Dependence Between Histogram Parameters and the Kernel Estimate of a Unimodal Probability Density

2019 ◽  
Vol 62 (9) ◽  
pp. 747-753 ◽  
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Kernel Estimate

On Estimation of a Functional of a Probability Density Function

1993 ◽  
Vol 43 (1-2) ◽  
pp. 13-24
Author(s):  
L. O. Odongo ◽  
M. Samanta
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Mean Square Error ◽  
Regularity Conditions ◽  
Mean Square ◽  
Simulation Studies ◽  
Kernel Estimate ◽  
Primary 62G07 ◽  
The Mean

The problem of estimating the integral of the square of a probability density function is considered, It is shown that under some regularity conditions the kernel estimate of this functional is asymptotically normally distributed. An expression for the smoothing parameter that minimizes the mean square error of the estimate is derived. Results of simulation studies are included. AMS (1980) Subject Classification: Primary 62G07 Secondary 60FOS.

Trimmed jackknife kernel estimate for the probability density function

1991 ◽  
Vol 12 (1) ◽  
pp. 19-26 ◽  
Author(s):  
Jagdish S. Rustagi ◽  
Walfredo R. Javier ◽  
Jose S. Victoria
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Kernel Estimate

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

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