Linear Functions of Concomitants of Order Statistics with Application to Nonparametric Estimation of a Regression Function

1981 ◽  
Vol 76 (375) ◽  
pp. 658-662 ◽  
Author(s):  
Shie-Shien Yang
Keyword(s):  
Order Statistics ◽  
Nonparametric Estimation ◽  
Regression Function ◽  
Linear Functions ◽  
Concomitants Of Order Statistics

scholarly journals Optimal designs for nonparametric estimation of zeros of regression functions

2012 ◽  
Vol 51 (1) ◽  
pp. 55-65
Author(s):  
Zdeněk Hlávka
Keyword(s):  
Confidence Interval ◽  
Nonparametric Estimation ◽  
Regression Function ◽  
Optimal Designs ◽  
Nonparametric Estimators ◽  
Regression Functions ◽  
Expected Width

ABSTRACT We investigate nonparametric estimators of zeros of a regression function and its derivatives and we derive the distribution of design points minimizing the expected width of a confidence interval and the expected variance of the proposed estimator.

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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