Displaying similar documents to “Graphical model selection for a particular class of continuous-time processes”

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...

A geometric point of view on mean-variance models

Piotr Jaworski (2003)

Applicationes Mathematicae

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This paper deals with the mathematics of the Markowitz theory of portfolio management. Let E and V be two homogeneous functions defined on ℝⁿ, the first linear, the other positive definite quadratic. Furthermore let Δ be a simplex contained in ℝⁿ (the set of admissible portfolios), for example Δ : x₁+ ... + xₙ = 1, x i ≥ 0 . Our goal is to investigate the properties of the restricted mappings (V,E):Δ → ℝ² (the so called Markowitz mappings) and to classify them. We introduce the notion of a...

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 ()...

A new weighted Gompertz distribution with applications to reliability data

Hassan S. Bakouch, Ahmed M. T. Abd El-Bar (2017)

Applications of Mathematics

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A new weighted version of the Gompertz distribution is introduced. It is noted that the model represents a mixture of classical Gompertz and second upper record value of Gompertz densities, and using a certain transformation it gives a new version of the two-parameter Lindley distribution. The model can be also regarded as a dual member of the log-Lindley- X family. Various properties of the model are obtained, including hazard rate function, moments, moment generating function, quantile...

A zero-inflated geometric INAR(1) process with random coefficient

Hassan S. Bakouch, Mehrnaz Mohammadpour, Masumeh Shirozhan (2018)

Applications of Mathematics

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Many real-life count data are frequently characterized by overdispersion, excess zeros and autocorrelation. Zero-inflated count time series models can provide a powerful procedure to model this type of data. In this paper, we introduce a new stationary first-order integer-valued autoregressive process with random coefficient and zero-inflated geometric marginal distribution, named ZIGINAR RC ( 1 ) process, which contains some sub-models as special cases. Several properties of the process are...

The splitting number can be smaller than the matrix chaos number

Heike Mildenberger, Saharon Shelah (2002)

Fundamenta Mathematicae

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Let χ be the minimum cardinality of a subset of ω 2 that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of a creature forcing we show that < χ is consistent. We thus answer a question by Vojtáš. We give two kinds of models for the strict inequality. The first is the combination of an ℵ₂-iteration of some proper forcing with adding ℵ₁ random reals. The second kind of models is obtained by adding δ random reals to a model of M A < κ for some δ ∈...

Von Bertalanffy's growth dynamics with strong Allee effect

J. Leonel Rocha, Sandra M. Aleixo (2012)

Discussiones Mathematicae Probability and Statistics

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Von Bertalanffy’s model is one of the most popular differential equation used in order to study the increase in average length or weight of fish. However, this model does not include demographic Allee effect. This phenomenon is known in the fisheries literature as “depensation”, which arises when populations decline rapidly at low densities. In this paper we develop and investigate new corrected von Bertalanffy’s models with Allee effects. The generalization that we propose results from...

On generalized conditional cumulative past inaccuracy measure

Amit Ghosh, Chanchal Kundu (2018)

Applications of Mathematics

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The notion of cumulative past inaccuracy (CPI) measure has recently been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order α and study the proposed measure for conditionally specified models of two components failed at different time instants, called generalized conditional CPI (GCCPI). Several properties, including the effect of monotone transformation and bounds...

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...

The magnetization at high temperature for a p-spin interaction model with external field

David Márquez-Carreras (2007)

Applicationes Mathematicae

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This paper is devoted to a detailed and rigorous study of the magnetization at high temperature for a p-spin interaction model with external field, generalizing the Sherrington-Kirkpatrick model. In particular, we prove that ⟨ σ i ⟩ (the mean of a spin with respect to the Gibbs measure) converges to an explicitly given random variable, and that ⟨σ₁⟩,...,⟨σₙ⟩ are asymptotically independent.

The discrete-time parabolic Anderson model with heavy-tailed potential

Francesco Caravenna, Philippe Carmona, Nicolas Pétrélis (2012)

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

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We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed ( 1 + d ) -dimensional polymer interacting with a random potential, which is constant in the deterministic direction and i.i.d. in the d orthogonal directions. The potential at each site is a positive random variable with a polynomial tail at infinity. We show that, as the size of the system diverges, the polymer extremity is localized almost surely at one single point which grows...