Asymptotic Form of the Covariance Matrix of Likelihood-Based Estimator in Multidimensional Linear System Model for the Case of Infinity Number of Nuisance Parameters
This article is devoted to the synthesis and analysis of the quality of the statistical estimate of parameters of a multidimensional linear system (MLS) with one input and <i>m</i> outputs. A nontrivial case is investigated when the one-dimensional input signal of MLS is a deterministic...
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MDPI AG
2024-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/3/473 |
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| author | Alexander Varypaev |
| author_facet | Alexander Varypaev |
| author_sort | Alexander Varypaev |
| collection | DOAJ |
| description | This article is devoted to the synthesis and analysis of the quality of the statistical estimate of parameters of a multidimensional linear system (MLS) with one input and <i>m</i> outputs. A nontrivial case is investigated when the one-dimensional input signal of MLS is a deterministic process, the values of which are unknown nuisance parameters. The estimate is based only on observations of MLS output signals distorted by random Gaussian stationary <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>m</mi></semantics></math></inline-formula>-dimensional noise with a known spectrum. It is assumed that the likelihood function of observations of the output signals of MLS satisfies the conditions of local asymptotic normality. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msqrt><mi>n</mi></msqrt></mrow></semantics></math></inline-formula>-consistency of the estimate is established. Under the assumption of asymptotic normality of an objective function, the limiting covariance matrix of the estimate is calculated for case where the number of observations tends to infinity. |
| first_indexed | 2024-03-08T03:53:05Z |
| format | Article |
| id | doaj.art-cdd2509fbc8d438c904e318c3b755074 |
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| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T03:53:05Z |
| publishDate | 2024-02-01 |
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| spelling | doaj.art-cdd2509fbc8d438c904e318c3b7550742024-02-09T15:18:28ZengMDPI AGMathematics2227-73902024-02-0112347310.3390/math12030473Asymptotic Form of the Covariance Matrix of Likelihood-Based Estimator in Multidimensional Linear System Model for the Case of Infinity Number of Nuisance ParametersAlexander Varypaev0Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, BulgariaThis article is devoted to the synthesis and analysis of the quality of the statistical estimate of parameters of a multidimensional linear system (MLS) with one input and <i>m</i> outputs. A nontrivial case is investigated when the one-dimensional input signal of MLS is a deterministic process, the values of which are unknown nuisance parameters. The estimate is based only on observations of MLS output signals distorted by random Gaussian stationary <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>m</mi></semantics></math></inline-formula>-dimensional noise with a known spectrum. It is assumed that the likelihood function of observations of the output signals of MLS satisfies the conditions of local asymptotic normality. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msqrt><mi>n</mi></msqrt></mrow></semantics></math></inline-formula>-consistency of the estimate is established. Under the assumption of asymptotic normality of an objective function, the limiting covariance matrix of the estimate is calculated for case where the number of observations tends to infinity.https://www.mdpi.com/2227-7390/12/3/473statistical estimatemultidimensional linear systemnuisance parametersasymptotic normalityasymptotic covariance matrix |
| spellingShingle | Alexander Varypaev Asymptotic Form of the Covariance Matrix of Likelihood-Based Estimator in Multidimensional Linear System Model for the Case of Infinity Number of Nuisance Parameters Mathematics statistical estimate multidimensional linear system nuisance parameters asymptotic normality asymptotic covariance matrix |
| title | Asymptotic Form of the Covariance Matrix of Likelihood-Based Estimator in Multidimensional Linear System Model for the Case of Infinity Number of Nuisance Parameters |
| title_full | Asymptotic Form of the Covariance Matrix of Likelihood-Based Estimator in Multidimensional Linear System Model for the Case of Infinity Number of Nuisance Parameters |
| title_fullStr | Asymptotic Form of the Covariance Matrix of Likelihood-Based Estimator in Multidimensional Linear System Model for the Case of Infinity Number of Nuisance Parameters |
| title_full_unstemmed | Asymptotic Form of the Covariance Matrix of Likelihood-Based Estimator in Multidimensional Linear System Model for the Case of Infinity Number of Nuisance Parameters |
| title_short | Asymptotic Form of the Covariance Matrix of Likelihood-Based Estimator in Multidimensional Linear System Model for the Case of Infinity Number of Nuisance Parameters |
| title_sort | asymptotic form of the covariance matrix of likelihood based estimator in multidimensional linear system model for the case of infinity number of nuisance parameters |
| topic | statistical estimate multidimensional linear system nuisance parameters asymptotic normality asymptotic covariance matrix |
| url | https://www.mdpi.com/2227-7390/12/3/473 |
| work_keys_str_mv | AT alexandervarypaev asymptoticformofthecovariancematrixoflikelihoodbasedestimatorinmultidimensionallinearsystemmodelforthecaseofinfinitynumberofnuisanceparameters |