Nonparametric Estimation of the Stationary Distribution of a Discrete-Time Semi-Markov ProcessGeorgiadis, Stylianos; Limnios, Nikolaos
doi: 10.1080/03610926.2013.768666pmid: N/A
In this article, we consider a discrete-time semi-Markov process with finite state space and an observation censored at an arbitrary fixed time. Some intermediate results concerning the empirical estimation of the mean recurrence times of the embedded Markov process and the mean sojourn times of the semi-Markov process are given. We study two nonparametric estimators for the stationary distribution of the semi-Markov process and examine their asymptotic properties, such as strong consistency and asymptotic normality, as the length of the observation tends to infinity. Finally, a numerical application is presented to illustrate the comparison of the two estimators.
Comparison of Frailty Models for Acute Leukemia Data under Gompertz Baseline DistributionHanagal, David D.; Sharma, Richa
doi: 10.1080/03610926.2013.769600pmid: N/A
In this article, we consider two different shared frailty regression models under the assumption of Gompertz as baseline distribution. Mostly assumption of gamma distribution is considered for frailty distribution. To compare the results with gamma frailty model, we consider the inverse Gaussian shared frailty model also. We compare these two models to a real life bivariate survival data set of acute leukemia remission times (Freireich et al., 1963). Analysis is performed using Markov Chain Monte Carlo methods. Model comparison is made using Bayesian model selection criterion and a well-fitted model is suggested for the acute leukemia data.
Analysis of Bivariate Survival Data using Shared Inverse Gaussian Frailty ModelHanagal, David D.; Sharma, Richa
doi: 10.1080/03610926.2013.768663pmid: N/A
In this article, we consider shared frailty model with inverse Gaussian distribution as frailty distribution and log-logistic distribution (LLD) as baseline distribution for bivariate survival times. We fit this model to three real-life bivariate survival data sets. The problem of analyzing and estimating parameters of shared inverse Gaussian frailty is the interest of this article and then compare the results with shared gamma frailty model under the same baseline for considered three data sets. Data are analyzed using Bayesian approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same group. The variance component estimation provides the estimated dispersion of the random effects. We carried out a test for frailty (or heterogeneity) using Bayes factor. Model comparison is made using information criteria and Bayes factor. We observed that the shared inverse Gaussian frailty model with LLD as baseline is the better fit for all three bivariate data sets.
Tests of Covariance Matrices for High Dimensional Multivariate Data Under Non NormalityAhmad, M. Rauf; Rosen, Dietrich Von
doi: 10.1080/03610926.2013.770533pmid: N/A
Ahmad and von Rosen (2014) presented test statistics for sphericity and identity of the covariance matrix of a multivariate normal distribution when the dimension, p, exceeds the sample size, n. In this note, we show that their statistics are robust to normality assumption, when normality is replaced with certain mild assumptions on the traces of the covariance matrix. Under such assumptions, the test statistics are shown to follow the same asymptotic normal distribution as under normality for large p, also when p > >n. The asymptotic normality is proved using the theory of U-statistics, and is based on very general conditions, particularly avoiding any relationship between n and p.
A Lasso-type Robust Variable Selection for Time-Course Microarray DataKim, Ji Young
doi: 10.1080/03610926.2013.770531pmid: N/A
Lasso has been widely used for variable selection because of its sparsity, and a number of its extensions have been developed. In this article, we propose a robust variant of Lasso for the time-course multivariate response, and develop an algorithm which transforms the optimization into a sequence of ridge regressions. The proposed method enables us to effectively handle multivariate responses and employs a basis representation of the regression parameters to reduce the dimensionality. We assess the proposed method through simulation and apply it to the microarray data.
Generalized Inverse Gamma Distribution and its Application in ReliabilityMead, M. E.
doi: 10.1080/03610926.2013.768667pmid: N/A
In this article, we introduce a new reliability model of inverse gamma distribution referred to as the generalized inverse gamma distribution (GIG). A generalization of inverse gamma distribution is defined based on the exact form of generalized gamma function of Kobayashi (1991). This function is useful in many problems of diffraction theory and corrosion problems in new machines. The new distribution has a number of lifetime special sub-models. For this model, some of its statistical properties are studied. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. We also demonstrate the usefulness of this distribution on a real data set.
Efficient Penalized Estimation for Linear Regression ModelMao, Guangyu
doi: 10.1080/03610926.2012.763094pmid: N/A
This paper develops new penalized estimation for linear regression model. We prove that the new method, which is referred to as efficient penalized estimation, is selection consistent, and more asymptotically efficient than the original one. Besides, we construct a new selector called efficient BIC Selector to tune the regularization parameter in the new estimation, which is shown to be consistent. Our simulation results suggest that the new method may bring significant improvement relative to the original penalized estimation. In addition, we employ a real data set to illustrate the application of the efficient penalized estimation.