Improved estimation in a general multivariate elliptical model (original) (raw)
Related papers
Adjusted Likelihood Inference in an Elliptical Multivariate Errors-in-Variables Model
Communications in Statistics - Theory and Methods, 2014
In this paper we obtain an adjusted version of the likelihood ratio test for errors-in-variables multivariate linear regression models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as a special case. We derive a modified likelihood ratio statistic that follows a chi-squared distribution with a high degree of accuracy. Our results generalize those in Melo & Ferrari (Advances in Statistical Analysis, 2010, 94, 75-87) by allowing the parameter of interest to be vector-valued in the multivariate errors-in-variables model. We report a simulation study which shows that the proposed test displays superior finite sample behavior relative to the standard likelihood ratio test.
Local influence in multivariate elliptical linear regression models
Linear Algebra and its Applications, 2002
Local influence is a method of sensitivity analysis for assessing the influence of small perturbations in a general statistical model. In the present paper, this popular method is applied to multivariate elliptical linear regression models. Several perturbation schemes, including perturbations in case-weights, explanatory variables and response variables are considered. The observed information matrix under the postulated model and Delta matrices under the corresponding perturbed models are derived. An assessment of local influence is made.
Statistical Methodology, 2014
In this paper we discuss estimation and diagnostic procedures in elliptical multivariate regression models with equicorrelated random errors. Two procedures are proposed for the parameter estimation and the local influence curvatures are derived under some usual perturbation schemes to assess the sensitivity of the maximum likelihood estimates (MLEs). Two motivating examples preliminarily analyzed under normal errors are reanalyzed considering appropriate elliptical distributions. The local influence approach is used to compare the sensitivity of the model estimates.
Bias correction for a class of multivariate nonlinear regression models
Statistics & Probability Letters, 1997
In this paper, we derive general formulae for second-order biases of maximum likelihood estimates which can be applied to a wide class of multivariate nonlinear regression models. The class of models we consider is very rich and includes a number of commonly used models in econometrics and statistics as special cases, such as the univariate nonlinear model and the multivariate linear model. Our formulae are easy to compute and give bias-corrected maximum likelihood estimates to order n -I, where n is the sample size, by means of supplementary weighted linear regressions. They are also simple enough to be used algebraically in order to obtain closed-form expressions in special cases. (~) 1997 Elsevier Science B.V.
Envelopes for elliptical multivariate linear regression
Statistica Sinica
We incorporate the idea of reduced rank envelope [7] to elliptical multivariate linear regres-4 sion to improve the efficiency of estimation. The reduced rank envelope model takes advantage 5 of both reduced rank regression and envelope model, and is an efficient estimation technique in 6 multivariate linear regression. However, it uses the normal log-likelihood as its objective func-7 tion, and is most effective when the normality assumption holds. The proposed methodology 8 considers elliptically contoured distributions and it incorporates this distribution structure into 9 the modeling. Consequently, it is more flexible and its estimator outperforms the estimator de-10 rived for the normal case. When the specific distribution is unknown, we present an estimator 11 that performs well as long as the elliptically contoured assumption holds.
Influence Diagnostics for Elliptical Multivariate Linear Regression Models
Communications in Statistics-theory and Methods, 2003
In this paper we present various diagnostic methods for elliptical multivariate regression models. We show that the expressions, and consequently the distribution of some usual standardized residuals, are invariant in the class of Elliptical models. This invariance is also verified for some influence measures of dropping observations, such as the Cook's distance. We also discuss the computation of the likelihood displacement as well as the normal curvature in the local influence method. An example with real data is given for illustration.
Theory of Probability and Mathematical Statistics, 2009
We consider an errors-in-variables nonlinear structural model where the density of the response belongs to the exponential family. We estimate regression parameters and the dispersion parameter as well as parameters of the hidden variable. Following the modified quasi-likelihood method we construct a joint estimator that has the minimal asymptotic covariance matrix in a wide class of estimators. The polynomial and gamma models are studied in more detail.
Bias correction in a multivariate normal regression model with general parameterization
Statistics & Probability Letters, 2009
This paper develops a bias correction scheme for a multivariate normal model under a general parameterization. In the model, the mean vector and the covariance matrix share the same parameters. It includes many important regression models available in the literature as special cases, such as (non)linear regression, errors-in-variables models, and so forth. Moreover, heteroscedastic situations may also be studied within our framework. We derive a general expression for the second-order biases of maximum likelihood estimates of the model parameters and show that it is always possible to obtain the second order bias by means of ordinary weighted lest-squares regressions. We enlighten such general expression with an errors-in-variables model and also conduct some simulations in order to verify the performance of the corrected estimates. The simulation results show that the bias correction scheme yields nearly unbiased estimators. We also present an empirical ilustration.
Local influence in elliptical linear regression models
Journal of the Royal Statistical Society: Series D (The Statistician), 1997
Influence diagnostic methods are extended in this paper to elliptical linear models. These include several symmetric multivariate distributions such as the normal, Student t-, Cauchy and logistic distributions, among others. For a particular perturbation scheme and for the likelihood displacement the diagnostics agree with those developed for the normal linear regression model by Cook when the coefficients and the scale parameter are treated separately. This result shows the invariance of the diagnostics with respect to the induced model in the elliptical linear family. However, if the coefficients and the scale parameter are treated jointly we have a different diagnostic for each induced model, which makes this approach helpful for selecting the less sensitive model in the elliptical linear family. An example on the salinity of water is given for illustration.