scholarly journals Invariant density estimation for a reflected diffusion using an Euler scheme

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Patrick Cattiaux ◽  
José R. León ◽  
Clémentine Prieur
Keyword(s):  
Density Estimation ◽  
Error Bound ◽  
Kernel Estimator ◽  
Euler Scheme ◽  
Compact Domain ◽  
Invariant Density ◽  
Reflected Diffusion

AbstractWe give an explicit error bound between the invariant density of an elliptic reflected diffusion in a smooth compact domain and the kernel estimator built on the symmetric Euler scheme introduced in [

Invariant density estimation

1976 ◽  
Vol 81 (4) ◽  
pp. 315-324 ◽  
Author(s):  
Wolfgang Wertz
Keyword(s):  
Density Estimation ◽  
Invariant Density

scholarly journals One Value of Smoothing Parameter vs Interval of Smoothing Parameter Values in Kernel Density Estimation

2018 ◽  
Vol 6 (332) ◽  
pp. 73-86
Author(s):  
Aleksandra Katarzyna Baszczyńska
Keyword(s):  
Density Function ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Ad Hoc ◽  
Kernel Density ◽  
Kernel Estimator ◽  
Smoothing Parameter ◽  
Smoothing Parameter Selection ◽  
Starting Point ◽  
Parameter Values

Ad hoc methods in the choice of smoothing parameter in kernel density estimation, al­though often used in practice due to their simplicity and hence the calculated efficiency, are char­acterized by quite big error. The value of the smoothing parameter chosen by Silverman method is close to optimal value only when the density function in population is the normal one. Therefore, this method is mainly used at the initial stage of determining a kernel estimator and can be used only as a starting point for further exploration of the smoothing parameter value. This paper pre­sents ad hoc methods for determining the smoothing parameter. Moreover, the interval of smooth­ing parameter values is proposed in the estimation of kernel density function. Basing on the results of simulation studies, the properties of smoothing parameter selection methods are discussed.

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 Integration by Parts for Point Processes and Monte Carlo Estimation

2007 ◽  
Vol 44 (3) ◽  
pp. 806-823 ◽  
Author(s):  
Nicolas Privault ◽  
Xiao Wei
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Lebesgue Measure ◽  
Density Estimation ◽  
Stochastic Models ◽  
Point Processes ◽  
Kernel Estimator ◽  
Integration By Parts ◽  
Bandwidth Parameter ◽  
Monte Carlo Estimation

We develop an integration by parts technique for point processes, with application to the computation of sensitivities via Monte Carlo simulations in stochastic models with jumps. The method is applied to density estimation with respect to the Lebesgue measure via a modified kernel estimator which is less sensitive to variations of the bandwidth parameter than standard kernel estimators. This applies to random variables whose densities are not analytically known and requires the knowledge of the point process jump times.

scholarly journals Integration by Parts for Point Processes and Monte Carlo Estimation

2007 ◽  
Vol 44 (03) ◽  
pp. 806-823
Author(s):  
Nicolas Privault ◽  
Xiao Wei
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Lebesgue Measure ◽  
Density Estimation ◽  
Stochastic Models ◽  
Point Processes ◽  
Kernel Estimator ◽  
Integration By Parts ◽  
Bandwidth Parameter ◽  
Monte Carlo Estimation

We develop an integration by parts technique for point processes, with application to the computation of sensitivities via Monte Carlo simulations in stochastic models with jumps. The method is applied to density estimation with respect to the Lebesgue measure via a modified kernel estimator which is less sensitive to variations of the bandwidth parameter than standard kernel estimators. This applies to random variables whose densities are not analytically known and requires the knowledge of the point process jump times.

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