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Methods for interval-censored data and testing for stochastic dominance
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0003-1205-3073
2018 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Metoder för intervallcensurerade data och test av stokastisk dominans (Swedish)
Abstract [en]

This thesis includes four papers: the first three of them are concerned with methods for interval-censored data, while the forth paper is devoted to testing for stochastic dominance.

In many studies, the variable of interest is observed to lie within an interval instead of being observed exactly, i.e., each observation is an interval and not a single value. This type of data is known as interval-censored. It may arise in questionnaire-based studies when the respondent gives an answer in the form of an interval without having pre-specified ranges. Such data are called self-selected interval data. In this context, the assumption of noninformative censoring is not fulfilled, and therefore the existing methods for interval-censored data are not necessarily applicable.

A problem of interest is to estimate the underlying distribution function. There are two main approaches to this problem: (i) parametric estimation, which assumes a particular functional form of the distribution, and (ii) nonparametric estimation, which does not rely on any distributional assumptions. In Paper A, a nonparametric maximum likelihood estimator for self-selected interval data is proposed and its consistency is shown. Paper B suggests a parametric maximum likelihood estimator. The consistency and asymptotic normality of the estimator are proven.

Another interesting problem is to infer whether two samples arise from identical distributions. In Paper C, nonparametric two-sample tests suitable for self-selected interval data are suggested and their properties are investigated through simulations.

Paper D concerns testing for stochastic dominance with uncensored data. The paper explores a testing problem which involves four hypotheses, that is, based on observations of two random variables X and Y, one wants to discriminate between four possibilities: identical survival functions, stochastic dominance of X over Y, stochastic dominance of Y over X, or crossing survival functions. Permutation-based tests suitable for two independent samples and for paired samples are proposed. The tests are applied to data from an experiment concerning the individual's willingness to pay for a given environmental improvement.

Place, publisher, year, edition, pages
Umeå: Umeå University , 2018. , p. 14
Series
Statistical studies, ISSN 1100-8989 ; 53
Keywords [en]
Interval-censored data, Informative censoring, Self-selected intervals, Questionnaire-based studies, Maximum likelihood, Permutation test, Two-sample test, Stochastic dominance, Four-decision test
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:umu:diva-150433ISBN: 978-91-7601-911-5 (print)OAI: oai:DiVA.org:umu-150433DiVA, id: diva2:1241348
Public defence
2018-09-19, Hörsal E, Humanisthuset, Umeå, 13:15 (English)
Opponent
Supervisors
Available from: 2018-08-29 Created: 2018-08-23 Last updated: 2018-08-29Bibliographically approved
List of papers
1. Nonparametric estimation for self-selected interval data collected through a two-stage approach
Open this publication in new window or tab >>Nonparametric estimation for self-selected interval data collected through a two-stage approach
2017 (English)In: Metrika (Heidelberg), ISSN 0026-1335, E-ISSN 1435-926X, Vol. 80, no 4, p. 377-399Article in journal (Refereed) Published
Abstract [en]

Self-selected interval data arise in questionnaire surveys when respondents are free to answer with any interval without having pre-specified ranges. This type of data is a special case of interval-censored data in which the assumption of noninformative censoring is violated, and thus the standard methods for interval-censored data (e.g. Turnbull's estimator) are not appropriate because they can produce biased results. Based on a certain sampling scheme, this paper suggests a nonparametric maximum likelihood estimator of the underlying distribution function. The consistency of the estimator is proven under general assumptions, and an iterative procedure for finding the estimate is proposed. The performance of the method is investigated in a simulation study.

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Informative interval censoring, Self-selected intervals, Nonparameric maximum likelihood estimation, Two-stage data collection, Questionnaire surveys
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-133619 (URN)10.1007/s00184-017-0610-7 (DOI)000399690100001 ()
Available from: 2017-04-17 Created: 2017-04-17 Last updated: 2018-08-27Bibliographically approved
2. Maximum likelihood estimation for survey data with informative interval censoring
Open this publication in new window or tab >>Maximum likelihood estimation for survey data with informative interval censoring
2019 (English)In: AStA Advances in Statistical Analysis, ISSN 1863-8171, E-ISSN 1863-818X, Vol. 103, no 2, p. 217-236Article in journal (Refereed) Published
Abstract [en]

Interval-censored data may arise in questionnaire surveys when, instead of being asked to provide an exact value, respondents are free to answer with any interval without having pre-specified ranges. In this context, the assumption of noninformative censoring is violated, and thus, the standard methods for interval-censored data are not appropriate. This paper explores two schemes for data collection and deals with the problem of estimation of the underlying distribution function, assuming that it belongs to a parametric family. The consistency and asymptotic normality of a proposed maximum likelihood estimator are proven. A bootstrap procedure that can be used for constructing confidence intervals is considered, and its asymptotic validity is shown. A simulation study investigates the performance of the suggested methods.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Informative interval censoring, Maximum likelihood, Parametric estimation, Questionnaire surveys, Self-selected intervals
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-148254 (URN)10.1007/s10182-018-00329-x (DOI)000468577500003 ()
Available from: 2018-07-21 Created: 2018-07-21 Last updated: 2019-06-11Bibliographically approved
3. Nonparametric two-sample tests for informatively interval-censored data
Open this publication in new window or tab >>Nonparametric two-sample tests for informatively interval-censored data
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-150431 (URN)
Available from: 2018-08-08 Created: 2018-08-08 Last updated: 2018-11-08
4. Testing for stochastic dominance: Procedures with four hypotheses
Open this publication in new window or tab >>Testing for stochastic dominance: Procedures with four hypotheses
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics Social Sciences Interdisciplinary
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-150432 (URN)
Available from: 2018-08-08 Created: 2018-08-08 Last updated: 2018-11-08

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