Likelihood-Based Inference for Multivariate Skew-Normal Regression Models

In this article, we present EM algorithms for performing maximum likelihood estimation for three multivariate skew-normal regression models of considerable practical interest. We also consider the restricted estimation of the parameters of certain important special cases of two models. The methodology developed is applied in the analysis of longitudinal data on dental plaque and cholesterol levels.     

Convergence of Discount Time Series Dynamic Linear Models

This article studies the limiting behavior of multiple discount time series dynamic linear models (TSDLMs). It is shown that, under mild conditions, all discount TSDLMs converge to the constant (time-invariant) TSDLM. In particular, the limiting posterior precision matrix of the superposition of multiple discount TSDLMs is explored. For non seasonal models, the elements of the limiting posterior precision of the states are given in a recurrence relationship, while for seasonal models the solution of a linear system provides the elements of the respective limiting precision matrix. The proposed methodology uses canonical Jordan forms and it is illustrated with a detailed example of simulated data featuring both trend and seasonal time series.     

Mixed Graphical Model Selection Using Holm's Procedure

The problem of selecting a graphical model is considered as a performing simultaneously multiple tests. The control of the overall Type I error on the selected graph is done using the so famous Holm's procedure. We prove that when we use a consistent edge exclusion test the selected graph is asymptotically equal to the true graph with probability at least equal to a fixed level 1 ? α. This method is then used for the selection of mixed concentration graph models by performing the χ²-edge exclusion test. We also apply the method to two classical examples and to simulated data. We compare the overall error of the selected model with the one obtained using the stepwise method. We establish that the control is better when we use the Holm's procedure.     

Testing Symmetry of the Error Distribution in Nonlinear Heteroscedastic Models

Using the empirical characteristic function, we derive a Cramér-von Mises test for symmetry of the error distribution in a class of nonlinear parametric heteroscedastic models. We study the convergence of the residual-based empirical distribution function. We establish a functional limit theorem for an empirical process of residuals, and investigate the asymptotic null distribution function of our test statistic. A simulation experiment is conducted to evaluate small-sample performances of our test.     

Estimating the order of moving average models: the max X2 method

The max X² technique for estimating rhe order of autoregressive processes (McClave (1976)) is extended to moving average models. The autöregressive-moving average duality is exploited by using the inverse autocorrelation function and the subset autoregression algorithm. The technique is demonstrated via simulations, and is applied to Box and Jenkins (1970) Series A.     

The analysis of some biological data

This paper considers the building of stochastic models and the related analysis of discrete data in two biological problems, The first arises from the reproduction of yeast cells, while the secondis concerned with the aggregation of nucleoli. Galton-Watson and aggregation models are constructed for the respective processes and their goodness of fit to the data tested     

Marginal homogeneity,symmetry, and independence

A contingency table of the mc form provides a convenient summary of data when c individuals in a matched set9 each belonging to a different one of c classifications, are identified as belonging to one of m categories, A study in which matched sets (c=3) of 1 case, 1 hospital control, and 1 neighborhood control are classified into one of m=4 occupational categories would be an example, Independence in the cxm tables for each of the matched sets implies symmetry in the summary mc table with consequent marginal homogeneity. Adaptation of the Mantel-Haenszel procedure for testing independence to the case of many cxm tables so as to yield a chi square with (cl)(ml) degrees of freedom (DF) provides a test of marginal homogeneity in the summary mc table. This can be viewed as a test of symmetry directed against alternatives which would make for marginal inhomogeneity and can differ     

Estimation of functions of the parameters of a normal distribution

Several authors have considered the problem of estimating parameters of a distribution after some fixed Gaussian inducing transformation has been applied to the observations. This paper extends this work to the situation where the observations represent a noisy version of a true process, the parameters of the latter requiring estimation     

A Discussion of Permutation Tests Conditional to Observed Responses in Unreplicated 2 M Full Factorial Designs

ABSTRACT

In this article we present a new solution to test for effects in unreplicated two-level factorial designs. The proposed test statistic, in case the error components are normally distributed, follows an F random variable, though our attention is on its nonparametric permutation version. The proposed procedure does not require any transformation of data such as residualization and it is exact for each effect and distribution-free. Our main aim is to discuss a permutation solution conditional to the original vector of responses. We give two versions of the same nonparametric testing procedure in order to control both the individual error rate and the experiment-wise error rate. A power comparison with Loughin and Noble's test is provided in the case of a unreplicated 2⁴ full factorial design.