The multivariate saddlepoint approximation to the distribution of estimators - A general approach

ABRIL, JUAN CARLOS; ABRIL, MARÍA DE LAS MERCEDES; MARTÍNEZ, CARLOS I.

ESTADISTICA (SANTIAGO DE CHILE)

Inter-American Statistical Institute

Lugar: Buenos Aires; Año: 2013 vol. 65 p. 21 - 47

0014-1135

We develop the theory of multivariate saddlepoint approximations. Our treatment differs from Barndorff-Nielsen and Cox (1979) in two aspects: (i) our results are satisfied for random vectors that are not necessarily sums of independent and identically distributed random vectors, and (ii) we consider that the sample is taken from any distribution, not necessarily a member of the exponential family of densities. We also show the relationship with the corresponding multivariate Edgeworth approximations whose general treatment was developed by Durbin (1980a), emphasizing that the basic assumptions that support the validity of both approaches are essentially similar. Finally, we present examples and perform an analysis of the results through comparisons between Monte Carlo simulations and the approximations obtained.