Smooth estimators of distribution and density functions
Computational Statistics & Data Analysis - Second special issue on optimization techniques in statistics
Nonparametric econometrics
Beta kernel estimators for density functions
Computational Statistics & Data Analysis
New approaches to nonparametric density estimation and selection of smoothing parameters
Computational Statistics & Data Analysis
Generalized Birnbaum-Saunders kernel density estimators and an analysis of financial data
Computational Statistics & Data Analysis
Nonparametric kernel density estimation near the boundary
Computational Statistics & Data Analysis
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The Gaussian kernel density estimator is known to have substantial problems for bounded random variables with high density at the boundaries. For independent and identically distributed data, several solutions have been put forward to solve this boundary problem. In this paper, we propose the gamma kernel estimator as a density estimator for positive time series data from a stationary @a-mixing process. We derive the mean (integrated) squared error and asymptotic normality. In a Monte Carlo simulation, we generate data from an autoregressive conditional duration model and a stochastic volatility model. We study the local and global behavior of the estimator and we find that the gamma kernel estimator outperforms the local linear density estimator and the Gaussian kernel estimator based on log-transformed data. We also illustrate the good performance of the h-block cross-validation method as a bandwidth selection procedure. An application to data from financial transaction durations and realized volatility is provided.