Displaying similar documents to “Optimal model selection in density estimation”

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...

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 ()...

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...

M -estimators of structural parameters in pseudolinear models

Friedrich Liese, Igor Vajda (1999)

Applications of Mathematics

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Real valued M -estimators θ ^ n : = min ∑ 1 n ρ ( Y i - τ ( θ ) ) in a statistical model with observations Y i ∼ F θ 0 are replaced by ℝ p -valued M -estimators β ^ n : = min ∑ 1 n ρ ( Y i - τ ( u ( z i T β ) ) ) in a new model with observations Y i ∼ F u ( z i t β 0 ) , where z i ∈ ℝ p are regressors, β 0 ∈ ℝ p is a structural parameter and u : ℝ → ℝ a structural function of the new model. Sufficient conditions for the consistency of β ^ n are derived, motivated by the sufficiency conditions for the simpler “parent estimator” θ ^ n . The result is a general method of consistent estimation in a class of nonlinear (pseudolinear) statistical...