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- Kuljus, Kristi, et al.
(author)
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Asymptotic linearity of a linear rank statistic in the case of symmetric nonidentically distributed variables
- 2013
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In: Statistics (Berlin). - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 47:1, s. 156-171
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Journal article (peer-reviewed)abstract
- Let Y 1, ...., Y n be independent but not identically distributed random variables with densities f 1, ...., f n symmetric around zero. Suppose c 1, n , ...., c n, n are given constants such that ? i c i, n =0 and . Denote the rank of Y i -? c i, n for any ??R by R(Y i -? c i, n ) and let a n (i) be a score defined via a score function ?. We study the linear rank statistic and prove that S n (?) is asymptotically uniformly linear in the parameter ? in any interval [-C, C], C>0.
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| 5. |
- Kuljus, Kristi, et al.
(author)
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Asymptotic normality of generalized maximum spacing estimators for multivariate observations
- 2020
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In: Scandinavian Journal of Statistics. - : Wiley. - 0303-6898 .- 1467-9469. ; 47, s. 968-989
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Journal article (peer-reviewed)abstract
- In this paper, the maximum spacing method is considered for multivariate observations. Nearest neighbor balls are used as a multidimensional analogue to univariate spacings. A class of information-type measures is used to generalize the concept of maximum spacing estimators of model parameters. Asymptotic normality of these generalized maximum spacing estimators is proved when the assigned model class is correct, that is, the true density is a member of the model class.
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| 8. |
- Kuljus, Kristi, et al.
(author)
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Asymptotic properties of a rank estimate in linear regression with symmetric non-identically distributed errors
- 2013
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In: Statistics (Berlin). - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 47:6, s. 1160-1183
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Journal article (peer-reviewed)abstract
- In this article, a simple linear regression model with independent and symmetric but non-identically distributed errors is considered. Asymptotic properties of the rank regression estimate defined in Jaeckel [Estimating regression coefficients by minimizing the dispersion of the residuals, Ann. Math. Statist. 43 (1972), pp. 1449-1458] are studied. We show that the studied estimator is consistent and asymptotically normally distributed. The cases of bounded and unbounded score functions are examined separately. The regularity conditions of the article are exemplified for finite mixture distributions.
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| 9. |
- Kuljus, Kristi
(author)
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Asymptotic risks of Viterbi segmentation
- 2010
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In: Research report (Centre of Biostochastics). - 1651-8543. ; , s. 1-25
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Journal article (other academic/artistic)abstract
- We consider the maximum likelihood (Viterbi) alignment of a hidden Markov model (HMM). In an HMM, the underlying Markov chain is usually hidden and the Viterbi alignment is often used as the estimate of it. This approach will be referred to as the Viterbi segmentation. The goodness of the Viterbi segmentation can be measured by several risks. In this paper, we prove the existence of asymptotic risks. Being independent of data, the asymptotic risks can be considered as the characteristics of the model that illustrate the long-run behavior of the Viterbi segmentation
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| 10. |
- Kuljus, Kristi
(author)
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Asymptotic risks of Viterbi segmentation
- 2012
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In: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149. ; 122, s. 3312-3341
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Journal article (peer-reviewed)
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