Kullback–Leibler information of a censored variable and its applications

In this paper, we study the Kullback–Leibler (KL) information of a censored variable, which we will simply call it censored KL information. The censored KL information is shown to have the necessary monotonicity property in addition to inherent properties of nonnegativity and characterization. We also present a representation of the censored KL information in terms of the relative risk and study its relation with the Fisher information in censored data. Finally, we evaluate the estimated censored KL information as a goodness-of-fit test statistic.     

On second-order improved estimation of a gamma scale parameter

This paper concludes our comprehensive study on point estimation of model parameters of a gamma distribution from a second-order decision theoretic point of view. It should be noted that efficient estimation of gamma model parameters for samples ‘not large’ is a challenging task since the exact sampling distributions of the maximum likelihood estimators and its variants are not known. Estimation of a gamma scale parameter has received less attention from the earlier researchers compared to shape parameter estimation. What we have observed here is that improved estimation of the shape parameter does not necessarily lead to improved scale estimation if a natural moment condition (which is also the maximum likelihood restriction) is satisfied. Therefore, this work deals with the gamma scale parameter estimation as a separate new problem, not as a by-product of the shape parameter estimation, and studies several estimators in terms of second-order risk.     

Exact Likelihood Equations for Autoregression Models with Multivariate Elliptically Contoured Distributions

Abstract

The multivariate elliptically contoured distributions provide a viable framework for modeling time-series data. It includes the multivariate normal, power exponential, t, and Cauchy distributions as special cases. For multivariate elliptically contoured autoregressive models, we derive the exact likelihood equations for the model parameters. They are closely related to the Yule-Walker equations and involve simple function of the data. The maximum likelihood estimators are obtained by alternately solving two linear systems and illustrated using the simulation data.     

A Likelihood-Based Approximation to the Cumulative Distribution Function of the Noncentral t Distribution

Optimal designs for estimating the parameters and also the optimum factor combinations in multiresponse experiments have been considered by various authors. However, till date, in mixture experiments optimum designs have been studied only in the single response case. In this article, attempt has been made to investigate optimum designs for estimating optimum mixing proportions in a multiresponse mixture experiment.     

An Efficient Estimation for Switching Regression Models: A Monte Carlo Study

This article investigates an efficient estimation method for a class of switching regressions based on the characteristic function (CF). We show that with the exponential weighting function, the CF-based estimator can be achieved from minimizing a closed form distance measure. Due to the availability of the analytical structure of the asymptotic covariance, an iterative estimation procedure is developed involving the minimization of a precision measure of the asymptotic covariance matrix. Numerical examples are illustrated via a set of Monte Carlo experiments examining the implementation, finite sample property and the efficiency of the proposed estimator.     

The Speed of Adjustment of Warrant Prices to Changes in Stock Prices

This article reports on work designed to measure the time required for a change in a stock's price to be fully reflected in the price of a warrant on that stock. The method employed to measure the adjustment speed is the bivariate transfer function technique of Box and Jenkins. An interesting aspect of the study is the use of trade-by-trade data for measuring stock and warrant returns. The evidence presented here suggests that warrant prices adjust quickly to changes in stock prices. In addition, evidence concerning the ability of the estimated models to forecast warrant prices is presented.     

Normalized Quadratic Systems of Consumer Demand Functions

Empirically estimated demand systems frequently fail to satisfy the appropriate theoretical curvature conditions. We propose and estimate two demand systems for which these conditions can be imposed globally; the first is derived from a normalized quadratic reciprocal indirect utility function and the second is derived from a normalized quadratic expenditure function. The former is flexible if there are no restrictions on its free parameters, but loses flexibility if the curvature conditions need to be imposed. The latter is flexible, in the class of functions satisfying local money metric scaling, even if the curvature conditions need to be imposed.     

Diagnostic tools in generalized Weibull linear regression models

We propose some statistical tools for diagnosing the class of generalized Weibull linear regression models [A.A. Prudente and G.M. Cordeiro, Generalized Weibull linear models, Comm. Statist. Theory Methods 39 (2010), pp. 3739–3755]. This class of models is an alternative means of analysing positive, continuous and skewed data and, due to its statistical properties, is very competitive with gamma regression models. First, we show that the Weibull model induces ma-ximum likelihood estimators asymptotically more efficient than the gamma model. Standardized residuals are defined, and their statistical properties are examined empirically. Some measures are derived based on the case-deletion model, including the generalized Cook's distance and measures for identifying influential observations on partial F-tests. The results of a simulation study conducted to assess behaviour of the global influence approach are also presented. Further, we perform a local influence analysis under the case-weights, response and explanatory variables perturbation schemes. The Weibull, gamma and other Weibull-type regression models are fitted into three data sets to illustrate the proposed diagnostic tools. Statistical analyses indicate that the Weibull model fitted into these data yields better fits than other common alternative models.     

Powers of Discrete Goodness-of-Fit Test Statistics for a Uniform Null Against a Selection of Alternative Distributions

The comparative powers of six discrete goodness-of-fit test statistics for a uniform null distribution against a variety of fully specified alternative distributions are discussed. The results suggest that the test statistics based on the empirical distribution function for ordinal data (Kolmogorov–Smirnov, Cramér–von Mises, and Anderson–Darling) are generally more powerful for trend alternative distributions. The test statistics for nominal (Pearson's chi-square and the nominal Kolmogorov–Smirnov) and circular data (Watson's test statistic) are shown to be generally more powerful for the investigated triangular (∨), flat (or platykurtic type), sharp (or leptokurtic type), and bimodal alternative distributions.