Alternate test statistics for a functional errors-in-variables model

Some test statistics for the structural coefficients of simultaneous equations model often referred to as the multivariate linear functional relationship model are proposed in this article. The following cases are considered: the covariance matrix of errors is either unknown, known up to a proportionality factor, or completely known. The exact and approximate distributions of the proposed test statistics, as well as those of some that are known, are also given.     

A multivariate long-memory model with structural breaks

This paper introduces a multivariate long-memory model with structural breaks. In the proposed framework, the time series exhibits possibly fractional orders of integration which are allowed to be different in each subsample. The break date is endogenously determined using a procedure that minimizes the residual sum of squares (RSS). Monte Carlo experiments show that this method for detecting breaks performs well in large samples. As an illustration, we estimate a trivariate VAR including prices, employment and GDP in both the US and Mexico. For the subsample preceding the break, our findings are similar to those of earlier studies based on a standard VAR approach in both the countries, such that the variables exhibit integer degrees of integration. On the contrary, the series is found to be fractionally integrated after the break, with the fractional differencing parameters being higher than one in the case of Mexico.     

On some tests for a multivariate linear functional relationship with replication

For testing problems of the coefficient vector and the interception of multivariate linear functional relationship with replicated observations, the likelihood ratio test statistics are considered. Their asymptotic distributions are obtained under each null hypothesis respectively.     

Asymptotic distributions of some test statistics for a linear functional relationship

We consider the testing problems of the structural parameters for the multivariate linear functional relationship model. We treat the likelihood ratio test statistics and the test statistics based on the asymptotic distributions of the maximum likelihood estimators. We derive their asymptotic distributions under each null hypothesis respectively. A simulation study is made to evaluate how we can trust our asymptotic results when the sample size is rather small.     

Mixture of linear mixed models using multivariate t distribution

Linear mixed models are widely used when multiple correlated measurements are made on each unit of interest. In many applications, the units may form several distinct clusters, and such heterogeneity can be more appropriately modelled by a finite mixture linear mixed model. The classical estimation approach, in which both the random effects and the error parts are assumed to follow normal distribution, is sensitive to outliers, and failure to accommodate outliers may greatly jeopardize the model estimation and inference. We propose a new mixture linear mixed model using multivariate t distribution. For each mixture component, we assume the response and the random effects jointly follow a multivariate t distribution, to conveniently robustify the estimation procedure. An efficient expectation conditional maximization algorithm is developed for conducting maximum likelihood estimation. The degrees of freedom parameters of the t distributions are chosen data adaptively, for achieving flexible trade-off between estimation robustness and efficiency. Simulation studies and an application on analysing lung growth longitudinal data showcase the efficacy of the proposed approach.     

A multivariate logit model with marginal canonical association

In this work, a generalization of the Goodman Association Model to the case of q, q > 2, categorical variables which is based on the idea of marginal modelling discussed by Gloneck–McCullagh is introduced; the difference between the proposed generalization and two models, previously introduced by Becker and Colombi, is discussed. The Becker generalization is not a marginal model because it does not imply Logit Models for the marginal probabilities, and because it is based on the conditional approach of modelling the association. The Colombi model is only partially a marginal model because it uses simple logit models for the univariate marginal probabilities but is based on the conditional approach of modelling the association. It is also shown that the maximum likelihood estimation of the parameters of the new model is feasible and, to compute the maximum likelihood estimates, an algorithm is proposed, which is a numerically convenient compromise between the constrained optimization approach of Lang and the straightforward use of the Fisher Scoring Algorithm suggested by Glonek–McCullagh.Finally, the proposed model is used to analyze a data set concerning work accidents which occurred to workers at some Italian firms during the years 1994–1996.     

Prediction distribution for a linear regression model with multivariate student-t error distribution

The distribution(s) of future response(s) given a set of data from an informative experiment is known as prediction distribution. The paper derives the prediction distribution(s) from a linear regression model with a multivari-ate Student-t error distribution using the structural relations of the model. We observe that the prediction distribution(s) are multivariate t-variate(s) with degrees of freedom which do not depend on the degrees of freedom of the error distribution.     

Testing for a change lit the regression matrix of a multivariate linear model

A Bayesian test procedure Is developed to test; the null hypothesis of no change In the regression matrix of a multivariate lin¬ear model against the alternative hypothesis of exactly one change The resulting test is based on the marginal posterior distribution of the change point; To illustrate the test procedure a numerical example using a bivariate regression model is considered.     

