| 1. |
- Ekström, Magnus, 1966-, et al.
(författare)
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A general measure of skewness
- 2012
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Ingår i: Statistics and Probability Letters. - : Elsevier. - 0167-7152 .- 1879-2103. ; 82:8, s. 1559-1568
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Tidskriftsartikel (refereegranskat)abstract
- A very general measure of skewness based on the quantiles is introduced, which includes several well-known measures as special cases. Sample versions of our measure may be used as test statistics for testing the hypothesis of symmetry about an unknown value. We provide large sample theory for such a statistic and discuss the asymptotic relative efficiencies of this against some competing test statistics for symmetry.
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| 2. |
- Angelov, Angel G., et al.
(författare)
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Four-decision tests for stochastic dominance, with an application to environmental psychophysics
- 2019
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier. - 0022-2496 .- 1096-0880. ; 93
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Tidskriftsartikel (refereegranskat)abstract
- If the survival function of a random variable X lies to the right of the survival function of a random variable Y, then X is said to stochastically dominate Y. Inferring stochastic dominance is particularly complicated because comparing survival functions raises four possible hypotheses: identical survival functions, dominance of X over Y, dominance of Y over X, or crossing survival functions. In this paper, we suggest four-decision tests for stochastic dominance suitable for paired samples. The tests are permutation-based and do not rely on distributional assumptions. One-sided Cramér–von Mises and Kolmogorov–Smirnov statistics are employed but the general idea may be utilized with other test statistics. The power to detect dominance and the different types of wrong decisions are investigated in an extensive simulation study. The proposed tests are applied to data from an experiment concerning the individual’s willingness to pay for a given environmental improvement.
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| 3. |
- Angelov, Angel G., et al.
(författare)
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Maximum likelihood estimation for survey data with informative interval censoring
- 2019
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Ingår i: AStA Advances in Statistical Analysis. - : Springer. - 1863-8171 .- 1863-818X. ; 103:2, s. 217-236
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 4. |
- Angelov, Angel G., 1983-
(författare)
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Methods for interval-censored data and testing for stochastic dominance
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 5. |
- Angelov, Angel G., et al.
(författare)
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Quantile regression with interval-censored data in questionnaire-based studies
- 2022
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Ingår i: Computational statistics (Zeitschrift). - : Springer Berlin/Heidelberg. - 0943-4062 .- 1613-9658.
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Tidskriftsartikel (refereegranskat)abstract
- Interval-censored data can 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 case, the assumption of independent censoring is not fulfilled, and therefore the ordinary methods for interval-censored data are not suitable. This paper explores a quantile regression model for self-selected interval data and suggests an estimator based on estimating equations. The consistency of the estimator is shown. Bootstrap procedures for constructing confidence intervals are considered. A simulation study indicates satisfactory performance of the proposed methods. An application to data concerning price estimates is presented.
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| 6. |
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| 7. |
- Angelov, Angel G., et al.
(författare)
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Tests of stochastic dominance with repeated measurements data
- 2023
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Ingår i: AStA Advances in Statistical Analysis. - : Springer. - 1863-8171 .- 1863-818X. ; 107:3, s. 443-467
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Tidskriftsartikel (refereegranskat)abstract
- The paper explores a testing problem which involves four hypotheses, that is, based on observations of two random variables X and Y, we wish to discriminate between four possibilities: identical survival functions, stochastic dominance of X over Y, stochastic dominance of Y over X, or crossing survival functions. Four-decision testing procedures for repeated measurements data are proposed. The tests are based on a permutation approach and do not rely on distributional assumptions. One-sided versions of the Cramér–von Mises, Anderson–Darling, and Kolmogorov–Smirnov statistics are utilized. The consistency of the tests is proven. A simulation study shows good power properties and control of false-detection errors. The suggested tests are applied to data from a psychophysical experiment.
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| 8. |
- Ekström, Magnus, 1966-, et al.
(författare)
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A class of asymptotically efficient estimators based on sample spacings
- 2020
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Ingår i: Test (Madrid). - : Springer Berlin/Heidelberg. - 1133-0686 .- 1863-8260. ; 29:3, s. 617-636
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider general classes of estimators based on higher-order sample spacings, called the Generalized Spacings Estimators. Such classes of estimators are obtained by minimizing the Csiszár divergence between the empirical and true distributions for various convex functions, include the "maximum spacing estimators" as well as the maximum likelihood estimators (MLEs) as special cases, and are especially useful when the latter do not exist. These results generalize several earlier studies on spacings-based estimation, by utilizing non-overlapping spacings that are of an order which increases with the sample size. These estimators are shown to be consistent as well as asymptotically normal under a fairly general set of regularity conditions. When the step size and the number of spacings grow with the sample size, an asymptotically efficient class of estimators, called the "Minimum Power Divergence Estimators", are shown to exist. Simulation studies give further support to the performance of these asymptotically efficient estimators in finite samples and compare well relative to the MLEs. Unlike the MLEs, some of these estimators are also shown to be quite robust under heavy contamination.
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| 9. |
- Ekström, Magnus, 1966-, et al.
(författare)
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A class of asymptotically efficient estimators based on sample spacings
- 2019
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Ingår i: EMS 2019 - Program and Book of Abstracts. ; , s. 95-95
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Konferensbidrag (refereegranskat)abstract
- We consider a general class of estimators based on higher-order sample spacings, called Minimum Power Divergence Estimators (MPDEs). Such estimators are obtained by minimizing approximations of so-called power divergences between distributions in the model and the true underlying distribution, and include the maximum product of spacings estimator as a special case. The maximum likelihood estimator (MLE) may be derived in a similar way using the Kullback-Leibler divergence. Spacings-based estimators are especially useful when MLEs do not exist. Our results generalize several earlier studies on spacings-based estimation, by utilizing non-overlapping spacings that are of an order which increases with the sample size. The MPDEs are shown to be consistent as well as asymptotically efficient under a fairly general set of regularity conditions. Simulation studies give further support to the performance of these asymptotically efficient estimators in finite samples, and compare well relative to the MLEs. Unlike the MLEs, some of these estimators are also shown to be quite robust under heavy contamination.
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| 10. |
- Ekström, Magnus, 1966-, et al.
(författare)
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A class of asymptotically efficient estimators based on sample spacings
- 2018
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Ingår i: The 27th Nordic Conference in Mathematical Statistics: Abstracts. - : University of Tartu. ; , s. 20-20
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We consider general classes of estimators based on higher-order sample spacings,called Generalized Spacings Estimators (GSEs). Such classes of estimators areobtained by minimizing approximations of Csisz´ar divergences between distributionsin the model and the true underlying distribution; maximum likelihood estimators(MLEs) may be derived in a similar way using the Kullback-Leibler divergence. Ourresults generalize several earlier studies on spacings-based estimation, by utilizingnon-overlapping spacings that are of an order which increases with the sample size.The GSEs are shown to be consistent as well as asymptotically normal under a fairlygeneral set of regularity conditions. When both the order of the spacings and thenumber of spacings grow with the sample size, an asymptotically efficient class ofestimators, called the “Minimum Power Divergence Estimators,” are shown to exist.Simulation studies give further support to the performance of these asymptoticallyefficient estimators in finite samples, and compare well relative to the MLEs as wellas corresponding estimators based on “overlapping” higher order spacings. Unlikethe MLEs, some of these estimators are also shown to be quite robust under heavycontamination.
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