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     

A class of semiparametric transormation frailty models with application to estimating treatment effects and heterogenity in aids clinical traials

Muitivariate failure time data are common in medical research; com¬monly used statistical models for such correlated failure-time data include frailty and marginal models. Both types of models most often assume pro¬portional hazards (Cox, 1972); but the Cox model may not fit the data well This article presents a class of linear transformation frailty models that in¬cludes, as a special case, the proportional hazards model with frailty. We then propose approximate procedures to derive the best linear unbiased es¬timates and predictors of the regression parameters and frailties. We apply the proposed methods to analyze results of a clinical trial of different dose levels of didansine (ddl) among HIV-infected patients who were intolerant of zidovudine (ZDV). These methods yield estimates of treatment effects and of frailties corresponding to patient groups defined by clinical history prior to entry into the trial.     

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.     

Clustering large number of extragalactic spectra of galaxies and quasars through canopies

Abstract

Cluster analysis is the distribution of objects into different groups or more precisely the partitioning of a data set into subsets (clusters) so that the data in subsets share some common trait according to some distance measure. Unlike classification, in clustering one has to first decide the optimum number of clusters and then assign the objects into different clusters. Solution of such problems for a large number of high dimensional data points is quite complicated and most of the existing algorithms will not perform properly. In the present work a new clustering technique applicable to large data set has been used to cluster the spectra of 702248 galaxies and quasars having 1,540 points in wavelength range imposed by the instrument. The proposed technique has successfully discovered five clusters from this 702,248X1,540 data matrix.     

A model with long-term survivors: negative binomial Birnbaum-Saunders

Abstract

We propose a cure rate survival model by assuming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to the event of interest has the Birnbaum-Saunders distribution. Further, the new model includes as special cases some well-known cure rate models published recently. We consider a frequentist analysis for parameter estimation of the negative binomial Birnbaum-Saunders model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We illustrate the usefulness of the proposed model in the analysis of a real data set from the medical area.     

Estimation of the covariance matrix with two-step monotone missing data

Abstract

We suggest shrinkage based technique for estimating covariance matrix in the high-dimensional normal model with missing data. Our approach is based on the monotone missing scheme assumption, meaning that missing values patterns occur completely at random. Our asymptotic framework allows the dimensionality p grow to infinity together with the sample size, N, and extends the methodology of Ledoit and Wolf (2004) Ledoit, O., Wolf, M. (2004). A well-conditioned estimator for large dimensional covariance matrices. J. Multivariate Anal. 88:365–411.[Crossref], [Web of Science ®] , [Google Scholar] to the case of two-step monotone missing data. Two new shrinkage-type estimators are derived and their dominance properties over the Ledoit and Wolf (2004) Ledoit, O., Wolf, M. (2004). A well-conditioned estimator for large dimensional covariance matrices. J. Multivariate Anal. 88:365–411.[Crossref], [Web of Science ®] , [Google Scholar] estimator are shown under the expected quadratic loss. We perform a simulation study and conclude that the proposed estimators are successful for a range of missing data scenarios.     

Bimodal skew-symmetric normal distribution

ABSTRACT

We introduce a new parsimonious bimodal distribution, referred to as the bimodal skew-symmetric Normal (BSSN) distribution, which is potentially effective in capturing bimodality, excess kurtosis, and skewness. Explicit expressions for the moment-generating function, mean, variance, skewness, and excess kurtosis were derived. The shape properties of the proposed distribution were investigated in regard to skewness, kurtosis, and bimodality. Maximum likelihood estimation was considered and an expression for the observed information matrix was provided. Illustrative examples using medical and financial data as well as simulated data from a mixture of normal distributions were worked.     

A proportional hazards model for the analysis of doubly censored competing risks data

ABSTRACT

Competing risks data are common in medical research in which lifetime of individuals can be classified in terms of causes of failure. In survival or reliability studies, it is common that the patients (objects) are subjected to both left censoring and right censoring, which is refereed as double censoring. The analysis of doubly censored competing risks data in presence of covariates is the objective of this study. We propose a proportional hazards model for the analysis of doubly censored competing risks data, using the hazard rate functions of Gray (1988 Gray, R.J. (1988). A class of k-sample tests for comparing the cumulative incidence of a competing risk. Ann. Statist. 16:1141–1154.[Crossref], [Web of Science ®] , [Google Scholar]), while focusing upon one major cause of failure. We derive estimators for regression parameter vector and cumulative baseline cause specific hazard rate function. Asymptotic properties of the estimators are discussed. A simulation study is conducted to assess the finite sample behavior of the proposed estimators. We illustrate the method using a real life doubly censored competing risks data.     

Recursive kernel estimate of the conditional quantile for functional ergodic data

ABSTRACT

In this article, we study the recursive kernel estimator of the conditional quantile of a scalar response variable Y given a random variable (rv) X taking values in a semi-metric space. Two estimators are considered. While the first one is given by inverting the double-kernel estimate of the conditional distribution function, the second estimator is obtained by using the robust approach. We establish the almost complete consistency of these estimates when the observations are sampled from a functional ergodic process. Finally, a simulation study is carried out to illustrate the finite sample performance of these estimators.     

Modeling of covariance structures of random effects and random errors in linear mixed models

Abstract

In this paper, we discuss how to model the mean and covariancestructures in linear mixed models (LMMs) simultaneously. We propose a data-driven method to modelcovariance structures of the random effects and random errors in the LMMs. Parameter estimation in the mean and covariances is considered by using EM algorithm, and standard errors of the parameter estimates are calculated through Louis’ (1982 Louis, T.A. (1982). Finding observed information using the EM algorithm. J. Royal Stat. Soc. B 44:98–130. [Google Scholar]) information principle. Kenward’s (1987 Kenward, M.G. (1987). A method for comparing profiles of repeated measurements. Appl. Stat. 36:296–308.[Crossref], [Web of Science ®] , [Google Scholar]) cattle data sets are analyzed for illustration,and comparison to the literature work is made through simulation studies. Our numerical analysis confirms the superiority of the proposed method to existing approaches in terms of Akaike information criterion.