Analyzing multiple vector autoregressions through matrix-variate normal distribution with two covariance matrices

Abstract

This article proposes a new approach to analyze multiple vector autoregressive (VAR) models that render us a newly constructed matrix autoregressive (MtAR) model based on a matrix-variate normal distribution with two covariance matrices. The MtAR is a generalization of VAR models where the two covariance matrices allow the extension of MtAR to a structural MtAR analysis. The proposed MtAR can also incorporate different lag orders across VAR systems that provide more flexibility to the model. The estimation results from a simulation study and an empirical study on macroeconomic application show favorable performance of our proposed models and method.     

Product partition latent variable model for multiple change-point detection in multivariate data

The product partition model (PPM) is a well-established efficient statistical method for detecting multiple change points in time-evolving univariate data. In this article, we refine the PPM for the purpose of detecting multiple change points in correlated multivariate time-evolving data. Our model detects distributional changes in both the mean and covariance structures of multivariate Gaussian data by exploiting a smaller dimensional representation of correlated multiple time series. The utility of the proposed method is demonstrated through experiments on simulated and real datasets.     

A NOTE ON EVANESCENT PROCESSES

This note examines the connection between μ-invariant measures for the transition function of a continuous-time Markov chain and those of its q-matrix, Q. The major result establishes a necessary and aufficient condition for a convergent μ-invariant measure for Q to be μ-inhant for the minimal transition function, P, under the assumption that P is honest. This corrects Theorem 6 of Vere-Jones (1969) and the first part of Corollary 1 of Pollett (1986), both of which assert that the above conclusion holds in the absence of this condition. The error was pointed out by E.A. van Doom (1991) and the counterexample which be presented provides the basis for the present arguments. In determining where the error occurred in the original proof, we are able to identify a simple sufficient condition for μ-invariance.     

Computing maximum likelihood estimates from type II doubly censored exponential data

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.     

Assessing goodness-of-fit of categorical regression models based on case-control data

Demonstrated equivalence between a categorical regression model based on case‐control data and an I‐sample semiparametric selection bias model leads to a new goodness‐of‐fit test. The proposed test statistic is an extension of an existing Kolmogorov–Smirnov‐type statistic and is the weighted average of the absolute differences between two estimated distribution functions in each response category. The paper establishes an optimal property for the maximum semiparametric likelihood estimator of the parameters in the I‐sample semiparametric selection bias model. It also presents a bootstrap procedure, some simulation results and an analysis of two real datasets.     

TESTING SPHERICITY UNDER A MIXTURE MODEL

The robustness of Mauchly's sphericity test criterion when sampling from a mixture of two multivariate normal distributions is studied. The distribution of the sphericity test criterion when the sample covariance matrix has a non-central Wishart density of rank one is derived in terms of Meijer's G-functions; its distribution under the mixture model is then deduced. The robustness is studied by computing actual significance levels of the test under the mixture model using the critical values under the usual normal model.     

一类混合指数型算子的一致逼近

主要讨论了一类混合指数型算子的一致逼近问题，并给出了逼近阶的估计和特征刻划。     

Testing symmetry under a skew Laplace model

We develop tests of hypothesis about symmetry based on samples from possibly asymmetric Laplace distributions and present exact and limiting distribution of the test statistics. We postulate that the test statistic derived under the Laplace model is a rational choice as a measure of skewness and can be used in testing symmetry for other, quite general classes of skew distributions. Our results are applied to foreign exchange rates for 15 currencies.