Nonparametric estimation of a probability density function and its derivatives. C-approach

被引：0
作者：
V. G. Alekseev
机构：
[1] Russian Academy of Sciences,Obukhov Institute of Atmospheric Physics
来源：
Optoelectronics, Instrumentation and Data Processing | 2009年 / 45卷 / 1期
关键词：
probability density function; nonparametric (kernel) estimator; uniform consistency of estimate with increasing sample size;
D O I：
10.1134/S8756699009010075
中图分类号：
学科分类号：
摘要：
Nonparametric (kernel) estimation of a probability density function f(x) for a sample of finite size is considered using the C-approach. The smoothness parameter β of the estimated probability density is introduced. For the case β > 2, it is shown that the convergence of the density estimate fn(x) to the function f(x) can be improved by using alternating-sign weight functions (higher-order weight functions). Estimation of the derivatives of a function is briefly considered using the same approach.
引用
收藏
页码：43 / 47
页数：4
相关论文
共 16 条
[1]  
Alexeev V. G.(2007)Nonparametric Estimation of a Probability Density Function and Its Derivatives: The Avtometriya 43 39-47
[2]  
Parzen E.(1962)-Approach Ann. Math. Statist. 33 1065-64
[3]  
Woodroofe M.(1967)On Estimation of a Probability Density Function and Mode Ann. Math. Statist. 38 475-22
[4]  
Wegman E. J.(1972)On the Maximum Deviation of the Sample Density Technometrics 14 533-undefined
[5]  
Silverman B. W.(1978)Nonparametric Probability Density Estimation: I. A Summary of Available Methods Ann. Statist. 6 177-undefined
[6]  
Khas’minskii R. Z.(1978)Weak and Strong Uniform Consistency of the Kernel Estimate of a Density and Its Derivatives Teor. Veroyatn. Primen. 23 824-undefined
[7]  
Schuster E. F.(1969)On the Lower-Bound Risks in Nonparametric Density Estimates in the Uniform Metric Ann. Math. Statist. 40 1187-undefined
[8]  
Kiefer J.(1961)Estimation of a Probability Density Function and Its Derivatives Pac. J. Math. 11 649-undefined
[9]  
Singh R. S.(1977)On Large Deviations of the Empiric D. F. of Vector Chance Variables and a Law of the Iterated Logarithm Ann. Statist. 5 394-undefined
[10]  
Alekseev V. G.(1973)Improvement on Some Known Nonparametric Uniformly Consistent Estimators of Derivatives of a Density Probl. Peredach. Inform. 9 42-undefined
12