Order restricted inference over countable preordered sets. Statistical aspects of neutron detection
(2018)- Abstract
- This thesis consists of four papers.
In the first paper, we study the isotonic regression estimator over a general countable preordered set. We obtain the limiting distribution of the estimator and study its properties. Also, it is shown that the isotonisation preserves the rate of convergence of the underlying estimator. We apply these results to the problems of estimation of a bimonotone regression function and estimation of a bimonotone probability mass function.
In the second paper, we propose a new method of estimating a discrete monotone probability mass function. We introduce a two-step procedure. First, we perform a model selection introducing the Akaike-type information criterion (CMAIC). Second, using the... (More) - This thesis consists of four papers.
In the first paper, we study the isotonic regression estimator over a general countable preordered set. We obtain the limiting distribution of the estimator and study its properties. Also, it is shown that the isotonisation preserves the rate of convergence of the underlying estimator. We apply these results to the problems of estimation of a bimonotone regression function and estimation of a bimonotone probability mass function.
In the second paper, we propose a new method of estimating a discrete monotone probability mass function. We introduce a two-step procedure. First, we perform a model selection introducing the Akaike-type information criterion (CMAIC). Second, using the selected class of models we construct a modified Grenander estimator by grouping the parameters in the constant regions and then projecting the grouped empirical estimator onto the isotonic cone. It is shown that the post-model-selection estimator performs asymptotically better, in $l_{2}$-sense, than the regular Grenander estimator.
In the third paper, we use a stochastic process approach to determine the neutron energy in a novel detector. The data from a multi-layer detector consists of counts of the number of absorbed neutrons along the sequence of the detector's layers, in which the neutron absorption probability is unknown. These results are combined with known results on the relation between the absorption probability and the wavelength to derive an estimator of the wavelength and to show consistency and asymptotic normality.
In the forth paper, the results of the third paper are generalised to the case of a multimode Poisson beam. We study the asymptotic properties of the maximum likelihood estimator of the spectrum and thinning parameters for the spectrum's components. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/b11b569f-772c-4fd0-870a-7608bbeb4a0e
- author
- Pastukhov, Vladimir LU
- supervisor
- opponent
-
- Professor Dümbgen, Lutz, Institute of Mathematical Statistics and Actuarial Science, University of Bern, Switzerland
- organization
- publishing date
- 2018-09
- type
- Thesis
- publication status
- published
- subject
- keywords
- Constrained inference, Isotonic regression, Density estimation, Grenander estimator, Limit distribution, Neutron detection
- pages
- 150 pages
- publisher
- Lund University, Faculty of Science, Centre for Mathematical Sciences
- defense location
- MH:G Matematikhuset, Sölvegatan 18, Lund
- defense date
- 2018-10-05 13:15:00
- ISBN
- 978-91-7753-808-0
- 978-91-7753-809-7
- language
- English
- LU publication?
- yes
- id
- b11b569f-772c-4fd0-870a-7608bbeb4a0e
- date added to LUP
- 2018-09-04 14:32:07
- date last changed
- 2024-02-13 15:12:29
@phdthesis{b11b569f-772c-4fd0-870a-7608bbeb4a0e,
abstract = {{This thesis consists of four papers. <br/><br/>In the first paper, we study the isotonic regression estimator over a general countable preordered set. We obtain the limiting distribution of the estimator and study its properties. Also, it is shown that the isotonisation preserves the rate of convergence of the underlying estimator. We apply these results to the problems of estimation of a bimonotone regression function and estimation of a bimonotone probability mass function.<br/><br/>In the second paper, we propose a new method of estimating a discrete monotone probability mass function. We introduce a two-step procedure. First, we perform a model selection introducing the Akaike-type information criterion (CMAIC). Second, using the selected class of models we construct a modified Grenander estimator by grouping the parameters in the constant regions and then projecting the grouped empirical estimator onto the isotonic cone. It is shown that the post-model-selection estimator performs asymptotically better, in $l_{2}$-sense, than the regular Grenander estimator. <br/><br/>In the third paper, we use a stochastic process approach to determine the neutron energy in a novel detector. The data from a multi-layer detector consists of counts of the number of absorbed neutrons along the sequence of the detector's layers, in which the neutron absorption probability is unknown. These results are combined with known results on the relation between the absorption probability and the wavelength to derive an estimator of the wavelength and to show consistency and asymptotic normality. <br/><br/>In the forth paper, the results of the third paper are generalised to the case of a multimode Poisson beam. We study the asymptotic properties of the maximum likelihood estimator of the spectrum and thinning parameters for the spectrum's components.}},
author = {{Pastukhov, Vladimir}},
isbn = {{978-91-7753-808-0}},
keywords = {{Constrained inference; Isotonic regression; Density estimation; Grenander estimator; Limit distribution; Neutron detection}},
language = {{eng}},
publisher = {{Lund University, Faculty of Science, Centre for Mathematical Sciences}},
school = {{Lund University}},
title = {{Order restricted inference over countable preordered sets. Statistical aspects of neutron detection}},
url = {{https://lup.lub.lu.se/search/files/50644484/Thesis.pdf}},
year = {{2018}},
}