On the asymptotic Mean Square Error of L1 kernel estimates of smooth functions
1987; Elsevier BV; Volume: 51; Issue: 3 Linguagem: Inglês
10.1016/0021-9045(87)90034-7
ISSN1096-0430
Autores Tópico(s)Liver Disease Diagnosis and Treatment
ResumoRates of convergence of Mean Squared Error of convolution type estimators of regression functions or density functions in E ∞ are derived, employing L 1 kernel functions. The idea is to let the order of the kernel (number of vanishing moments) tend to infinity with increasing number of observations. In this setting, the rate n −1 is achieved if and only if the function to be estimated has a specific property. For a broad class of functions, the optimal rate is seen to be O( α n 1 2 n ) , where ( α n e ) xn ∼ n .
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