On estimation of parameters of Gaussian stationary processes

1979 ◽  
Vol 16 (3) ◽  
pp. 575-591 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Density ◽  
Stationary Process ◽  
Parametric Family ◽  
Stationary Processes ◽  
Estimation Of Parameters ◽  
Spectral Densities ◽  
Gaussian Stationary Process

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.

On estimation of parameters of Gaussian stationary processes

1979 ◽  
Vol 16 (03) ◽  
pp. 575-591 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Density ◽  
Stationary Process ◽  
Parametric Family ◽  
Stationary Processes ◽  
Estimation Of Parameters ◽  
Spectral Densities ◽  
Gaussian Stationary Process

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 D 1 (·), D 2(·) respectively, which measure the nearness of fθ (x) to g (x). Then we investigate some asymptotic behavior of with respect to efficiency and robustness.

Non-Stationary Processes and Spectrum

1968 ◽  
Vol 20 ◽  
pp. 1203-1206 ◽  
Author(s):  
K. Nagabhushanam ◽  
C. S. K. Bhagavan
Keyword(s):  
Spectral Density ◽  
Density Function ◽  
Stationary Process ◽  
Spectral Density Function ◽  
Stationary Processes ◽  
Gaussian Stationary Process ◽  
Discrete Parameter ◽  
Image Position

In 1964, L. J. Herbst (3) introduced the generalized spectral density Function1for a non-stationary process {X(t)} denned by1where {η(t)} is a real Gaussian stationary process of discrete parameter and independent variates, the (a;)'s and (σj)'s being constants, the latter, which are ordered in time, having their moduli less than a positive number M.

On estimation of the integrals of certain functions of spectral density

1980 ◽  
Vol 17 (01) ◽  
pp. 73-83 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Continuous Function ◽  
Spectral Density ◽  
Stationary Process ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Gaussian Stationary Process

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.

On estimation of the integrals of certain functions of spectral density

1980 ◽  
Vol 17 (1) ◽  
pp. 73-83 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Continuous Function ◽  
Spectral Density ◽  
Stationary Process ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Gaussian Stationary Process

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.

scholarly journals On a Necessary Condition for the Sample Path Continuity of Weakly Stationary Processes

1970 ◽  
Vol 38 ◽  
pp. 103-111 ◽  
Author(s):  
Izumi Kubo
Keyword(s):  
Distribution Function ◽  
Asymptotic Behavior ◽  
Spectral Distribution ◽  
Covariance Function ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Sample Path ◽  
Necessary Condition ◽  
Stationary Processes ◽  
Spectral Distribution Function

We shall discuss the sample path continuity of a stationary process assuming that the spectral distribution function F(λ) is given. Many kinds of sufficient conditions have been given in terms of the covariance function or the asymptotic behavior of the spectral distribution function.

Simple trigonometric models for narrow-band stationary processes

1982 ◽  
Vol 19 (A) ◽  
pp. 333-343
Author(s):  
A. M. Hasofer
Keyword(s):  
Stationary Process ◽  
Finite Interval ◽  
Narrow Band ◽  
Stationary Processes ◽  
Gaussian Stationary Process ◽  
Trigonometric Sum

Over a finite interval, a Gaussian stationary process can be approximated by a finite trigonometric sum, and the error introduced by the approximation can be exactly bounded, as far as the distribution of the upper tail of the maximum is concerned. A simple case is exhibited, where a narrow band process is well approximated by means of a two-term trigonometric representation.

Asymptotic properties of the periodogram of a discrete stationary process

1967 ◽  
Vol 4 (03) ◽  
pp. 508-528 ◽  
Author(s):  
Richard A. Olshen
Keyword(s):  
Stochastic Process ◽  
Spectral Density ◽  
Stationary Process ◽  
Asymptotic Properties ◽  
Spectral Densities ◽  
Image Position ◽  
Erratic Behavior

Suppose x 1,…, xN are indefinitely many observations on a stochastic process which is weakly stationary with spectral density f(λ), – π ≦ λ ≦ π. An asymptotically unbiased, and to that extent plausible, estimate of 4rf(λ)is the periodogram Yet the periodograms of processes which possess spectral densities are notoriously subject to erratic behavior.

Simple trigonometric models for narrow-band stationary processes

1982 ◽  
Vol 19 (A) ◽  
pp. 333-343 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Stationary Process ◽  
Finite Interval ◽  
Narrow Band ◽  
Stationary Processes ◽  
Gaussian Stationary Process ◽  
Trigonometric Sum

Over a finite interval, a Gaussian stationary process can be approximated by a finite trigonometric sum, and the error introduced by the approximation can be exactly bounded, as far as the distribution of the upper tail of the maximum is concerned. A simple case is exhibited, where a narrow band process is well approximated by means of a two-term trigonometric representation.

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