Asymptotic behavior of the logarithm of the likelihood function when the spectral density has polynomial zeros

1984 ◽  
Vol 25 (3) ◽  
pp. 1113-1125
Author(s):  
M. S. Ginovyan
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Density ◽  
Likelihood Function ◽  
Polynomial Zeros

Asymptotic Behavior of Temporal Aggregates in the Frequency Domain

2013 ◽  
Vol 5 (1) ◽  
pp. 47-60 ◽  
Author(s):  
Uwe Hassler ◽  
Henghsiu Tsai
Keyword(s):  
Time Series ◽  
Asymptotic Behavior ◽  
Spectral Density ◽  
Frequency Domain ◽  
Fractional Integration ◽  
Integrated Processes

AbstractThe classical aggregation result by Tiao (1972, Asymptotic Behavior of Temporal Aggregates of Time Series, Biometrika 59, 525–531) is generalized for a weak set of assumptions. The innovations driving the integrated processes are only required to be stationary with integrable spectral density. The derivation is settled in the frequency domain. In case of fractional integration, it is demonstrated that the order of integration is preserved with growing aggregation under the same set of assumptions.

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.

scholarly journals Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Ralf Zimmermann
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Gaussian Processes ◽  
Likelihood Function ◽  
Covariance Structure ◽  
Kriging Model ◽  
Correlation Matrices ◽  
Covariance Functions ◽  
Method Of Maximum Likelihood ◽  
Model Training

The covariance structure of spatial Gaussian predictors (aka Kriging predictors) is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood. In this work, the asymptotic behavior of the maximum likelihood of spatial Gaussian predictor models as a function of its hyperparameters is investigated theoretically. Asymptotic sandwich bounds for the maximum likelihood function in terms of the condition number of the associated covariance matrix are established. As a consequence, the main result is obtained:optimally trained nondegenerate spatial Gaussian processes cannot feature arbitrary ill-conditioned correlation matrices. The implication of this theorem on Kriging hyperparameter optimization is exposed. A nonartificial example is presented, where maximum likelihood-based Kriging model training is necessarily bound to fail.

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.

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