2 results
On estimation of the integrals of certain functions of spectral density
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- Journal:
- Journal of Applied Probability / Volume 17 / Issue 1 / March 1980
- Published online by Cambridge University Press:
- 14 July 2016, pp. 73-83
- Print publication:
- March 1980
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Let g(x) be the spectral density of a Gaussian stationary process. Then, for each continuous function ψ (x) we shall give an estimator of
whose asymptotic variance is O(n–1), where Φ(·) is an appropriate known function. Also we shall investigate the asymptotic properties of its estimator.
whose asymptotic variance is On estimation of parameters of Gaussian stationary processes
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- Journal:
- Journal of Applied Probability / Volume 16 / Issue 3 / September 1979
- Published online by Cambridge University Press:
- 14 July 2016, pp. 575-591
- Print publication:
- September 1979
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In fitting a certain parametric family of spectral densities fθ (x) to a Gaussian stationary process with the true spectral density g (x), we propose two estimators of θ, say
by minimizing two criteria D1 (·), D2(·) respectively, which measure the nearness of fθ (x) to g (x). Then we investigate some asymptotic behavior of 
with respect to efficiency and robustness.
by minimizing two criteria 
with respect to efficiency and robustness.