The traditional textbook approach to avoiding the dummy trap problem is to delete a category from each qualitative variable. We illustrate an alternative constraint introduced by Sweeney and Ulveling (1972) which can be used to transform conventional dummy variable coefficients. This constraint...

Five decades ago, Bhattacharyya established a series of lower bounds for the variance of an unbiased estimator, since then called the Bhattacharyya bounds. In 1974 Blight and Rao have shown that the series of Bhattacharyya bounds converges to the variance of the best unbiased estimator. In this...

Gibbs sampling has had great success in the analysis of mixture models. In particular, the "latent varaible" formulation of the mixture model greatly reduces computational complexity. However, one failing of this approach is the possible existence of almost-absorbing states, called trapping...

Let the distribution of X wander throught a simple quadratic natural exponential family on R^d. We show that any functions g: R^d - R such that E(g^2(X)) exists, is characterized by its first moments (Eg(X)). This characterization yields a construction of g when E(G(X)) is konwn. A few examples...

Within the framework of the general theory of multidimensional polynomials, we wish to investigate the orthogonal polynomials associated to the Gamma-Gaussian and negative multinomial-gamma measures. We obtain a mixing of Laguerre, Hermite and Charlier polynomials. We relate this study to the...

We consider the local empirical measure indexed by a function class. Under some reglarity assumptions, we give a large deviations principle for this process. A non standard functional law of the iterated logarithm is infered from our large deviations principle.

More than one hundred years, Appell introduced a polynomials class characterized by the exponentials form of its generatrice function. This class is well known on R and the aim of the paper is to offer a multidimensional analysis in two directions: we indicate a classical characterization of the...

We find a condition for the normalized sequence of independent and identically distriubted random nuclear operators to satisfy the Central Limit Theorem.

The Jordan Form of the VAR's Companion matrix is used for proving the equivalence between the statement that there are no jordan blocks of order two or higher in the Jordan matrix and the conditions of Granger's Representation Theorem for an I(1) series. Furthermore, a Diagonal polynomial matrix...

In this paper a Superiority and Inferiority Ranking (SIR) method is proposed. This new method uses two types of information, the superiority and the inferiority information, to derive two types of flows, the superiority flow and the inferiority flow, by which the set of alternatives are ranked...