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Equivariant adjusted least squares estimator in two-line fitting model

Sergiy Shklyar

https://doi.org/10.15559/16-VMSTA47

Pub. online: 21 Mar 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 1 (2016), pp. 19–45

Abstract

We consider the two-line fitting problem. True points lie on two straight lines and are observed with Gaussian perturbations. For each observed point, it is not known on which line the corresponding true point lies. The parameters of the lines are estimated.

This model is a restriction of the conic section fitting model because a couple of two lines is a degenerate conic section. The following estimators are constructed: two projections of the adjusted least squares estimator in the conic section fitting model, orthogonal regression estimator, parametric maximum likelihood estimator in the Gaussian model, and regular best asymptotically normal moment estimator.

The conditions for the consistency and asymptotic normality of the projections of the adjusted least squares estimator are provided. All the estimators constructed in the paper are equivariant. The estimators are compared numerically.

Equivariant adjusted least squares estimator in two-line fitting model

Sergiy Shklyar

https://doi.org/10.15559/16-MSTA47

Pub. online: 21 Mar 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 1 (2016), pp. 19–45

Abstract

Functional limit theorems for additive and multiplicative schemes in the Cox–Ingersoll–Ross model

Yuliia Mishura Yevheniia Munchak

https://doi.org/10.15559/16-VMSTA48

Pub. online: 3 Mar 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 1 (2016), pp. 1–17

Abstract

In this paper, we consider the Cox–Ingersoll–Ross (CIR) process in the regime where the process does not hit zero. We construct additive and multiplicative discrete approximation schemes for the price of asset that is modeled by the CIR process and geometric CIR process. In order to construct these schemes, we take the Euler approximations of the CIR process itself but replace the increments of the Wiener process with iid bounded vanishing symmetric random variables. We introduce a “truncated” CIR process and apply it to prove the weak convergence of asset prices. We establish the fact that this “truncated” process does not hit zero under the same condition considered for the original nontruncated process.

Functional limit theorems for additive and multiplicative schemes in the Cox–Ingersoll–Ross model

Yuliia Mishura Yevheniia Munchak

https://doi.org/10.15559/16-MSTA48

Pub. online: 3 Mar 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 1 (2016), pp. 1–17

Abstract

2010 Mathematics Subject Classification index

https://doi.org/10.15559/15-VMSTA24MI

Pub. online: 31 Dec 2015 Type: 2010 Mathematics Subject Classification Index

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), pp. 447–450

2010 Mathematics Subject Classification index

https://doi.org/10.15559/15-MSTA24MI

Pub. online: 31 Dec 2015 Type: 2010 Mathematics Subject Classification Index

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), pp. 447–450

Subject index

https://doi.org/10.15559/15-VMSTA24SI

Pub. online: 31 Dec 2015 Type: Subject Index

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), pp. 445–446

Subject index

https://doi.org/10.15559/15-MSTA24SI

Pub. online: 31 Dec 2015 Type: Subject Index

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), pp. 445–446

Author index

https://doi.org/10.15559/15-VMSTA24AI

Pub. online: 31 Dec 2015 Type: Author Index

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), p. 443

Author index

https://doi.org/10.15559/15-MSTA24AI

Pub. online: 31 Dec 2015 Type: Author Index

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), p. 443

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