Displaying similar documents to “Optimal trend estimation in geometric asset price models”

Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes

Jiří Dvořák, Michaela Prokešová (2016)

Applications of Mathematics

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We consider a flexible class of space-time point process models—inhomogeneous shot-noise Cox point processes. They are suitable for modelling clustering phenomena, e.g. in epidemiology, seismology, etc. The particular structure of the model enables the use of projections to the spatial and temporal domain. They are used to formulate a step-wise estimation method to estimate different parts of the model separately. In the first step, the Poisson likelihood approach is used to estimate...

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...

Optimal model selection in density estimation

Matthieu Lerasle (2012)

Annales de l'I.H.P. Probabilités et statistiques

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In order to calibrate a penalization procedure for model selection, the statistician has to choose a shape for the penalty and a leading constant. In this paper, we study, for the marginal density estimation problem, the resampling penalties as general estimators of the shape of an ideal penalty. We prove that the selected estimator satisfies sharp oracle inequalities without remainder terms under a few assumptions on the marginal density s and the collection of models. We also study...

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...

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 ()...

An estimator for parameters of a nonlinear nonnegative multidimensional AR(1) process

Jiří Anděl (1998)

Applications of Mathematics

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Let 𝕖 t = ( e t 1 , ⋯ , e t p ) ' be a p -dimensional nonnegative strict white noise with finite second moments. Let h i j ( x ) be nondecreasing functions from [ 0 , ∞ ) onto [ 0 , ∞ ) such that h i j ( x ) ≤ x for i , j = 1 , ⋯ , p . Let 𝕌 = ( u i j ) be a p × p matrix with nonnegative elements having all its roots inside the unit circle. Define a process 𝕏 t = ( X t 1 , ⋯ , X t p ) ' by X t j = u j 1 h 1 j ( X t - 1 , 1 ) + ⋯ + u j p h p j ( X t - 1 , p ) + e t j for j = 1 , ⋯ , p . A method for estimating 𝕌 from a realization 𝕏 1 , ⋯ , 𝕏 n is proposed. It is proved that the estimators are strongly consistent.

Intermittent estimation for finite alphabet finitarily Markovian processes with exponential tails

Gusztáv Morvai, Benjamin Weiss (2021)

Kybernetika

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We give some estimation schemes for the conditional distribution and conditional expectation of the the next output following the observation of the first n outputs of a stationary process where the random variables may take finitely many possible values. Our schemes are universal in the class of finitarily Markovian processes that have an exponential rate for the tail of the look back time distribution. In addition explicit rates are given. A necessary restriction is that the scheme...

More general credibility models

Virginia Atanasiu (2009)

Mathematica Bohemica

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This communication gives some extensions of the original Bühlmann model. The paper is devoted to semi-linear credibility, where one examines functions of the random variables representing claim amounts, rather than the claim amounts themselves. The main purpose of semi-linear credibility theory is the estimation of μ 0 ( θ ) = E [ f 0 ( X t + 1 ) | θ ] (the net premium for a contract with risk parameter θ ) by a linear combination of given functions of the observable variables: X ̲ ' = ( X 1 , X 2 , ... , X t ) . So the estimators mainly considered here...