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On construction of confidence intervals for a mean of dependent data

Jan Ćwik, Jan Mielniczuk (2001)

Discussiones Mathematicae Probability and Statistics

In the report, the performance of several methods of constructing confidence intervals for a mean of stationary sequence is investigated using extensive simulation study. The studied approaches are sample reuse block methods which do not resort to bootstrap. It turns out that the performance of some known methods strongly depends on a model under consideration and on whether a two-sided or one-sided interval is used. Among the methods studied, the block method based on weak convergence result by...

On the asymptotic form of convex hulls of Gaussian random fields

Youri Davydov, Vygantas Paulauskas (2014)

Open Mathematics

We consider a centered Gaussian random field X = X t : t ∈ T with values in a Banach space 𝔹 defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution of X t is independent of t. We consider the asymptotic behavior of closed convex hulls W n = convX t : t ∈ T n, where (T n) is an increasing sequence of subsets of T. We show that under some conditions of weak dependence for the random field under consideration and some sequence (b n)n≥1 with probability 1, (in the sense...

On the consistency of sieve bootstrap prediction intervals for stationary time series

Roman Różański, Adam Zagdański (2004)

Discussiones Mathematicae Probability and Statistics

In the article, we consider construction of prediction intervals for stationary time series using Bühlmann's [8], [9] sieve bootstrapapproach. Basic theoretical properties concerning consistency are proved. We extend the results obtained earlier by Stine [21], Masarotto and Grigoletto [13] for an autoregressive time series of finite order to the rich class of linear and invertible stationary models. Finite sample performance of the constructed intervals is investigated by computer simulations.

One Bootstrap suffices to generate sharp uniform bounds in functional estimation

Paul Deheuvels (2011)

Kybernetika

We consider, in the framework of multidimensional observations, nonparametric functional estimators, which include, as special cases, the Akaike–Parzen–Rosenblatt kernel density estimators ([1, 18, 20]), and the Nadaraya–Watson kernel regression estimators ([16, 22]). We evaluate the sup-norm, over a given set 𝐈 , of the difference between the estimator and a non-random functional centering factor (which reduces to the estimator mean for kernel density estimation). We show that, under suitable general...

Ordenes de convergencia para las aproximaciones normal y bootstrap en estimación no paramétrica de la función de densidad.

Ricardo Cao Abad (1990)

Trabajos de Estadística

Este artículos concierne las distribuciones usadas para construir intervalos de confianza para la función de densidad en una situación no paramétrica. Se comparan los órdenes de convergencia para el límite normal, su aproximación "plug in" y el método bootstrap. Se deduce que el bootstrap se comporta mejor que las otras dos aproximaciones tanto en su forma clásica como con la aproximación bootstrap normal.

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