scholarly journals Pointwise convergence rates and central limit theorems for kernel density estimators in linear processes

2006 ◽  
Vol 76 (16) ◽  
pp. 1756-1760 ◽  
Author(s):  
Anton Schick ◽  
Wolfgang Wefelmeyer
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Pointwise Convergence ◽  
Convergence Rates ◽  
Kernel Density ◽  
Central Limit Theorems ◽  
Linear Processes ◽  
Kernel Density Estimators ◽  
Density Estimators

Non-central limit theorems and convergence rates

2018 ◽  
Vol 95 ◽  
pp. 3-15 ◽  
Author(s):  
Vo Anh ◽  
Andriy Olenko ◽  
V. Vaskovych
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Convergence Rates ◽  
Central Limit Theorems

CENTRAL LIMIT THEOREMS FOR WEIGHTED SUMS OF LINEAR PROCESSES: LP -APPROXIMABILITY VERSUS BROWNIAN MOTION

2009 ◽  
Vol 25 (3) ◽  
pp. 748-763 ◽  
Author(s):  
Kairat T. Mynbaev
Keyword(s):  
Brownian Motion ◽  
Central Limit ◽  
Asymptotic Expansions ◽  
Limit Theorems ◽  
Stochastic Calculus ◽  
Central Limit Theorems ◽  
Weighted Sums ◽  
Linear Processes

Standardized slowly varying regressors are shown to be Lp-approximable. This fact allows us to provide alternative proofs of asymptotic expansions of nonstochastic quantities and central limit results due to P.C.B. Phillips, under a less stringent assumption on linear processes. The recourse to stochastic calculus related to Brownian motion can be completely dispensed with.

scholarly journals Nonparametric density estimators based on nonstationary absolutely regular random sequences

1996 ◽  
Vol 9 (3) ◽  
pp. 233-254 ◽  
Author(s):  
Michel Harel ◽  
Madan L. Puri
Keyword(s):  
Central Limit ◽  
Markov Processes ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Density Estimator ◽  
Random Sequences ◽  
Arma Processes ◽  
Density Estimators

In this paper, the central limit theorems for the density estimator and for the integrated square error are proved for the case when the underlying sequence of random variables is nonstationary. Applications to Markov processes and ARMA processes are provided.

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