Estimation in additive models and ANOVA-like applications

A well-known property of cumulant generating function is used to estimate the first four order cumulants, using least-squares estimators. In the case of additive models, empirical best linear unbiased predictors are also obtained. Pairs of independent and identically distributed models associated with the treatments of a base design are used to obtain unbiased estimators for the fourth-order cumulants. An application to real data is presented, showing the good behaviour of the least-squares estimators and the great flexibility of our approach.info:eu-repo/semantics/publishedVersio

A unifying framework for kk-statistics, polykays and their multivariate generalizations

Through the classical umbral calculus, we provide a unifying syntax for single and multivariate $k$-statistics, polykays and multivariate polykays. From a combinatorial point of view, we revisit the theory as exposed by Stuart and Ord, taking into account the Doubilet approach to symmetric functions. Moreover, by using exponential polynomials rather than set partitions, we provide a new formula for $k$-statistics that results in a very fast algorithm to generate such estimators.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6163 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Symbolic computation of moments of sampling distributions

By means of the notion of umbrae indexed by multisets, a general method to express estimators and their products in terms of power sums is derived. A connection between the notion of multiset and integer partition leads immediately to a way to speed up the procedures. Comparisons of computational times with known procedures show how this approach turns out to be more efficient in eliminating much unnecessary computation.Comment: 21 pages, 7 table

Modelos aditivos - ajustamento, elipsóides de confiança e intervalos de perdição

Modelos aditivos são dados por [...]Bi-additive Models are given by [...

Asymptotic Expansions of Moments and Cumulants

Many parameters may be expanded as series with terms involving products of expectations and their estimates expanded as series involving products of averages. The computation of moments and cumulants of such estimates may be organized if the terms of the series expansions of parameters, estimates and their moments are considered as functions applied to lists. The lists form a vectors space associated with a quotient space of the polynomial algebra whose basis is the monomials involving random variables. Simple identities relating the functions induce transformations of lists. The computations reduce to the transformation of lists. The transformations themselves are computed for a collection of standard objects using a set of fundamental identities. These transformations are the bases for quite complex calculations. The framework permits the calculation of results which would otherwise involve complementary set partitions, k-statistics, and pattern functions. The examples given include..