排序方式: 共有5条查询结果,搜索用时 0 毫秒
1
1.
Often, many complicated statistics used as estimators or test statistics take the form of the (multivariate) empirical distribution function evaluated at a random vector (Vn). Denote such statistics by Sn. This paper describes methods for the study of various asymptotic properties of Sn. First, under minimal assumptions, a weak asymptotic representation for Sn is derived. This result may be used to show the asymptotic normality of Sn. Second, under slightly more stringent regularity conditions, an almost sure representation of Sn, with suitable order (as.) of the remainder term is studied and then a law of the iterated logarithm for Sn, is derived. In this context, strong convergence results from a sequential point of view are also studied. Finally, weak convergence to a Brownian motion process is established. As an application, we show the limiting normality of Sn, for a random number of summands. 相似文献
2.
We propose a measure for independence of group of random variables, given by a sum of cross-cumulants of a given order n . A similar measure was known for the case of fourth-order cross-cumulants from the JADE algorithm for ICA (independent component analysis). We derive a formula for its calculation using cumulant tensors. In the case n=4 our formula allows efficient calculation of this measure, using cumulant matrices. Much attention is devoted to the case of six-order cross-cumulants, aiming to show that this measure can be calculated using again cumulant matrices. 相似文献
3.
4.
We are concerned with estimators which improve upon the best invariant estimator, in estimating a location parameter θ. If the loss function is L(θ - a) with L convex, we give sufficient conditions for the inadmissibility of δ0 (X) = X. If the loss is a weighted sum of squared errors, we find various classes of estimators δ which are better than δ0 . In general, δ is the convolution of δ1 (an estimator which improves upon δ0 outside of a compact set) with a suitable probability density in Rp . The critical dimension of inadmissibility depends on the estimator δ1 We also give several examples of estimators δ obtained in this way and state some open problems. 相似文献
5.
Madan L. Puri Dan A. Ralescu Stefan S. Ralescu 《Australian & New Zealand Journal of Statistics》1984,26(3):277-283
In this note we provide sufficient conditions for the minimaxity of linear estimators of the form aX+b in the one-parameter exponential family for estimating a differentiable function g(θ) with normalized quadratic loss. We provide some examples which show that the natural estimator X is minimax in estimating a function of the parameter (different from the mean). 相似文献
1