56,154 research outputs found
Nonparametric Density Estimation for Positive Time Series
The Gaussian kernel density estimator is known to have substantial problems for bounded random variables with high density at the boundaries. For i.i.d. data several solutions have been put forward to solve this boundary problem. In this paper we propose the gamma kernel estimator as density estimator for positive data from a stationary ?-mixing process. We derive the mean integrated squared error, almost sure convergence and asymptotic normality. In a Monte Carlo study, where we generate data from an autoregressive conditional duration model and a stochastic volatility model, we find that the gamma kernel outperforms the local linear density estimator. An application to data from financial transaction durations, realized volatility and electricity price data is provided.Gamma kernel, nonparametric density estimation, mixing process, transaction durations, realised volatility.
Estimation in semi-parametric regression with non-stationary regressors
In this paper, we consider a partially linear model of the form
, , where is a
null recurrent Markov chain, is a sequence of either strictly
stationary or non-stationary regressors and is a stationary
sequence. We propose to estimate both and by a
semi-parametric least-squares (SLS) estimation method. Under certain
conditions, we then show that the proposed SLS estimator of is still
asymptotically normal with the same rate as for the case of stationary time
series. In addition, we also establish an asymptotic distribution for the
nonparametric estimator of the function . Some numerical examples are
provided to show that our theory and estimation method work well in practice.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ344 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Decompounding on compact Lie groups
Noncommutative harmonic analysis is used to solve a nonparametric estimation
problem stated in terms of compound Poisson processes on compact Lie groups.
This problem of decompounding is a generalization of a similar classical
problem. The proposed solution is based on a char- acteristic function method.
The treated problem is important to recent models of the physical inverse
problem of multiple scattering.Comment: 26 pages, 3 figures, 25 reference
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