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A consumption-investment problem modelled as a discounted Markov decision process

Hugo Cruz-Suárez, Raúl Montes-de-Oca, Gabriel Zacarías (2011)

Kybernetika

In this paper a problem of consumption and investment is presented as a model of a discounted Markov decision process with discrete-time. In this problem, it is assumed that the wealth is affected by a production function. This assumption gives the investor a chance to increase his wealth before the investment. For the solution of the problem there is established a suitable version of the Euler Equation (EE) which characterizes its optimal policy completely, that is, there are provided conditions...

Adaptive tests of homogeneity for a Poisson process

M. Fromont, B. Laurent, P. Reynaud-Bouret (2011)

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

We propose to test the homogeneity of a Poisson process observed on a finite interval. In this framework, we first provide lower bounds for the uniform separation rates in -norm over classical Besov bodies and weak Besov bodies. Surprisingly, the obtained lower bounds over weak Besov bodies coincide with the minimax estimation rates over such classes. Then we construct non-asymptotic and non-parametric testing procedures that are adaptive in the sense that they achieve, up to a possible logarithmic...

Asymptotics for the L p -deviation of the variance estimator under diffusion

Paul Doukhan, José R. León (2004)

ESAIM: Probability and Statistics

We consider a diffusion process X t smoothed with (small) sampling parameter ε . As in Berzin, León and Ortega (2001), we consider a kernel estimate α ^ ε with window h ( ε ) of a function α of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the L p deviations such as 1 h h ε p 2 α ^ ε - α p p - 𝔼 α ^ ε - α p p .

Asymptotics for the Lp-deviation of the variance estimator under diffusion

Paul Doukhan, José R. León (2010)

ESAIM: Probability and Statistics

We consider a diffusion process Xt smoothed with (small) sampling parameter ε. As in Berzin, León and Ortega (2001), we consider a kernel estimate α ^ ε with window h(ε) of a function α of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the Lp deviations such as 1 h h ε p 2 α ^ ε - α p p - I E α ^ ε - α p p .

Estimation in models driven by fractional brownian motion

Corinne Berzin, José R. León (2008)

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

Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0<H<1. When 1/2<H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ  x and μ(x)=μ or μ(x)=μ  x, we propose a central limit theorem for estimators of H and of σ based on regression methods. Then we give tests of the hypothesis on σ for these models. We also consider functional estimation on σ(⋅)...

Inference about stationary distributions of Markov chains based on divergences with observed frequencies

María Luisa Menéndez, Domingo Morales, Leandro Pardo, Igor Vajda (1999)

Kybernetika

For data generated by stationary Markov chains there are considered estimates of chain parameters minimizing φ –divergences between theoretical and empirical distributions of states. Consistency and asymptotic normality are established and the asymptotic covariance matrices are evaluated. Testing of hypotheses about the stationary distributions based on φ –divergences between the estimated and empirical distributions is considered as well. Asymptotic distributions of φ –divergence test statistics are...

Investigation of periodicity for dependent observations

Tomáš Cipra (1984)

Aplikace matematiky

It is proved that Hannan's procedure for statistical test of periodicity in the case of time series with dependent observations can be combined with Siegel's improvement of the classical Fischer's test of periodicity. Simulations performed in the paper show that this combination can increase the power of Hannan's test when at least two periodicities are present in the time series with dependent observations.

Smoothing and occupation measures of stochastic processes

Mario Wschebor (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

This is a review paper about some problems of statistical inference for one-parameter stochastic processes, mainly based upon the observation of a convolution of the path with a non-random kernel. Most of the results are known and presented without proofs. The tools are first and second order approximation theorems of the occupation measure of the path, by means of functionals defined on the smoothed paths. Various classes of stochastic processes are considered starting with the Wiener process,...

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