Local influence in box-cox transformation for multivariate regression data

The Box-Cox power family of transformations for multivariate regression data is considered. The influence of cases on the maximum likelihood estimators of the transformation parameters is investigated using the local influence approach, An example is given to- illustrate the local influence method and to show the effectiveness of the method.     

Local influence in multilevel models

The authors study the local influence of observations in multilevel regression models. To this end, they perturb simultaneously the variances, responses and design matrix. To measure the local change caused by these perturbations, they use generalized Cook statistics for the fixed and random parameter estimates. Closed form local influence measures also allow them to assess the joint influence of various observations. They suggest a simple computation method and illustrate their results using two examples.     

Exact testing in multivariate regression

An F statistic due to Rao (1951,1973) tests uniform mixed linear restrictions in the multivariateregression model. In combination with a generalization of the Bera-Evans-Savin exact functional relationship between the W, LR, and LM statistics, Rao's F serves to unify a number of exact test procedures commonly applied in disparate empirical literatures. Examples in demand analysis and asset pricing are provided. The availability of exact tests of restrictions in certain nonlinear models when the model is linear under the null, originally explored by Milliken-Graybill (1970), is extended to multivariate regression. Generalized RESET, J-, and Hausman-Wu tests are resented. As an extension of Dufour (1989), bounds tests exist for nonlinear and inequality restrictions. Applications include conservative bound tests for symmetry or negativity of the substitution matrix in demand systems.     

Multiple deletion measures and conditional influence in regression model

The joint effect of the deletion of the ith and jih cases is given by Gray and Ling (1984), they discussed the influence measures for influential subsets in linear regression analysis. The present paper is concerned with multiple sets of deletion measures in the linear regression model. In particular we are interested in the effects of the jointly and conditional influence analysis for the detection of two influential subsets.     

Assessing case influence on confidence intervals in nonlinear regression

Diagnostic techniques are proposed for assessing the influence of individual cases on confidence intervals in nonlinear regression. The technique proposed uses the method of profile t-plots applied to the case-deletion model. The effect of the geometry of the statistical model on the influence measures is assessed, and an algorithm for computing case-deleted confidence intervals is described. This algorithm provides a direct method for constructing a simple diagnostic measure based on the ratio of the lengths of confidence intervals. The generalization of these methods to multiresponse models is discussed.     

Local influence in binary regression models,and its correspondence with global influence

We develop local influence diagnostics for a general binary regression model,and apply these methods to case-weight perturbations in four examples. In addition, we illustrate the correspondence between case-deletion diagnostics and local case-weight perturbation slopes and curvatures. We demonstrate that local influence diagnostics can provide a more computationally efficient means for obtaining analogous information to that yielded by case-deletion diagnostics, which can be thought of as global influence perturbations. We also assess the global consistency of patterns of local influence using these data examples.     

Local influence in ridge semiparametric models

ABSTRACT

Ridge penalized least-squares estimators has been suggested as an alternative to the minimum penalized sum of squares estimates in the presence of collinearity among the explanatory variables in semiparametric regression models (SPRMs). This paper studies the local influence of minor perturbations on the ridge estimates in the SPRM. The diagnostics under the perturbation of ridge penalized sum of squares, response variable, explanatory variables and ridge parameter are considered. Some local influence diagnostics are given. A Monte Carlo simulation study and a real example are used to illustrate the proposed perturbations.     

Local influence in seemingly unrelated regression model with ridge estimate

Local influence is a well-known method for identifying the influential observations in a dataset and commonly needed in a statistical analysis. In this paper, we study the local influence on the parameters of interest in the seemingly unrelated regression model with ridge estimation, when there exists collinearity among the explanatory variables. We examine two types of perturbation schemes to identify influential observations: the perturbation of variance and the perturbation of individual explanatory variables. Finally, the efficacy of our proposed method is illustrated by analyzing [13 A. Munnell, Why has productivity declined? Productivity and public investment, New Engl. Econ. Rev. (1990), pp. 3–22. [Google Scholar]] productivity dataset.     

Diagnostics in multivariate generalized Birnbaum-Saunders regression models

Birnbaum–Saunders (BS) models are receiving considerable attention in the literature. Multivariate regression models are a useful tool of the multivariate analysis, which takes into account the correlation between variables. Diagnostic analysis is an important aspect to be considered in the statistical modeling. In this paper, we formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models. We consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption. We also consider the local influence approach and study how a perturbation may impact on the estimation of model parameters. We implement the obtained results in the R software, which are illustrated with real-world multivariate data to show their potential applications.     

Bias corrected estimates in multivariate student t regression models

The t distribution has proved to be a useful alternative to the normal distribution especially When robust estimation is desired. We consider the multivariate nonlinear Student-t regression model and show that the biased of the estimates of the regression coefficients can be computed from an auxiliary generalized linear regression. We give a formula for the biases of the estimates of the parameters in the scale matrix, which also can be computed by means of a generalized linear regression. We briefly discuss some important special cases and present simulation results which indicate that our bias-corrected estimates outperform the uncorrected ones in small samples.     

