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Asymptotic normality of discretized maximum likelihood estimator for drift parameter in homogeneous diffusion model

Kostiantyn Ralchenko

https://doi.org/10.15559/15-VMSTA21

Pub. online: 13 Apr 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 1 (2015), pp. 17–28

Abstract

We prove the asymptotic normality of the discretized maximum likelihood estimator for the drift parameter in the homogeneous ergodic diffusion model.

Nonparametric Bayesian inference for multidimensional compound Poisson processes

Shota Gugushvili Frank van der Meulen Peter Spreij

https://doi.org/10.15559/15-VMSTA20

Pub. online: 13 Mar 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 1 (2015), pp. 1–15

Abstract

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_{0}$ and intensity $\lambda _{0}$. We take a nonparametric Bayesian approach to the problem and determine posterior contraction rates in this context, which, under some assumptions, we argue to be optimal posterior contraction rates. In particular, our results imply the existence of Bayesian point estimates that converge to the true parameter pair $(r_{0},\lambda _{0})$ at these rates. To the best of our knowledge, construction of nonparametric density estimators for inference in the class of discretely observed multidimensional Lévy processes, and the study of their rates of convergence is a new contribution to the literature.

2010 Mathematics Subject Classification index

https://doi.org/10.15559/15-VMSTA12MI

Pub. online: 12 Feb 2015 Type: 2010 Mathematics Subject Classification Index

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 215–217

Subject index

https://doi.org/10.15559/15-VMSTA12SI

Pub. online: 12 Feb 2015 Type: Subject Index

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 213–214

Author index

https://doi.org/10.15559/15-VMSTA12AI

Pub. online: 12 Feb 2015 Type: Author Index

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), p. 211

Testing hypotheses on moments by observations from a mixture with varying concentrations

Alexey Doronin Rostyslav Maiboroda

https://doi.org/10.15559/15-VMSTA19

Pub. online: 4 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 195–209

Abstract

A mixture with varying concentrations is a modification of a finite mixture model in which the mixing probabilities (concentrations of mixture components) may be different for different observations. In the paper, we assume that the concentrations are known and the distributions of components are completely unknown. Nonparametric technique is proposed for testing hypotheses on functional moments of components.

Asymptotics for functionals of powers of a periodogram

Lyudmyla Sakhno

https://doi.org/10.15559/15-VMSTA15

Pub. online: 4 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 181–194

Abstract

We present large sample properties and conditions for asymptotic normality of linear functionals of powers of the periodogram constructed with the use of tapered data.

Practical approaches to the estimation of the ruin probability in a risk model with additional funds

Yuliya Mishura Olena Ragulina Oleksandr Stroyev

https://doi.org/10.15559/15-VMSTA18

Pub. online: 2 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 167–180

Abstract

We deal with a generalization of the classical risk model when an insurance company gets additional funds whenever a claim arrives and consider some practical approaches to the estimation of the ruin probability. In particular, we get an upper exponential bound and construct an analogue to the De Vylder approximation for the ruin probability. We compare results of these approaches with statistical estimates obtained by the Monte Carlo method for selected distributions of claim sizes and additional funds.

A martingale bound for the entropy associated with a trimmed filtration on

R^{d}

Alexei Kulik Taras Tymoshkevych

https://doi.org/10.15559/15-VMSTA16

Pub. online: 2 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 151–165

Abstract

Using martingale methods, we provide bounds for the entropy of a probability measure on ${\mathbb{R}}^{d}$ with the right-hand side given in a certain integral form. As a corollary, in the one-dimensional case, we obtain a weighted log-Sobolev inequality.

A criterion for testing hypotheses about the covariance function of a stationary Gaussian stochastic process

Yuriy Kozachenko Viktor Troshki

https://doi.org/10.15559/15-VMSTA17

Pub. online: 29 Jan 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 139–149

Abstract

We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_{p}(\mathbb{T})$, $p\ge 1$, is constructed.

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Online ISSN: 2351-6054
Print ISSN: 2351-6046

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