On the asymptotic normality of kernel regression estimators of the mode in the nonparametric random design model

2003 ◽  
Vol 115 (1) ◽  
pp. 123-144 ◽  
Author(s):  
Klaus Ziegler
Keyword(s):  
Asymptotic Normality ◽  
Kernel Regression ◽  
Design Model ◽  
Random Design ◽  
Regression Estimators

scholarly journals UNIFORM CONVERGENCE RATES OVER MAXIMAL DOMAINS IN STRUCTURAL NONPARAMETRIC COINTEGRATING REGRESSION

2017 ◽  
Vol 33 (6) ◽  
pp. 1387-1417 ◽  
Author(s):  
James A. Duffy
Keyword(s):  
Regression Model ◽  
Uniform Convergence ◽  
Lower Order ◽  
Unit Root ◽  
Autoregressive Model ◽  
Convergence Rates ◽  
Kernel Regression ◽  
Infinite Variance ◽  
Standard Unit ◽  
Regression Estimators

This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these rates apply is much wider than the domains that have been considered in the existing literature, and can be chosen so as to contain as large a fraction of the sample as desired in the limit. Second, our results allow the regression disturbance to be serially correlated, and cross-correlated with the regressor; previous work on this problem (of obtaining uniform rates) having been confined entirely to the setting of an exogenous regressor. Third, we permit the bandwidth to be data-dependent, requiring it to satisfy only certain weak asymptotic shrinkage conditions. Our assumptions on the regressor process are consistent with a very broad range of departures from the standard unit root autoregressive model, allowing the regressor to be fractionally integrated, and to have an infinite variance (and even infinite lower-order moments).

Asymptotic normality of regression estimators with long memory errors

1996 ◽  
Vol 29 (4) ◽  
pp. 317-335 ◽  
Author(s):  
Liudas Giraitis ◽  
Hira L Koul ◽  
Donatas Surgailis
Keyword(s):  
Asymptotic Normality ◽  
Long Memory ◽  
Memory Errors ◽  
Regression Estimators

Kernel regression estimators for signal recovery

1997 ◽  
Vol 31 (3) ◽  
pp. 185-198 ◽  
Author(s):  
M. Pawlak ◽  
U. Stadtmüller
Keyword(s):  
Kernel Regression ◽  
Signal Recovery ◽  
Regression Estimators
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