Rates of strong uniform consistency for local least squares kernel regression estimators

2007 ◽  
Vol 77 (14) ◽  
pp. 1526-1534 ◽  
Author(s):  
David Blondin
Keyword(s):  
Least Squares ◽  
Kernel Regression ◽  
Uniform Consistency ◽  
Regression Estimators ◽  
Strong Uniform Consistency

Functional least squares estimators in an additive effects outliers model

1990 ◽  
Vol 48 (2) ◽  
pp. 299-319 ◽  
Author(s):  
Sunil K. Dhar
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Gaussian Process ◽  
Least Squares ◽  
Strong Consistency ◽  
Additive Effects ◽  
Uniform Consistency ◽  
Least Squares Estimators

AbstractConsider the additive effects outliers (A.O.) model where one observes , with The sequence of r.v.s is independent of and , are i.i.d. with d.f. , where the d.f.s Ln, n ≦ 0, are not necessarily known and εj's are i.i.d.. This paper discusses the asymptotic behavior of functional least squares estimators under the above model. Uniform consistency and uniform strong consistency of these estimators are proven. The weak convergence of these estimators to a Gaussian process and their asymptotic biases are also discussed under the above A.O. model.

LOCALLY WEIGHTED LEAST SQUARES KERNEL REGRESSION AND STATISTICAL EVALUATION OF LIDAR MEASUREMENTS

1996 ◽  
Vol 7 (4) ◽  
pp. 401-416 ◽  
Author(s):  
ULLA HOLST ◽  
OLA HÖSSJER ◽  
CLAES BJÖRKLUND ◽  
PÄR RAGNARSON ◽  
HANS EDNER
Keyword(s):  
Least Squares ◽  
Statistical Evaluation ◽  
Weighted Least Squares ◽  
Kernel Regression ◽  
Lidar Measurements
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