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Erratum to “Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model

A X = B

”

Alexander Kukush Yaroslav Tsaregorodtsev

https://doi.org/10.15559/16-VMSTA53

Pub. online: 16 May 2016 Type: Erratum

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 2 (2016), p. 105

Erratum to “Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model

A X = B

”

Alexander Kukush Yaroslav Tsaregorodtsev

https://doi.org/10.15559/16-MSTA53

Pub. online: 16 May 2016 Type: Erratum

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 2 (2016), p. 105

Asymptotics of exponential moments of a weighted local time of a Brownian motion with small variance

Alexei Kulik Daryna Sobolieva

https://doi.org/10.15559/16-VMSTA49

Pub. online: 5 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 1 (2016), pp. 95–103

Abstract

We prove a large deviation type estimate for the asymptotic behavior of a weighted local time of $\varepsilon W$ as $\varepsilon \to 0$.

Asymptotics of exponential moments of a weighted local time of a Brownian motion with small variance

Alexei Kulik Daryna Sobolieva

https://doi.org/10.15559/16-MSTA49

Pub. online: 5 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 1 (2016), pp. 95–103

Abstract

We prove a large deviation type estimate for the asymptotic behavior of a weighted local time of $\varepsilon W$ as $\varepsilon \to 0$.

Random convolution of inhomogeneous distributions with

O

-exponential tail

Svetlana Danilenko Simona Paškauskaitė Jonas Šiaulys

https://doi.org/10.15559/16-VMSTA52

Pub. online: 4 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 1 (2016), pp. 79–94

Abstract

Let $\{\xi _{1},\xi _{2},\dots \}$ be a sequence of independent random variables (not necessarily identically distributed), and η be a counting random variable independent of this sequence. We obtain sufficient conditions on $\{\xi _{1},\xi _{2},\dots \}$ and η under which the distribution function of the random sum $S_{\eta }=\xi _{1}+\xi _{2}+\cdots +\xi _{\eta }$ belongs to the class of $\mathcal{O}$-exponential distributions.

Random convolution of inhomogeneous distributions with

O

-exponential tail

Svetlana Danilenko Simona Paškauskaitė Jonas Šiaulys

https://doi.org/10.15559/16-MSTA52

Pub. online: 4 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 1 (2016), pp. 79–94

Abstract

Minimax interpolation of sequences with stationary increments and cointegrated sequences

Maksym Luz Mikhail Moklyachuk

https://doi.org/10.15559/16-VMSTA51

Pub. online: 1 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 1 (2016), pp. 59–78

Abstract

We consider the problem of optimal estimation of the linear functional $A_{N}\xi ={\sum _{k=0}^{N}}a(k)\xi (k)$ depending on the unknown values of a stochastic sequence $\xi (m)$ with stationary increments from observations of the sequence $\xi (m)+\eta (m)$ at points of the set $\mathbb{Z}\setminus \{0,1,2,\dots ,N\}$, where $\eta (m)$ is a stationary sequence uncorrelated with $\xi (m)$. We propose formulas for calculating the mean square error and the spectral characteristic of the optimal linear estimate of the functional in the case of spectral certainty, where spectral densities of the sequences are exactly known. We also consider the problem for a class of cointegrated sequences. We propose relations that determine the least favorable spectral densities and the minimax spectral characteristics in the case of spectral uncertainty, where spectral densities are not exactly known while a set of admissible spectral densities is specified.

Minimax interpolation of sequences with stationary increments and cointegrated sequences

Maksym Luz Mikhail Moklyachuk

https://doi.org/10.15559/16-MSTA51

Pub. online: 1 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 1 (2016), pp. 59–78

Abstract

Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model

A X = B

Alexander Kukush Yaroslav Tsaregorodtsev

https://doi.org/10.15559/16-VMSTA50

Pub. online: 29 Mar 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 1 (2016), pp. 47–57

Abstract

We consider a multivariate functional measurement error model $AX\approx B$. The errors in $[A,B]$ are uncorrelated, row-wise independent, and have equal (unknown) variances. We study the total least squares estimator of X, which, in the case of normal errors, coincides with the maximum likelihood one. We give conditions for asymptotic normality of the estimator when the number of rows in A is increasing. Under mild assumptions, the covariance structure of the limit Gaussian random matrix is nonsingular. For normal errors, the results can be used to construct an asymptotic confidence interval for a linear functional of X.

Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model

A X = B

Alexander Kukush Yaroslav Tsaregorodtsev

https://doi.org/10.15559/16-MSTA50

Pub. online: 29 Mar 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 1 (2016), pp. 47–57

Abstract

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