On asymptotic distribution of prediction in functional linear regression

There has been substantial recent attention on problems involving a functional linear regression model with scalar response. Among them, there have been few works dealing with asymptotic distribution of prediction in functional linear regression models. In recent literature, the centeral limit theorem for prediction has been discussed, but the proof and conditions under which the random bias terms for a fixed predictor converge to zero have been ignored so that the impact of these terms on the convergence of the prediction has not been well understood. Clarifying the proof and conditions under which the bias terms converge to zero, we show that the asymptotic distribution of the prediction is normal. Furthermore, we have derived those results related to other terms that already obtained by others, under milder conditions. Finally, we conduct a simulation study to investigate performance of the asymptotic distribution under various parameter settings.     

The likelihood ratio test for high-dimensional linear regression model

The paper considers a significance test of regression variables in the high-dimensional linear regression model when the dimension of the regression variables p, together with the sample size n, tends to infinity. Under two sightly different cases, we proved that the likelihood ratio test statistic will converge in distribution to a Gaussian random variable, and the explicit expressions of the asymptotical mean and covariance are also obtained. The simulations demonstrate that our high-dimensional likelihood ratio test method outperforms those using the traditional methods in analyzing high-dimensional data.     

General multivariate linear models for longitudional studies

Longitudinal studies occcur frequently in many different disciplines. To fully utilize the potential value of the information contained in a longitudinal data, various multivariate linear models have been proposed. The methodology and analysis are somewhat unique in their own ways and their relationships are not well understood and presented. This article describes a general multivaritate linear model for longitudinal data and attempts to provide a constructive formulation of the components in the mean response profile. The objective is to point out the extension and connections of some well-known models that have been obscured by different areas of application. More imporiantly, the model is expressed in a unified regression form from the subject matter considerations. Such an approach is simpler and more intuitive than other ways to modeling and parameter estimation. As a cmsequeace the analyses of the general class cf models for longitudional data can be casily implemented with standard software.     

Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A.G. Patriota and A.J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655–1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.     

Sow aspects of robustness in thr functional errors-in-variables regression model

For the functional errors-in-varinbles regression model, we define a class of robust regression estimators and study their properties     

Monitoring means and covariances of multivariate non linear time series with heavy tails

In this paper, the focus is on sequential analysis of multivariate financial time series with heavy tails. The mean vector and the covariance matrix of multivariate non linear models are simultaneously monitored by modifying conventional control charts to identify structural changes in the data. The considered target process is a constant conditional correlation model (cf. Bollerslev, 1990 Bollerslev, T. (1990). Modeling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model. Rev. Econ. Stat. 72:498–505.[Crossref], [Web of Science ®] , [Google Scholar]), an extended constant conditional correlation model (cf. He and Teräsvirta, 2004 He, C., Teräsvirta, T. (2004). An extended constant conditional correlation GARCH model and its fourth-moment structure. Economet. Theory 20:904–926.[Crossref], [Web of Science ®] , [Google Scholar]), a dynamic conditional correlation model (cf. Engle, 2002 Engle, R.F. (2002). Dynamic conditional correlation: A simple class of multivariate GARCH models. J. Bus. Econ. Stat. 20(3):339–350.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), or a generalized dynamic conditional correlation model (cf. Capiello et al., 2006 Capiello, L., Engle, R., Sheppard, K. (2006). Asymmetric correlations in the dynamics of global equity and bond returns. J. Financial Economet. 4(4):537–572.[Crossref] , [Google Scholar]). For statistical surveillance we use control charts based on residuals. Further, the procedures are constructed for t-distribution. The detection speed of these charts is compared via Monte Carlo simulation. In the empirical study, the procedure with the best performance is applied to log-returns of the stock market indices FTSE and CAC.     

Descriptive tests for the identification of outliers in the errors in variables linear model

In this paper the most commonly used diagnostic criteria for the identification of outliers or leverage points in the ordinary regression model are reviewed. Their use in the context of the errors-in-variables (e.v.) linear model is discussed and evidence is given that under the e.v. model assumptions the distinction between outliers and leverage points no longer exists.     

Detection of outliers in the multivariate linear regression model

In this article we suggest multivariate kurtosis as a statistic for detection of outliers in a multivariate linear regression model. The statistic has some local optimality properties.     

On the bias and mean square error of the least square estimator in a regression model with two inequality constraints and multivariate t error terms

We derive and numerically evaluate the bias and mean square error of the inequality constrained least squares estimator in a model with two inequality constraints and multivariate terror terms. Our results suggest that qualitatively, the estimator properties found for models with normal errors carry over to the case of multivariate terrors.