ARMA MODELS REALIZATION AND IMPULSE RESPONSES

A parallel is made between the role played by covariances in the determination of auto-regressive models and the role played by impulse responses in the determination of ARMA models.

Auto-regressive models are known to maximize the Burg-entropy under covariance constraints. Auto-regressive-moving-average models give the maximum of the Burg-entropy among processes sharing the same covariances and impulse responses up to a certain lag. Such models are constructed by iterative or algebraic methods under the different constraints.

A new recursive method of identification of the order of an ARMA model is also developed, based on the generalized reflection coefficients.     

Model‐based linear clustering

The authors propose a profile likelihood approach to linear clustering which explores potential linear clusters in a data set. For each linear cluster, an errors‐in‐variables model is assumed. The optimization of the derived profile likelihood can be achieved by an EM algorithm. Its asymptotic properties and its relationships with several existing clustering methods are discussed. Methods to determine the number of components in a data set are adapted to this linear clustering setting. Several simulated and real data sets are analyzed for comparison and illustration purposes. The Canadian Journal of Statistics 38: 716–737; 2010 © 2010 Statistical Society of Canada     

Large‐sample tests of extreme‐value dependence for multivariate copulas

Starting from the characterization of extreme‐value copulas based on max‐stability, large‐sample tests of extreme‐value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula of the data and a multiplier technique for obtaining approximate p‐values for the derived statistics. The asymptotic validity of the multiplier approach is established, and the finite‐sample performance of a large number of candidate test statistics is studied through extensive Monte Carlo experiments for data sets of dimension two to five. In the bivariate case, the rejection rates of the best versions of the tests are compared with those of the test of Ghoudi et al. (1998) recently revisited by Ben Ghorbal et al. (2009). The proposed procedures are illustrated on bivariate financial data and trivariate geological data. The Canadian Journal of Statistics 39: 703–720; 2011. © 2011 Statistical Society of Canada     

A review of some adaptive statistical techniques

We present several methods for full, partial, and practical adaptation. Selector statistics that are measures of skewness, peakedness, and tailweight are used, primarily in estimating loca-tion in some single-sample situations. We note several practical adaptive techniques in current use, including illustrations in-volving stepwise regression, analysis of variance, ridge regres-sion, and splines. We suggest some areas in which future develop-ment of adaptive methods is needed:density estimation; M, R, and L estimation in regression; and dependent data. There is also a need to develop better selector statistics.