Posterior analysis,prediction and reliability in three-parameter weibull distributions

The paper develops Bayesian analysis in the context of samples from three-parameter Weibull distributions and shows how to tackle the problems of prediction and estimation of reliability curves. As Johnson, Kotz and Balakrishnan ( 1994 ) mentioned, the prediction problems for the three-parameter Weibull model seem to be unresolved and is certainly worth looking into (p.671). Posterior analysis organized around Gibbs sampling is shown to perform well. An application to stock returns is used to illustrate the potential of the approach.     

Modified ridge analyses under nonstandard

A well-known procedure for the optimization of a second-degree response function over a spherical region of interest is that of ridge analysis. Khuri and Myers (1979) introduced a modification of this procedure by incorporating a certain constraint on the prediction variance. Both procedures, however, assume that the response variable has a constant variance throughtout the experimental region. In the present article, we consider two extensions to Khuri and Myers modifioed ridge analysis. The first extension relaxes the constant variance assumption. In the second extension. generalised linear models are used instead of the trasitional linear model. which are commenly used in responce variables that are not necessaily continusly distribution, including these have discreate distributions, Two examples are presented to illustrate the implementation of the proposed extensions.     

Regression Properties for Asymmetric Generalized Scale Mixtures of Multivariate Gaussian Variables

Analytical properties of regression and the variance–covariance matrix of asymmetric generalized scale mixture of multivariate Gaussian variables are presented. The analysis includes an in-depth analytical investigation of the first two conditional moments of the mixing variable. Exact computable expressions for the prediction and the conditional variance are presented for the generalized hyperbolic distribution using the inversion theorem for Fourier transforms. An application to financial log returns is demonstrated via the classical Euler approximation. The methodology is illustrated by analyzing the regression of intraday log returns for CISCO against the corresponding data from S&P 500.     

Likelihood-Based Inference for Multivariate Skew-Normal Regression Models

In this article, we present EM algorithms for performing maximum likelihood estimation for three multivariate skew-normal regression models of considerable practical interest. We also consider the restricted estimation of the parameters of certain important special cases of two models. The methodology developed is applied in the analysis of longitudinal data on dental plaque and cholesterol levels.     

Convergence of Discount Time Series Dynamic Linear Models

This article studies the limiting behavior of multiple discount time series dynamic linear models (TSDLMs). It is shown that, under mild conditions, all discount TSDLMs converge to the constant (time-invariant) TSDLM. In particular, the limiting posterior precision matrix of the superposition of multiple discount TSDLMs is explored. For non seasonal models, the elements of the limiting posterior precision of the states are given in a recurrence relationship, while for seasonal models the solution of a linear system provides the elements of the respective limiting precision matrix. The proposed methodology uses canonical Jordan forms and it is illustrated with a detailed example of simulated data featuring both trend and seasonal time series.     

Mixed Graphical Model Selection Using Holm's Procedure

The problem of selecting a graphical model is considered as a performing simultaneously multiple tests. The control of the overall Type I error on the selected graph is done using the so famous Holm's procedure. We prove that when we use a consistent edge exclusion test the selected graph is asymptotically equal to the true graph with probability at least equal to a fixed level 1 ? α. This method is then used for the selection of mixed concentration graph models by performing the χ²-edge exclusion test. We also apply the method to two classical examples and to simulated data. We compare the overall error of the selected model with the one obtained using the stepwise method. We establish that the control is better when we use the Holm's procedure.     

Testing Symmetry of the Error Distribution in Nonlinear Heteroscedastic Models

Using the empirical characteristic function, we derive a Cramér-von Mises test for symmetry of the error distribution in a class of nonlinear parametric heteroscedastic models. We study the convergence of the residual-based empirical distribution function. We establish a functional limit theorem for an empirical process of residuals, and investigate the asymptotic null distribution function of our test statistic. A simulation experiment is conducted to evaluate small-sample performances of our test.     

Nonparametric Trend Estimation for Periodic Autoregressive Time Series

A periodically stationary time series has seasonal variances. A local linear trend estimation is proposed to accommodate unequal variances. A comparison of this proposed estimator with the estimator commonly used for a stationary time series is provided. The optimal bandwidth selection for this new trend estimator is discussed.     

Estimating the order of moving average models: the max X2 method

The max X² technique for estimating rhe order of autoregressive processes (McClave (1976)) is extended to moving average models. The autöregressive-moving average duality is exploited by using the inverse autocorrelation function and the subset autoregression algorithm. The technique is demonstrated via simulations, and is applied to Box and Jenkins (1970) Series A.