scholarly journals Asymptotic Normality of Nearest Neighbor Regression Function Estimates Based on Nonstationary Dependent Observations

1995 ◽  
Vol 15 (3-4) ◽  
pp. 255-290
Author(s):  
Michel Harel ◽  
Madan L. Puri
Keyword(s):  
Asymptotic Normality ◽  
Nearest Neighbor ◽  
Regression Function ◽  
Dependent Observations

scholarly journals NONPARAMETRIC ESTIMATION WITH AGGREGATED DATA

2002 ◽  
Vol 18 (2) ◽  
pp. 420-468 ◽  
Author(s):  
Oliver Linton ◽  
Yoon-Jae Whang
Keyword(s):  
Monte Carlo ◽  
Characteristic Function ◽  
Asymptotic Normality ◽  
Nonparametric Estimation ◽  
Regression Function ◽  
Rates Of Convergence ◽  
Monte Carlo Experiment ◽  
Aggregated Data ◽  
Practical Performance ◽  
Consistency And Asymptotic Normality

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intrafamily component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behavior of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experiment.

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