Titlebook: Self-Normalized Processes; Limit Theory and Sta Victor H. Peña,Tze Leung Lai,Qi-Man Shao Book 2009 Springer-Verlag Berlin Heidelberg 2009 B

杀人

NAG

Laws of the Iterated Logarithm for Self-Normalized Processesom variables with finite variances (see (2.2)) to martingales that are self-normalized by the conditional variances. We then consider self-normalization by a function of the sum of squared martingale differences as in de la Peña et al. (2004). This self-normalization yields a universal upper LIL tha

壁画

Multivariate Self-Normalized Processes with Matrix Normalizationltivariate setting in which At is a vector and Bt is a positive definite matrix. Section 14.1 describes the basic concept of matrix square roots and the literature on its application to self-normalization. Section 14.2 extends the moment and exponential inequalities in Chap. 13 to multivariate self-

异端

The ,-Statistic and Studentized Statisticsiate .-distribution, Hotelling‘s .-statistic and the .-distribution, all derived from sampling theory of a normal (or multivariate normal) distribution with unknown variance (or covariance matrix). It then develops the asymptotic distributions of these self-normalized sample means even when the popu

outset

Pseudo-Maximization in Likelihood and Bayesian Inferencethe null hypothesis that the mean of a normal distribution is μ, when the variance ō. is unknown and estimated by the sample variance s.. In Sect. 17.1 we consider another class of self-normalized statistics, called . (GLR) statistics, which are extensions of likelihood ratio (LR) statistics (for te

cipher

crutch

Stein’s Method and Self-Normalized Berry–Esseen Inequalitymial approximations. In this chapter we give an overview of the use of Stein‘s method for normal approximations. We start with basic results on the Stein equations and their solutions and then prove several classical limit theorems and the Berry—Esseen inequality for self-normalized sums.

裙带关系

隐士

Pseudo-Maximization via Method of Mixtureslities for self-normalized processes. In Sect. 11.3 we describe a class of mixing density functions that are particularly useful for developing . and exponential inequalities for self-normalized processes, details of which are given in the next chapter.

Explosive