Behaviour of third order terms in quadratic approximations of LR- statistics in multivariate generalized linear models. (English) Zbl 0587.62100

Kredler, Christian

Ann. Stat. 14, 326-335 (1986).

The size of error is investigated when the log-likelihood of multivariate generalized linear models is approximated by a quadratic function. The nonquadratic tail is characterized by analyzing the cubic part of the log-likelihood. In a local analysis simple bounds for that part can be expressed in terms of expectations of the related random variables for arbitrary sample size N. Additionally global error bounds are given for the univariate case.

MSC:

62H10	Multivariate distribution of statistics
62E10	Characterization and structure theory of statistical distributions
62E20	Asymptotic distribution theory in statistics
62F03	Parametric hypothesis testing
62J02	General nonlinear regression

Keywords:

third derivative structure of an exponential family; third moments; quadratic approximation error; variable selection; size of error; log- likelihood of multivariate generalized linear models; global error bounds