Search

A special source of difficulty in the statistical analysis is the possibility that some subjects may not have a complete observation of the response variable. Such incomplete observation of the response variable is called censoring. Censorship can occur for a variety of reasons, including limitations of measurement equipment, design of the experiment, and non-occurrence of the event of interest until the end of the study. In the presence of censoring, the dependence of the response variable on the explanatory variables can be explored through regression analysis. In this paper, we propose to examine the censorship problem in context of the class of asymmetric, i.e., we have proposed a linear regression model with censored responses based on skew scale mixtures of normal distributions. We develop a Monte Carlo EM (MCEM) algorithm to perform maximum likelihood inference of the parameters in the proposed linear censored regression models with skew scale mixtures of normal distributions. The MCEM algorithm has been discussed with an emphasis on the skew-normal, skew Student-t-normal, skew-slash and skew-contaminated normal distributions. To examine the performance of the proposed method, we present some simulation studies and analyze a real dataset. [ABSTRACT FROM AUTHOR]

This article presents the Markov chain Monte Carlo (MCMC) statistical technique. The impact on the discipline is deep and durable, because these methods have opened new horizons in the scale of the problems that one can deal with, thus enhancing the position of statistics in most applied fields. The MCMC revolution has in particular boosted Bayesian statistics to new heights by providing a virtually universal tool for dealing with integration problems. This can be seen in the explosion of papers dealing with complex models, hierarchical modelings, nonparametric Bayesian estimation, and spatial statistics. This trend has also created new synergies with mathematicians and probabilists, as well as econometricians, engineers, ecologists, astronomers, and others, for theoretical requests and practical implications of MCMC techniques. The main factor in the success of MCMC algorithms is that they can be implemented with little effort in a large variety of settings. This is obviously true of the Gibbs sampler, which provided some conditional distributions are available as shown by the BUGS software. We mentioned BUGS and CODA as existing software dedicated to MCMC algorithms but much remains to be done before MCMC becomes part of commercial software.

The article presents a rejoinder to comments made on their article "A Statistical Model for Position Emission Tomography." Being a very active, multidisciplinary, field of research, it is hard to keep track of who suggested what and in what context, so in attempting to answer scholar Donald B. Rubin's question we are likely to overlook some contributors. The first use of a pixel model for an organ appeared in scholar G.N. Hounsfield's original development of X-ray computerized tomography. In 1978 scholars gave a short account of this early development in the field, including images produced using Hounsfield's algorithms. The fact that the physics of Position Emission Tomography (PET) is different, and inherently more stochastic, than that of X-ray transmission tomography has been common knowledge. Realizing that the additional randomness of PET calls for a more statistical way of thinking, scholars A.J. Rockmore and A.Macovski suggested estimating the emission density in PET, using a maximum-likelihood approach. Their paper fell short of identifying the connection between the tube count and the emission density. This omission on their part is probably a result of being unaware of the development of statistical methods for incomplete data.

This paper presents a piecewise regression method for continuous models containing max or min operators, or both. This method does not require knowledge of the zone in which a shift in regimes occurs. Moreover, it allows the application of analytical derivatives to maximize the likelihood function, which greatly simplifies the estimation of the model. The method proposed exhibits fast convergence and can be used for an arbitrary number of regimes and variables. [ABSTRACT FROM AUTHOR]

In this article, the author presents his views on a paper by David Oakes on statistical analysis. Oakes's paper demonstrates the impossibility of constructing a joint distribution for an infinite sequence of events that could be guaranteed to have the calibration property for any possible sequence of outcomes. Imagine a statistician attempting to model the sequence of events, which she observes sequentially. She might start off with a simple Bernoulli model. For any currently adopted model, she could form estimates of its parameters based on current data and use these to provide a forecast probability for the next event. The author argues that any such statistical analysis must be regarded as empirically invalidated unless its infinite sequence of forecasts is calibrated. Consequently, Oakes's result shows that, no matter how cleverly one tries to tune model-building, testing, estimation procedures, and so on, there is no guarantee of success. There will always be data sequences that will be impossible to track. It is further shown that, for any data sequence, any two computable distributions that are both suitably calibrated must give forecasts whose differences tend to zero, so that calibrated forecasts are "asymptotically unique" and so, in a sense, objectively valid.

Statisticians like Good and Gaskins have given to bump-hunters an inventive approach that uses the special structure of their maximum penalized-likelihood, MPL procedure. This article demonstrates the usefulness of nonparametric density-estimation techniques for unearthing features such as modes in the body of the data without concern for possible tail pathologies. With medical data the estimation and comparison of modes has proved more revealing than simpler tests. For example, the discovery of bimodal bivariate density functions in lipid data has led to clarification of the roles of certain cardiovascular risk factors. Investigators interested in the statistical significance of modes should also find Good and Gaskins's paper useful. The important algorithms presented in this paper deal with optimization of the smoothness or variance-bias trade-off of the density estimate and with removal of potential bumps by surgery.