Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval

2010 ◽  
Vol 54 (2) ◽  
pp. 473-495 ◽  
Author(s):  
Masayuki Hirukawa
Keyword(s):  
Density Estimation ◽  
Bias Correction ◽  
Unit Interval ◽  
Kernel Type

scholarly journals Miscellanea Kernel-Type Density Estimation on the Unit Interval

Biometrika ◽  
2007 ◽  
Vol 94 (4) ◽  
pp. 977-984 ◽  
Author(s):  
M.C. Jones ◽  
D.A. Henderson
Keyword(s):  
Density Estimation ◽  
Unit Interval ◽  
Kernel Type

scholarly journals A concentration inequality for interval maps with an indifferent fixed point

2009 ◽  
Vol 29 (4) ◽  
pp. 1097-1117 ◽  
Author(s):  
J.-R. CHAZOTTES ◽  
P. COLLET ◽  
F. REDIG ◽  
E. VERBITSKIY
Keyword(s):  
Fixed Point ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Density Estimation ◽  
Kernel Density ◽  
Unit Interval ◽  
Empirical Measure ◽  
Concentration Inequality ◽  
Interval Maps ◽  
Correlation Properties

AbstractFor a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of n variables, K:[0,1]n→ℝ, which are separately Lipschitz. The proof is based on coupling and decay of correlation properties of the map. We also present applications of this inequality to the almost-sure central limit theorem, the kernel density estimation, the empirical measure and the periodogram.

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.

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