Confidence Intervals for the Hyperparameters in Structural Models

This article deals with the bootstrap as an alternative method to construct confidence intervals for the hyperparameters of structural models. The bootstrap procedure considered is the classical nonparametric bootstrap in the residuals of the fitted model using a well-known approach. The performance of this procedure is empirically obtained through Monte Carlo simulations implemented in Ox. Asymptotic and percentile bootstrap confidence intervals for the hyperparameters are built and compared by means of the coverage percentages. The results are similar but the bootstrap procedure is better for small sample sizes. The methods are applied to a real time series and confidence intervals are built for the hyperparameters.     

Simulations of Some Doubly Stochastic Poisson Point Processes

Computer simulations of point processes are important either to verify the results of certain theoretical calculations that can be very awkward at times or to obtain practical results when these calculations become almost impossible. One of the most common methods for the simulation of nonstationary Poisson processes is random thinning. Its extension when the intensity becomes random (doubly stochastic Poisson processes) depends on the structure of this intensity. If the random density takes only discrete values, which is a common situation in many physical problems where quantum mechanics introduces discrete states, it is shown that the thinning method can be applied without error. We study in particular the case of binary density and present the kind of theoretical calculations that then become possible. The results of various experiments realized with data obtained by simulation show a fairly good agreement with the theoretical calculations.     

A multiparameter extension of two stage modified shrinkage estimator

A multiparameter extension is made to modified two stage shrinkage estimator proposed by Handa andKambo (1990), For aparticular class of shrinkage estimator, the local optimality of the extended modified estimator is shown over the two stage shrinkage estimator defined by Bhattacharya and Prakasa Rao(1990) in terms of quadratic loss.     

A robust process capability index

The existing process capability indices (PCI's) assume that the distribution of the process being investigated is normal. For non-normal distributions, PCI's become unreliable in that PCI's may indicate the process is capable when in fact it is not. In this paper, we propose a new index which can be applied to any distribution. The proposed indexC_f:, is directly related to the probability of non-conformance of the process. For a given random sample, the estimation of C_f boils down to estimating non-parametrically the tail probabilities of an unknown distribution. The approach discussed in this paper is based on the works by Pickands (1975) and Smith (1987). We also discuss the construction of bootstrap confidence intervals of C_f: based on the so-called accelerated bias correction method (BC _a:). Several simulations are carried out to demonstrate the flexibility and applicability of C_f:. Two real life data sets are analyzed using the proposed index.     

A variance shift model for detection of outliers in the linear mixed measurement error models

ABSTRACT

In this paper, we extend a variance shift model, previously considered in the linear mixed models, to the linear mixed measurement error models using the corrected likelihood of Nakamura (1990 Nakamura, T. (1990). Corrected score function for errors in variables models: methodology and application to generalized linear models. Biometrika 77:127–137.[Crossref], [Web of Science ®] , [Google Scholar]). This model assumes that a single outlier arises from an observation with inflated variance. We derive the score test and the analogue of the likelihood ratio test, to assess whether the ith observation has inflated variance. A parametric bootstrap procedure is implemented to obtain empirical distributions of the test statistics. Finally, results of a simulation study and an example of real data are presented to illustrate the performance of proposed tests.     

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.     

Combinatoric classification of multivariate normal variates

Consider classifying an n × I observation vector as coming from one of two multivariate normal distributions which differ both in mean vectors and covariance matrices. A class of dis-crimination rules based upon n independent univariate discrim-inate functions is developed yielding exact misclassification probabilities when the population parameters are known. An efficient search of this class to select the procedure with minimum expected misclassification is made by employing an algorithm of the implicit enumeration type used in integer programming. The procedure is applied to the classification of male twins as either monozygotic or dizygotic.