An invariance principle for linear combinations of order statistics

Hölderian Invariance Principle for Hilbertian Linear Processes

Let (ξn)n≥1 be the polygonal partial sums processes built on the linear processes Xn = ∑ i≥0 ai( n−i), n ≥ 1, where ( i)i∈Z are i.i.d., centered random elements in some separable Hilbert space H and the ai’s are bounded linear operators H → H, with ∑i≥0‖ai‖ < ∞. We investigate functional central limit theorem for ξn in the Hölder spaces H o ρ(H) of functions x : [0, 1] → H such that ‖x(t+ h) − ...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Sure Invariance Principle for Multivariate Kolmogorov - Smirnov Statistics

Non-linear Bayesian prediction of generalized order statistics for liftime models

In this paper, we obtain  Bayesian prediction intervals as well as Bayes predictive estimators under square error loss for generalized order statistics when the distribution of the underlying population belongs to a family which includes several important distributions.

An invariance principle for random planar maps

We show a new invariance principle for the radius and other functionals of a class of conditioned ‘Boltzmann-Gibbs’distributed random planar maps. It improves over the more restrictive case of bipartite maps that was discussed in Marckert and Miermont (2006). As in the latter paper, we make use of a bijection between planar maps and a class of labelled multitype trees, due to Bouttier et al. (2...