Bernstein polynomial estimation of a spectral density
We consider an application of Bernstein polynomials for estimating a spectral density of a stationary process. The resulting estimator can be interpreted as a convex combination of the (Daniell) kernel spectral density estimators at m points, the coefficients of which are probabilities of the binomial distribution bin(m - 1, |lambda|/pi), lambda is an element of pi == [ - pi, pi] being the frequency where the spectral density estimation is made. Several asymptotic properties are investigated under conditions of the degree m. We also discuss methods of data-driven choice of the degree m. For a comparison with the ordinary kernel method, a Monte Carlo simulation illustrates our methodology and examines its performance in small sample. Copyright 2005 Blackwell Publishing Ltd.
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Volume (Year): 27 (2006)
Issue (Month): 2 (03)
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