Local influence analysis for regression models with scale mixtures of skew-normal distributions

The robust estimation and the local influence analysis for linear regression models with scale mixtures of multivariate skew-normal distributions have been developed in this article. The main virtue of considering the linear regression model under the class of scale mixtures of skew-normal distributions is that they have a nice hierarchical representation which allows an easy implementation of inference. Inspired by the expectation maximization algorithm, we have developed a local influence analysis based on the conditional expectation of the complete-data log-likelihood function, which is a measurement invariant under reparametrizations. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex and with Cook's well-known approach it can be very difficult to obtain measures of the local influence. Some useful perturbation schemes are discussed. In order to examine the robust aspect of this flexible class against outlying and influential observations, some simulation studies have also been presented. Finally, a real data set has been analyzed, illustrating the usefulness of the proposed methodology.     

Local influence regression diagnostics for gamma data

The local influence diagnostics proposed in general terms irl Cook (1986), Thomas and Cook (1989) and Billor and Loynes (1993). arc adapted for gamma data. A data set prcviously analysed using different methods is then reexamined, and conclusions based on wing the new approach are made.     

Local influence for generalized linear mixed models

The authors describe a method for assessing model inadequacy in maximum likelihood estimation of a generalized linear mixed model. They treat the latent random effects in the model as missing data and develop the influence analysis on the basis of a Q‐function which is associated with the conditional expectation of the complete‐data log‐likelihood function in the EM algorithm. They propose a procedure to detect influential observations in six model perturbation schemes. They also illustrate their methodology in a hypothetical situation and in two real cases.     

Variable selection in partially linear hazard regression for multivariate failure time data

The aim of this paper is to explore variable selection approaches in the partially linear proportional hazards model for multivariate failure time data. A new penalised pseudo-partial likelihood method is proposed to select important covariates. Under certain regularity conditions, we establish the rate of convergence and asymptotic normality of the resulting estimates. We further show that the proposed procedure can correctly select the true submodel, as if it was known in advance. Both simulated and real data examples are presented to illustrate the proposed methodology.     

Computation of determinantal subset influence in regression

One of the important goals of regression diagnostics is the detection of cases or groups of cases which have an inordinate impact on the regression results. Such observations are generally described as influential. A number of influence measures have been proposed, each focusing on a different aspect of the regression. For single cases, these measures are relatively simple and inexpensive to calculate. However, the detection of multiple-case or joint influence is more difficult on two counts. First, calculation of influence for a single subset is more involved than for an individual case, and second, the sheer number of subsets of cases makes the computation overwhelming for all but the smallest data sets.Barrett and Gray (1992) described methods for efficiently examining subset influence for those measures that can be expressed as the trace of a product of positive semidefinite (psd) matrices. There are, however, other popular measures that do not take this form, but rather are expressible as the ratio of determinants of psd matrices. This article focuses on reducing the computation for the determinantal ratio measures by making use of upper and lower bounds on the influence to limit the number of subsets for which the actual influence must be explicitly determined.     

Model averaging for multivariate multiple regression models

The theories and applications of model averaging have been developed comprehensively in the past two decades. In this paper, we consider model averaging for multivariate multiple regression models. In order to make use of the correlation information of the dependent variables sufficiently, we propose a model averaging method based on Mahalanobis distance which is related to the correlation of the dependent variables. We prove the asymptotic optimality of the resulting Mahalanobis Mallows model averaging (MMMA) estimators under certain assumptions. In the simulation study, we show that the proposed MMMA estimators compare favourably with model averaging estimators based on AIC and BIC weights and the Mallows model averaging estimators from the single dependent variable regression models. We further apply our method to the real data on urbanization rate and the proportion of non-agricultural population in ethnic minority areas of China.     

A predictive approach to the detection of additional information in a multivariate regression model

A predictive approach for the detection of additional information in a multivariate linear regression model is considered for the case of known and unknown error covariance matrices. The predictive density of future Observations on the additional variables under the model that they carry no information has been compared with the predictive density under the model that they do carry information. The Kullback-Leibler measure of divergence is used as a measure of comparison between the models.     

Tests of heteroscedasticity and correlation in multivariate t regression models with AR and ARMA errors

Heteroscedasticity checking in regression analysis plays an important role in modelling. It is of great interest when random errors are correlated, including autocorrelated and partial autocorrelated errors. In this paper, we consider multivariate t linear regression models, and construct the score test for the case of AR(1) errors, and ARMA(s,d) errors. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score tests, are studied. Based on modified profile likelihood, the adjusted score test is also developed. The finite sample performance of the tests is investigated through Monte Carlo simulations, and also the tests are illustrated with two real data sets.     

Simultaneous transformations and influence in regression

Influence of simultaneous transformations on the response and some of explanatory variables to the same level in the linear regression is considered. An approximate, but useful diagnostic procedure is developed for practical use. An example is then given for illustrations.     

More on local influence in pllincipal components analysis

Local influence on the eigenvalues of sample covariance matrices in

principal components analysis is examined for a reasonable modification of Shi's (1997) perturbation scheme, The modification is suggested for samples from populations with both unknown mean vector and covariance matrix. While Shi's detection indexes (1997) consist of only quadratic terms, the modified perturbation scheme leads to detection indexes constituted by both linear and quadratic terms associated with centralized observations. These linear and quadratic terms reflect local influences on the first two sample moments. Examples are investigated based on the two detection indexes.