LARGE DEVIATION LOCAL LIMIT-THEOREMS FOR RATIO STATISTICS

Let {T(n), n greater-than-or-equal-to 1} be an arbitrary sequence of nonlattice random variables and let {S(n), n greater-than-or-equal-to 1} be another sequence of positive random variables. Assume that the sequences are independent. In this paper we obtain asymptotic expression for the density function of the ratio statistic R(n) = T(n)/S(n) based on simple conditions on the moment generating functions of T(n) and S(n). When S(n) = n, our main result reduces to that of Chaganty and Sethuraman[Ann. Probab. 13(1985):97-114]. We also obtain analogous results when T(n) and S(n) are both lattice random variables. We call our theorems large deviation local limit theorems for R(n), since the conditions of our theorems imply that R(n) --> c in probability for some constant c. We present some examples to illustrate our theorems

Discussion of "Generalized Estimating Equations: Notes on the Choice of the Working Correlation Matrix"

Objective: To discuss generalized estimating equations as an extension of generalized linear models by commenting on the paper of Ziegler and Vens "Generalized Estimating Equations. Notes on the Choice of the Working Correlation Matrix". Methods: Inviting an international group of experts to comment on this paper. Results: Several perspectives have been taken by the discussants. Econometricians have established parallels to the generalized method of moments (GMM). Statisticians discussed model assumptions and the aspect of missing data Applied statisticians; commented on practical aspects in data analysis. Conclusions: In general, careful modeling correlation is encouraged when considering estimation efficiency and other implications, and a comparison of choosing instruments in GMM and generalized estimating equations, (GEE) would be worthwhile. Some theoretical drawbacks of GEE need to be further addressed and require careful analysis of data This particularly applies to the situation when data are missing at rando

Nonnegative definite solutions to matrix equations with applications to multivariate test statistics

Primary 62H10, 62E15, Secondary 15A63,