Displaying similar documents to “Estimation of polynomials in the regression model”

The linear model with variance-covariance components and jackknife estimation

Jaromír Kudeláš (1994)

Applications of Mathematics

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Let θ * be a biased estimate of the parameter ϑ based on all observations x 1 , ⋯ , x n and let θ - i * ( i = 1 , 2 , ⋯ , n ) be the same estimate of the parameter ϑ obtained after deletion of the i -th observation. If the expectation of the estimators θ * and θ - i * are expressed as E ( θ * ) = ϑ + a ( n ) b ( ϑ ) E ( θ - i * ) = ϑ + a ( n - 1 ) b ( ϑ ) i = 1 , 2 , ⋯ , n , where a ( n ) is a known sequence of real numbers and b ( ϑ ) is a function of ϑ , then this system of equations can be regarded as a linear model. The least squares method gives the generalized jackknife estimator. Using this method, it is possible to obtain...

Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values

Wiktor Oktaba (1998)

Applications of Mathematics

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The aim of this paper is to characterize the Multivariate Gauss-Markoff model ( M G M ) as in () with singular covariance matrix and missing values. M G M D P 2 model and completed M G M D P 2 Q model are obtained by three transformations D , P and Q (cf. ()) of M G M . The unified theory of estimation (Rao, 1973) which is of interest with respect to M G M has been used. The characterization is reached by estimation of parameters: scalar σ 2 and linear combination λ ' B ¯ ( B ¯ = v e c B ) as in (), (), () as well as by the model of the form ()...