Departure from normality of increasing-dimension martingales |
| |
Authors: | Ignacio Arbué s |
| |
Affiliation: | S.G. de Estadísticas Industriales y Agrarias, Instituto Nacional de Estadística, Castellana, 183, 28071, Madrid, Spain |
| |
Abstract: | In this paper, we consider sequences of vector martingale differences of increasing dimension. We show that the Kantorovich distance from the distribution of the k(n)-dimensional average of n martingale differences to the corresponding Gaussian distribution satisfies certain inequalities. As a consequence, if the growth of k(n) is not too fast, then the Kantorovich distance converges to zero. Two applications of this result are presented. The first is a precise proof of the asymptotic distribution of the multivariate portmanteau statistic applied to the residuals of an autoregressive model and the second is a proof of the asymptotic normality of the estimates of a finite autoregressive model when the process is an AR(∞) and the order of the model grows with the length of the series. |
| |
Keywords: | 60F05 60B12 62M10 |
本文献已被 ScienceDirect 等数据库收录! |
|