| Dewey Class |
519.2 |
| Titolo |
Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series ([EBook] /) / by K. Dzhaparidze. |
| Autore |
Dzhaparidze, K. |
| Other name(s) |
SpringerLink (Online service) |
| Pubblicazione |
New York, NY : : Springer New York, , 1986. |
| Physical Details |
324 p. : online resource. |
| Serie |
Springer Series in Statistics 0172-7397 |
| ISBN |
9781461248422 |
| Summary Note |
. . ) (under the assumption that the spectral density exists). For this reason, a vast amount of periodical and monographic literature is devoted to the nonparametric statistical problem of estimating the function tJ( T) and especially that of leA) (see, for example, the books [4,21,22,26,56,77,137,139,140,]). However, the empirical value t;; of the spectral density I obtained by applying a certain statistical procedure to the observed values of the variables Xl' . . . , X , usually depends in n a complicated manner on the cyclic frequency). . This fact often presents difficulties in applying the obtained estimate t;; of the function I to the solution of specific problems rela ted to the process X . Theref ore, in practice, the t obtained values of the estimator t;; (or an estimator of the covariance function tJ~( T» are almost always "smoothed," i. e. , are approximated by values of a certain sufficiently simple function 1 = 1.: |
| Contents note |
I Properties of Maximum Likelihood Function for a Gaussian Time Series -- 1. General Expression for the log Likelihood -- 2. Asymptotic Expression for the “Principal Part” of the log Likelihood -- 3. The Asymptotic Differentiability of Gaussian Distributions with Spectral Densities Separated from Zero -- 4. The Asymptotic Differentiability of Gaussian Distributions with Spectral Densities Possessing Fixed Zeros -- Appendix 1 -- Appendix 2 -- Appendix 3. Remarks and Bibliography -- II Estimation of Parameters by Means of P. Whittle’s Method -- 1. Asymptotic Maximum Likelihood Estimators -- 2. Properties of Asymptotic Maximum Likelihood Estimators in the Case of Strictly Positive Spectral Density -- 3. Consistency, Asymptotic Normality, and Asymptotic Efficiency of the Estimator $$\mathop \theta \limits \sim $$ in the Case of Spectral Density Possessing Fixed Zeros -- 4. Examples of Determination of Asymptotic Maximum Likelihood Estimators -- 5. Asymptotic Maximum Likelihood Estimator of the Spectrum of Processes Distorted by “White Noise” -- 6. Least-Squares Estimation of Parameters of a Spectrum of a Linear Process -- 7. Estimation by Means of the Whittle Method of Spectrum Parameters of General Processes Satisfying the Strong Mixing Condition -- Appendix 1 -- Appendix 2 -- Appendix 3. Remarks and Bibliography -- III Simplified Estimators Possessing “Nice” Asymptotic Properties -- 1. Asymptotic Properties of Simplified Estimators -- 2. Examples of Preliminary Consistent Estimators -- 3. Examples of Constructing Simplified Estimators -- Appendix 1. Remarks and Bibliography -- IV Testing Hypotheses on Spectrum Parameters of a Gaussian Time Series -- 1. Testing Simple Hypotheses -- 2. Testing Composite Hypotheses (The Case of a Sequence of General “Asymptotically Differentiable Experiments”) -- 3. Testing of Composite Hypothesis about a Parameter of a Spectrum of a Gaussian Time Series -- Appendix 1. Remarks and Bibliography -- V Goodness-of-Fit Tests for Testing the Hypothesis about the Spectrum of Linear Processes -- 1. A Class of Goodness-of-Fit Tests for Testing a Simple Hypothesis about the Spectrum of Linear Processes -- 2. X2 Test for Testing a Simple Hypothesis about the Spectrum of a Linear Process -- 3. Goodness-of-Fit Test for Testing Composite Hypotheses about the Spectrum of a Linear Process -- Appendix 1. Remarks and Bibliography. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-1-4612-4842-2 |
| Link alle Opere Legate |
Riferimenti soggetto: .
Applications of Mathematics .
Applied mathematics .
Engineering mathematics .
Mathematics .
Probabilities .
Probability theory and stochastic processes .
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