Semiparametric estimation for stationary processes whose spectra have an unknown pole
| dc.creator | Hidalgo, Javier | |
| dc.date | 2005-08-17 | |
| dc.date.accessioned | 2026-07-07T08:07:10Z | |
| dc.date.available | 2026-07-07T08:07:10Z | |
| dc.description | We consider the estimation of the location of the pole and memory parameter, λ^0 and α, respectively, of covariance stationary linear processes whose spectral density function f(λ) satisfies f(λ)\sim C| λ-λ^0| ^{-α} in a neighborhood of λ^0. We define a consistent estimator of λ^0 and derive its limit distribution Z_{λ^0}. As in related optimization problems, when the true parameter value can lie on the boundary of the parameter space, we show that Z_{λ^0} is distributed as a normal random variable when λ^0\in (0,π), whereas for λ^0=0 or π, Z_{λ^0} is a mixture of discrete and continuous random variables with weights equal to 1/2. More specifically, when λ^0=0, Z_{λ^0} is distributed as a normal random variable truncated at zero. Moreover, we describe and examine a two-step estimator of the memory parameter α, showing that neither its limit distribution nor its rate of convergence is affected by the estimation of λ^0. Thus, we reinforce and extend previous results with respect to the estimation of αwhen λ^0 is assumed to be known a priori. A small Monte Carlo study is included to illustrate the finite sample performance of our estimators. | |
| dc.description | Published at http://dx.doi.org/10.1214/009053605000000318 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0508317 | |
| dc.identifier | http://arxiv.org/abs/math/0508317 | |
| dc.identifier | Annals of Statistics 2005, Vol. 33, No. 4, 1843-1889 | |
| dc.identifier | doi:10.1214/009053605000000318 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130854 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62M15 (Primary) 62G05, 62G20 (Secondary) | |
| dc.title | Semiparametric estimation for stationary processes whose spectra have an unknown pole | |
| dc.type | text |