اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدStrong Approximation of Empirical Copula Processes by Gaussian Processes
227
0
0.0
(
0
)
تأليف
Salim Bouzebda
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm.
قيم البحث
اقرأ أيضاً
We derive strong approximations to the supremum of the non-centered empirical process indexed by a possibly unbounded VC-type class of functions by the suprema of the Gaussian and bootstrap processes. The bounds of these approximations are non-asympt
otic, which allows us to work with classes of functions whose complexity increases with the sample size. The construction of couplings is not of the Hungarian type and is instead based on the Slepian-Stein methods and Gaussian comparison inequalities. The increasing complexity of classes of functions and non-centrality of the processes make the results useful for applications in modern nonparametric statistics (Gin{e} and Nickl, 2015), in particular allowing us to study the power properties of nonparametric tests using Gaussian and bootstrap approximations.
The purpose of this note is to provide an approximation for the generalized bootstrapped empirical process achieving the rate in Kolmos et al. (1975). The proof is based on much the same arguments as in Horvath et al. (2000). As a consequence, we est
ablish an approximation of the bootstrapped kernel-type density estimator
We consider the nonparametric functional estimation of the drift of a Gaussian process via minimax and Bayes estimators. In this context, we construct superefficient estimators of Stein type for such drifts using the Malliavin integration by parts fo
rmula and superharmonic functionals on Gaussian space. Our results are illustrated by numerical simulations and extend the construction of James--Stein type estimators for Gaussian processes by Berger and Wolpert [J. Multivariate Anal. 13 (1983) 401--424].
We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares si
nce this sum is often used for estimating the long-memory parameter. We show that the limit is not Gaussian but can be expressed using the non-Gaussian Rosenblatt process defined as a Wiener It^o integral of order 2. This happens even if the original process is defined through a Hermite polynomial of order higher than 2.
In this contribution we introduce weakly locally stationary time series through the local approximation of the non-stationary covariance structure by a stationary one. This allows us to define autoregression coefficients in a non-stationary context,
which, in the particular case of a locally stationary Time Varying Autoregressive (TVAR) process, coincide with the generating coefficients. We provide and study an estimator of the time varying autoregression coefficients in a general setting. The proposed estimator of these coefficients enjoys an optimal minimax convergence rate under limited smoothness conditions. In a second step, using a bias reduction technique, we derive a minimax-rate estimator for arbitrarily smooth time-evolving coefficients, which outperforms the previous one for large data sets. In turn, for TVAR processes, the predictor derived from the estimator exhibits an optimal minimax prediction rate.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
