Premium
Bernstein polynomial estimation of a spectral density
Author(s) -
Kakizawa Yoshihide
Publication year - 2006
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2005.00465.x
Subject(s) - mathematics , estimator , kernel density estimation , bernstein polynomial , monte carlo method , kernel (algebra) , spectral density estimation , polynomial , density estimation , maximum entropy spectral estimation , regular polygon , statistics , mathematical analysis , combinatorics , geometry , fourier transform , principle of maximum entropy
. 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, | λ |/ π ), λ ∈ Π ≡ [− π , π ] 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.