TY - JOUR
T1 - Generalized Birnbaum-Saunders kernel density estimators and an analysis of financial data
AU - Marchant, Carolina
AU - Bertin, Karine
AU - Leiva, Víctor
AU - Saulo, Helton
N1 - Funding Information:
The authors wish to thank the Editor-in-Chief, Prof. Stanley Azen, an anonymous Associate Editor, and two anonymous referees for their comments on an earlier version of this manuscript, which resulted in this improved version. Carolina Marchant gratefully acknowledges financial support from a scholarship CONICYT of the Chilean government. Research work of Karine Bertin was partially supported by grant FONDECYT 1090285 and by “ Stochastic Analysis Research Network ”, grant ACT1112 CONICYT-PIA, from the Chilean government. Research work of Víctor Leiva was partially supported by grant FONDECYT 1120879 from the Chilean government. Helton Saulo gratefully acknowledges financial support from CAPES of the Brazilian government.
PY - 2013
Y1 - 2013
N2 - The kernel method is a nonparametric procedure used to estimate densities with support in R. When nonnegative data are modeled, the classical kernel density estimator presents a bias problem in the neighborhood of zero. Several methods have been developed to reduce this bias, which include the boundary kernel, data transformation and reflection methods. An alternative proposal is to use kernel estimators based on distributions with nonnegative support, as is the case of the Birnbaum-Saunders (BS), gamma, inverse Gaussian and lognormal models. Generalized BS (GBS) distributions have received considerable attention, due to their properties and their flexibility in modeling different types of data. In this paper, we propose, characterize and implement the kernel method based on GBS distributions to estimate densities with nonnegative support. In addition, we provide a simple method to choose the corresponding bandwidth. In order to evaluate the performance of these new estimators, we conduct a Monte Carlo simulation study. The obtained results are illustrated by analyzing financial real data.
AB - The kernel method is a nonparametric procedure used to estimate densities with support in R. When nonnegative data are modeled, the classical kernel density estimator presents a bias problem in the neighborhood of zero. Several methods have been developed to reduce this bias, which include the boundary kernel, data transformation and reflection methods. An alternative proposal is to use kernel estimators based on distributions with nonnegative support, as is the case of the Birnbaum-Saunders (BS), gamma, inverse Gaussian and lognormal models. Generalized BS (GBS) distributions have received considerable attention, due to their properties and their flexibility in modeling different types of data. In this paper, we propose, characterize and implement the kernel method based on GBS distributions to estimate densities with nonnegative support. In addition, we provide a simple method to choose the corresponding bandwidth. In order to evaluate the performance of these new estimators, we conduct a Monte Carlo simulation study. The obtained results are illustrated by analyzing financial real data.
KW - High frequency data
KW - Kernel nonparametric method
KW - Kurtosis
KW - Monte Carlo method
KW - R statistical computation language
UR - http://www.scopus.com/inward/record.url?scp=84875918138&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2013.01.013
DO - 10.1016/j.csda.2013.01.013
M3 - Article
AN - SCOPUS:84875918138
SN - 0167-9473
VL - 63
SP - 1
EP - 15
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
ER -