncation PLE and the censoring-truncation PLE. For the data subject to left-truncation or both left-truncation and right-censoring, it is shown that these two PLEs can be expressed as inverse-probability-weighted averages.     

Wild Bootstrap of the Sample Mean in the Infinite Variance Case

It is well known that the standard independent, identically distributed (iid) bootstrap of the mean is inconsistent in a location model with infinite variance (α-stable) innovations. This occurs because the bootstrap distribution of a normalised sum of infinite variance random variables tends to a random distribution. Consistent bootstrap algorithms based on subsampling methods have been proposed but have the drawback that they deliver much wider confidence sets than those generated by the iid bootstrap owing to the fact that they eliminate the dependence of the bootstrap distribution on the sample extremes. In this paper we propose sufficient conditions that allow a simple modification of the bootstrap (Wu, 1986 Wu , C. F. J. ( 1986 ). Jackknife, bootstrap, and other resampling methods . Annals of Statistics 14 : 1261 – 1295 .[Crossref], [Web of Science ®] , [Google Scholar]) to be consistent (in a conditional sense) yet to also reproduce the narrower confidence sets of the iid bootstrap. Numerical results demonstrate that our proposed bootstrap method works very well in practice delivering coverage rates very close to the nominal level and significantly narrower confidence sets than other consistent methods.     

Out-of-Bag Estimation of the Optimal Hyperparameter in SubBag Ensemble Method

SubBag is a technique by combining bagging and random subspace methods to generate ensemble classifiers with good generalization capability. In practice, a hyperparameter K of SubBag—the number of randomly selected features to create each base classifier—should be specified beforehand. In this article, we propose to employ the out-of-bag instances to determine the optimal value of K in SubBag. The experiments conducted with some UCI real-world data sets show that the proposed method can make SubBag achieve the optimal performance in nearly all the considered cases. Meanwhile, it occupied less computational sources than cross validation procedure.     

Generalized RCINAR(p) Process with Signed Thinning Operator

We propose a new integer-valued time series process, called generalized pth-order random coefficient integer-valued autoregressive process with signed thinning operator. This kind of process is appropriate for modeling negative integer-valued time series; strict stationarity and ergodicity of the process are established. Estimators of the model's parameters are derived and their properties are studied via simulation. We apply our process to a real data example.