The Monte Carlo EM method for estimating multivariate tobit latent variable models

We propose a multivariate tobit (MT) latent variable model that is defined by a confirmatory factor analysis with covariates for analysing the mixed type data, which is inherently non-negative and sometimes has a large proportion of zeros. Some useful MT models are special cases of our proposed model. To obtain maximum likelihood estimates, we use the expectation maximum algorithm with its E-step via the Gibbs sampler made feasible by Monte Carlo simulation and its M-step greatly simplified by a sequence of conditional maximization. Standard errors are evaluated by inverting a Monte Carlo approximation of the information matrix using Louis's method. The methodology is illustrated with a simulation study and a real example.     

Retrospective Change Point Detection: From Parametric to Distribution Free Policies

The literature displays change point detection problems in the context of one of the key issues that belong to testing statistical hypotheses. The main focus in this article is to review recent retrospective change point policies and propose new relevant procedures. Commonly, applied quality control purposes have declared statements of the change point problems. Various biostatistical and engineering applications cause consideration of an extended form of the change point problem. In this article, we consider parametric and distribution free generalized change point detection policies, attending to different contexts of optimality and robustness of the procedures. We conducted a broad Monte Carlo study to compare various parametric and nonparametric tests, also investigating a sensitivity of the change point detection policies with respect to assumptions required for correct executions of the procedures. An example based on real biomarker measurements is provided to judge our conclusions.     

Estimation of Change Point in Generalized Variance Control Chart

In this study, using maximum likelihood estimation, a considerably effective change point model is proposed for the generalized variance control chart in which the required statistics are calculated with its distributional properties. The procedure, when used with generalized variance control charts, would be helpful for practitioners both controlling the multivariate process dispersion and detecting the time of the change in variance-covariance matrix of a process. The procedure starts after the chart issues a signal. Several structural changes for the variance-covariance matrix are considered and the precision and the accuracy of the proposed method is discussed.     

Estimation and Testing in Elliptical Functional Measurement Error Models

The purpose of this article is to investigate estimation and hypothesis testing by maximum likelihood and method of moments in functional models within the class of elliptical symmetric distributions. The main results encompass consistency and asymptotic normality of the method of moments estimators. Also, the asymptotic covariance matrix of the maximum likelihood estimator is derived, extending some existing results in elliptical distributions. A measure of asymptotic relative efficiency is reported. Wald-type statistics are considered and numerical results obtained by Monte Carlo simulation to investigate the performance of estimators and tests are provided for Student-t and contaminated normal distributions. An application to a real dataset is also included.     

Asymptotic properties of MLE for partially observed fractional diffusion system with dependent noises

The paper studies long time asymptotic properties of the maximum likelihood estimator (MLE) for the signal drift parameter in a partially observed fractional diffusion system with dependent noise. Using the method of weak convergence of likelihoods due to Ibragimov and Khasminskii [1981. Statistics of Random Processes. Springer, New-York], consistency, asymptotic normality and convergence of the moments are established for MLE. The proof is based on Laplace transform computations which was introduced in Brouste and Kleptsyna [2008. Asymptotic properties of MLE for partially observed fractional diffusion system, preprint].     

Upper Confidence Limits on Excess Risk for Quantitative Responses

The definition and observation of clear-cut adverse health effects for continuous (quantitative) responses, such as altered body weights or organ weights, are difficult propositions. Thus, methods of risk assessment commonly used for binary (quantal) toxic responses such as cancer are not directly applicable. In this paper, two methods for calculating upper confidence limits on excess risk for quantitative toxic effects are proposed, based on a particular definition of an adverse quantitative response. The methods are illustrated with data from a dose-response study, and their performance is evaluated with a Monte Carlo simulation study.     

Proportional Hazards in Information Security

Nonparametric methods can be used to analyze failure times and estimate probability distributions for failures of systems due to successful attacks on confidentiality, integrity, and availability in information security. However, such methods do not take full advantage of supplemental information regarding the configurations of systems in an information infrastructure that is usually also available. One approach, which does take advantage of such information, views the risks of systems failing from various causes as competing risks and determines the correlation coefficients of different treatments to system longevity. Since the times and causes of failure in such studies are usually uncorrelated, the hazards associated with each risk are proportional. By correlating system survival times to the use of specific design enhancements and security countermeasures, as well as to system exposure based on choice of operational functionality, guidance can be obtained for making investments in information security.     

Curved Exponential Family Models for Social Networks

Curved exponential family models are a useful generalization of exponential random graph models (ERGMs). In particular, models involving the alternating k-star, alternating k-triangle, and alternating k-twopath statistics of Snijders et al (2006) may be viewed as curved exponential family models. This article unifies recent material in the literature regarding curved exponential family models for networks in general and models involving these alternating statistics in particular. It also discusses the intuition behind rewriting the three alternating statistics in terms of the degree distribution and the recently introduced shared partner distributions. This intuition suggests a redefinition of the alternating k-star statistic. Finally, this article demonstrates the use of the statnet package in R for fitting models of this sort, comparing new results on an oft-studied network dataset with results found in the literature.     

SOME RESAMPLING PROCEDURES UNDER SYMMETRY

This paper investigates the properties of bootstrap and related methods assuming that the underlying distribution is symmetric but otherwise unknown. In particular it studies the percentile-t, nonparametric tilting and empirical likelihood and finds that the performance of percentile-t and non-parametric tilting methods can be improved by incorporating the symmetry into the resampling procedure. However, for symmetric empirical likelihood, the Bartlett correctability no longer holds, although use of bootstrap calibration restores the good coverage properties typically associated with Bartlett correction. This surprising result shows that Bartlett correctability is a very delicate property.     

Laplace approximations for censored linear regression models

We consider approximate Bayesian inference about scalar parameters of linear regression models with possible censoring. A second-order expansion of their Laplace posterior is seen to have a simple and intuitive form for logconcave error densities with nondecreasing hazard functions. The accuracy of the approximations is assessed for normal and Gumbel errors when the number of regressors increases with sample size. Perturbations of the prior and the likelihood are seen to be easily accommodated within our framework. Links with the work of DiCiccio et al. (1990) and Viveros and Sprott (1987) extend the applicability of our results to conditional frequentist inference based on likelihood-ratio statistics.