Catálogo de publicaciones - libros

The bivariate exponential conditionals (BEC) distribution here is proposed as a probability model for accelerated life testing. For the conditional experiments, the exponentiality of its conditionals, nonpositivity of its correlation, and nonlinearity of its regressions along with its amenability to development of elegant statistical inference procedures, provide sufficient motivation. It is also shown that this model enhances derivation and statistical inference for unconditional reliability when random stress is also envisaged in the experiments, as in many real-life scenarios.

This chapter deals with the problem of local sensitivity analysis, that is, how sensitive the results of a statistical analysis are to a change in the data. A closed formula for the calculation of local sensitivities in optimization problems is applied to some optimization problems in statistics, including regression, maximum likelihood, and other situations involving ordered and data constrained parameters. In addition, a general method for evaluating the sensitivities for the method of moments is obtained. The methods are illustrated with several examples.

The t -distribution is a very usual distribution for several test statistics because a normal distribution is frequently assumed as underlying model. Even in some tests based on robust statistics, such as the test based on the sample trimmed mean, a t -distribution is used as distribution for the standardized sample trimmed mean if the underlying model is normal. Nevertheless, it is necessary to have a deeper understanding of the behaviour of these kind of tests and the computations of their key elements, such as the p -value and the critical value, with small samples, when the underlying model is close but different from the normal distribution. In this paper, we obtain good analytic approximations, with small samples, for the p -value and the critical value of a t -test (i.e., a test with a t -distribution for the test statistic under a normal model), studying its behaviour when the underlying distribution is close but different from the normal model. We conclude the paper with a discussion on some robustness properties of t -tests.

The purpose of the paper is to attract attention to the chi-square goodness-of-fit test computation employing the SAS System possibilities. The results of the analysis based on the chi-square goodness-of-fit test application prove that the limit value for the theoretical expectations should be taken into consideration while computing and interpreting the chi-square test results. A computational procedure should be analyzed. Typical examples including analysis of the actual data and modeled sample of the generated values have been considered, and comparative analyses of the output results have been carried out. Suggested additional options in regard to possibilities concerning the chisquare goodness-of-fit test application serve for increasing the reliability of the interpretation of the output results.

The Bayesian analysis of the variable selection problem in linear regression when using objective priors needs some form of encompassing the class of all submodels of the full linear model as they are nonnested models. After we provide a nested setting, objective intrinsic priors suitable for computing model posterior probabilities, on which the selection is based, can be derived. The way of encompassing the models is not unique and there is no clear indications for the optimal way. Typically, the class of linear models are encompassed into the full model. In this paper, we explore a new way of encompassing the class of linear models that consequently produces a new method for variable selection. This method seems to have some advantages with respect to the usual one. Specific intrinsic priors and model posterior probabilities are provided along with some of their main properties. Comparisons are made with R ^2 and adjusted R ^2, along with other frequentist methods for variable selection as lasso . Some illustrations on simulated and real data are provided.

Let Y and Z be two random vectors with joint density f(y, z |θ), where θ∈Θ is an unknown parameter vector, and consider predicting Z based on y , the observed value of Y . We investigate Bayesian and decision-theoretic approaches to this problem, taking into account the loss function and the prior distribution of θ. Exploring connections between statistical prediction and decision theory, we find that a prediction problem can be reduced to a standard decision theory problem if the induced loss function is allowed to depend on the observed data y in addition to the unknown parameter θ and the decision d . In general, the predictive posterior density f(z | y ) may not contain all information necessary for obtaining optimum predictions, but the posterior density f (θ| y ) is adequate for that purpose. Some admissibility results are also discussed.

In this chapter, we consider 2× k contingency tables and derive a new family of test statistics for detecting positive dependence in them. The family of test statistics introduced here is based on the φ-divergence measures of which the likelihood ratio test is a special case.

This chapter compares models for dimension reduction in time series and tests of the dimension of the dynamic structure. We consider both stationary and nonstationary time series and discuss principal components, canonical analysis, scalar component models, reduced rank models, and factor models. The unifying view of canonical correlation analysis between the present and past values of the series is emphasized. Then, we review some of the tests based on canonical correlation analysis to find the dimension of the dynamic relationship among the time series. Finally, the procedures are compared through a real data example.

The hat problem arose in the context of computational complexity. It started as a puzzle, but the problem has been found to have connections with coding theory and has reached the research frontier of mathematics, statistics and computer science. In this article, some variations of the hat problem are presented along with their solutions. An application is indicated.