BIAS CORRECTION AT END POINTS IN KERNEL DENSITY ESTIMATION

2021 ◽  
Vol 10 (12) ◽  
pp. 3515-3531
Author(s):  
H. Bouredji ◽  
A. Sayah
Keyword(s):  
Monte Carlo ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Bias Correction ◽  
Kernel Density ◽  
Real Data ◽  
Boundary Region ◽  
Finite Sample ◽  
New Approach ◽  
The Right

In this paper, we propose a new approach of boundary correction for kernel density estimation with the support $[0,1]$, in particular at the right endpoints and we derive the theoretical properties of this new estimator and show that it asymptotically reduce the order of bias at the boundary region, whereas the order of variance remains unchanged. Our Monte Carlo simulations demonstrate the good finite sample performance of our proposed estimator. Two examples with real data are provided.

Body tail adaptive kernel density estimation for nonnegative heavy-tailed data

2021 ◽  
Vol 27 (1) ◽  
pp. 57-69
Author(s):  
Yasmina Ziane ◽  
Nabil Zougab ◽  
Smail Adjabi
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Kernel Estimator ◽  
Real Data ◽  
Density Region ◽  
Data Set ◽  
Bandwidth Parameter ◽  
Adaptive Kernel ◽  
Heavy Tailed

Abstract In this paper, we consider the procedure for deriving variable bandwidth in univariate kernel density estimation for nonnegative heavy-tailed (HT) data. These procedures consider the Birnbaum–Saunders power-exponential (BS-PE) kernel estimator and the bayesian approach that treats the adaptive bandwidths. We adapt an algorithm that subdivides the HT data set into two regions, high density region (HDR) and low-density region (LDR), and we assign a bandwidth parameter for each region. They are derived by using a Monte Carlo Markov chain (MCMC) sampling algorithm. A series of simulation studies and real data are realized for evaluating the performance of a procedure proposed.

scholarly journals NEW APPROACH FOR BANDWIDTH SELECTION IN THE KERNEL DENSITY ESTIMATION BASED ON

2018 ◽  
Vol 51 (1) ◽  
pp. 57-83
Author(s):  
Hamza Dhaker ◽  
◽  
Papa Ngom ◽  
El Hadji Deme ◽  
Malick Mbodj ◽  
...  
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Bandwidth Selection ◽  
Kernel Density ◽  
New Approach

scholarly journals Speaking Stata: Density Probability Plots

2005 ◽  
Vol 5 (2) ◽  
pp. 259-273 ◽  
Author(s):  
Nicholas J. Cox
Keyword(s):  
Order Statistics ◽  
Density Function ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Real Data ◽  
Continuous Variable ◽  
Quantile Plots ◽  
Probability Plots ◽  
Parameter Values

Density probability plots show two guesses at the density function of a continuous variable, given a data sample. The first guess is the density function of a specified distribution (e.g., normal, exponential, gamma, etc.) with appropriate parameter values plugged in. The second guess is the same density function evaluated at quantiles corresponding to plotting positions associated with the sample's order statistics. If the specified distribution fits well, the two guesses will be close. Such plots, suggested by Jones and Daly in 1995, are explained and discussed with examples from simulated and real data. Comparisons are made with histograms, kernel density estimation, and quantile–quantile plots.

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