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Linear regression by observations from mixture with varying concentrations

Daryna Liubashenko Rostyslav Maiboroda

https://doi.org/10.15559/15-VMSTA41

Pub. online: 4 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), pp. 343–353

Abstract

We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the least-squares estimator is proposed for estimation of the regression coefficients. Consistency and asymptotic normality of the estimates is demonstrated.

Linear regression by observations from mixture with varying concentrations

Daryna Liubashenko Rostyslav Maiboroda

https://doi.org/10.15559/15-MSTA41

Pub. online: 4 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), pp. 343–353

Abstract

Extreme residuals in regression model. Minimax approach

Aleksander Ivanov Ivan Matsak Sergiy Polotskiy

https://doi.org/10.15559/15-VMSTA40CNF

Pub. online: 5 Oct 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 3 (2015): PRESTO-2015, pp. 297–308

Abstract

We obtain limit theorems for extreme residuals in linear regression model in the case of minimax estimation of parameters.

Extreme residuals in regression model. Minimax approach

Aleksander Ivanov Ivan Matsak Sergiy Polotskiy

https://doi.org/10.15559/15-MSTA40CNF

Pub. online: 5 Oct 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 3 (2015): PRESTO-2015, pp. 297–308

Abstract

We obtain limit theorems for extreme residuals in linear regression model in the case of minimax estimation of parameters.

Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions

Tommi Sottinen Lauri Viitasaari

https://doi.org/10.15559/15-VMSTA39CNF

Pub. online: 2 Oct 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 3 (2015): PRESTO-2015, pp. 287–295

Abstract

We show that every multiparameter Gaussian process with integrable variance function admits a Wiener integral representation of Fredholm type with respect to the Brownian sheet. The Fredholm kernel in the representation can be constructed as the unique symmetric square root of the covariance. We analyze the equivalence of multiparameter Gaussian processes by using the Fredholm representation and show how to construct series expansions for multiparameter Gaussian processes by using the Fredholm kernel.

Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions

Tommi Sottinen Lauri Viitasaari

https://doi.org/10.15559/15-MSTA39CNF

Pub. online: 2 Oct 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 3 (2015): PRESTO-2015, pp. 287–295

Abstract

Gärtner–Ellis condition for squared asymptotically stationary Gaussian processes

Marina Kleptsyna Alain Le Breton Bernard Ycart

https://doi.org/10.15559/15-VMSTA38CNF

Pub. online: 2 Oct 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 3 (2015): PRESTO-2015, pp. 267–286

Abstract

We establish the Gärtner–Ellis condition for the square of an asymptotically stationary Gaussian process. The same limit holds for the conditional distribution given any fixed initial point, which entails weak multiplicative ergodicity. The limit is shown to be the Laplace transform of a convolution of gamma distributions with Poisson compound of exponentials. A proof based on the Wiener–Hopf factorization induces a probabilistic interpretation of the limit in terms of a regression problem.

Gärtner–Ellis condition for squared asymptotically stationary Gaussian processes