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 twostep procedure. First, we perform a model selection introducing the Akaiketype 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 twostep procedure. First, we perform a model selection introducing the Akaiketype 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 postmodelselection 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 multilayer 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/b11b569f772c4fd0870a7608bbeb4a0e
 author
 Pastukhov, Vladimir ^{LU}
 supervisor

 Dragi Anevski ^{LU}
 opponent

 Professor Dümbgen, Lutz, Institute of Mathematical Statistics and Actuarial Science, University of Bern, Switzerland
 organization
 publishing date
 201809
 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
 20181005 13:15:00
 ISBN
 9789177538080
 9789177538097
 language
 English
 LU publication?
 yes
 id
 b11b569f772c4fd0870a7608bbeb4a0e
 date added to LUP
 20180904 14:32:07
 date last changed
 20181121 21:41:25
@phdthesis{b11b569f772c4fd0870a7608bbeb4a0e, 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 twostep procedure. First, we perform a model selection introducing the Akaiketype 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 postmodelselection 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 multilayer 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 = {9789177538080}, 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}, }