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

Wiktor Oktaba

Displaying similar documents to “Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values”

Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model

Wiktor Oktaba (1995)

Applications of Mathematics

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By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant $| σ^{2} \sum |$ in the MGM model $(U, X B, σ^{2} \sum \otimes V)$ , $\sum > 0$ , scalar $σ^{2} > 0$ , with a matrix $V \geq 0$ . A known $n \times p$ random matrix $U$ has the expected value $E (U) = X B$ , where the $n \times d$ matrix $X$ is a known matrix of an experimental design, $B$ is an unknown $d \times p$ matrix of parameters and $σ^{2} \sum \otimes V$ is the covariance matrix of $U, \otimes$ being the symbol...

Gaussian model selection

Lucien Birgé, Pascal Massart (2001)

Journal of the European Mathematical Society

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Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in...

On the optimization of initial conditions for a model parameter estimation

Matonoha, Ctirad, Papáček, Štěpán, Kindermann, Stefan

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The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP...

Variance components estimation in generalized orthogonal models

Célia Fernandes, Paulo Ramos, Sandra Saraiva Ferreira, João Tiago Mexia (2007)

Discussiones Mathematicae Probability and Statistics

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The model $y = \sum_{j = 1}^{w} X_{j} β ̲_{j} + e ̲$ is generalized orthogonal if the orthogonal projection matrices on the range spaces of matrices $X_{j}$ , j = 1, ..., w, commute. Unbiased estimators are obtained for the variance components of such models with cross-nesting.

On two methods for the parameter estimation problem with spatio-temporal FRAP data

Papáček, Štěpán, Jablonský, Jiří, Matonoha, Ctirad

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FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem...