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Estimators of semiparametric truncated and censored regression models
Umeå University, Faculty of Social Sciences, Department of Statistics.
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis contributes in several ways to the existing knowledge on estimation of truncated, censored, and left truncated right censored (LTRC) regression models. Three new semiparametric estimators are proposed, allowing for asymmetric error distributions. A bootstrap method for estimation of the covariance matrix of the quadratic mode estimator (QME) is proposed and studied. In addition, finite sample properties of estimators for truncated, censored, and LTRC data are studied within simulation studies and applications with real data.

The first paper consists of a simulation study of the QME and other estimators of truncated regression models. The paper contributes with results suggesting the bootstrap technique being potentially useful for estimation of the QME covariance matrix.

In the second paper estimators of truncated and censored semiparametric regression models are proposed. These estimators are generalizations of the QME and the winsorized mean estimator (WME) by allowing asymmetric ``trimming'' of observations. Consistency and asymptotic normality of the estimators are shown.

By combining the two moment restrictions used to derive the estimators in the second paper, a consistent estimator of LTRC regression models is proposed in the third paper.

The fourth paper contains an application where LTRC interpurchase intervals of cars are analysed. Results regarding the interpurchase behaviour of consumers are provided, as are results on estimator properties.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 2005. , 25 p.
Series
Statistical studies, ISSN 1100-8989 ; 34
Keyword [en]
Statistics, LTRC, consistency, asymtotic normality, bootstrap, interpurchase intervals
Keyword [sv]
Statistik
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:umu:diva-540ISBN: 91-7305-891-2 (print)OAI: oai:DiVA.org:umu-540DiVA: diva2:143771
Distributor:
Statistik, 90187, Umeå
Public defence
2005-06-03, N450, Naturvetarhuset, Umeå Universitet, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2005-05-16 Created: 2005-05-16 Last updated: 2009-08-21Bibliographically approved
List of papers
1. Finite sample properties of the QME
Open this publication in new window or tab >>Finite sample properties of the QME
2004 (English)In: Communications in statistics. Simulation and computation, ISSN 0361-0918, Vol. 33, no 3, 567-583 p.Article in journal (Refereed) Published
Abstract [en]

Bias and MSE of the QME are studied by means of simulation. A bootstrap estimator of the QME covariance matrix is also included in the study. The simulation is based on travel distances reported in the Swedish Travel Habit Survey. The results are in accordance with the asymptotic properties of the QME. For example, the QME is better than other suggested estimators under asymmetric distributions of the error term. The results also suggest that the bootstrap technique is potentially useful for estimation of the QME covariance matrix.

Keyword
Truncated regression, semi-parameteric estimators, simulation, bootstrap, covariance matrix estimation
Identifiers
urn:nbn:se:umu:diva-4604 (URN)10.1081/SAC-200033267 (DOI)
Available from: 2005-05-16 Created: 2005-05-16 Last updated: 2009-08-21Bibliographically approved
2. Estimators of regression parameters for truncated and censored data
Open this publication in new window or tab >>Estimators of regression parameters for truncated and censored data
2006 (English)In: Metrika, ISSN 1435-926X, Vol. 63, no 3, 329-341 p.Article in journal (Refereed) Published
Abstract [en]

Estimators of parameters in semi-parametric left truncated and right censored regression models are proposed. In contrast to the majority of existing estimators, the proposed estimators do not require the error term of the regression model to have a symmetric distribution. In addition the estimators use asymmetric “trimming” of observations. Consistency and asymptotic normality of the estimators are shown. Finite sample properties are considered in a small simulation study. For the left truncated case, an empirical application illustrates the usefulness of the estimator.

Place, publisher, year, edition, pages
SpringerLink, 2006
Keyword
Truncated, censored, semi-parametric, regression
Identifiers
urn:nbn:se:umu:diva-4605 (URN)10.1007/s00184-005-0023-x (DOI)
Note
Ändrat till published 21/8-09Available from: 2005-05-16 Created: 2005-05-16 Last updated: 2009-08-21Bibliographically approved
3. A semiparametric regression estimator under left truncation and right censoring
Open this publication in new window or tab >>A semiparametric regression estimator under left truncation and right censoring
2008 (English)In: Statistics and Probability Letters, ISSN 0167-7152, Vol. 78, no 16, 2567-2571 p.Article in journal (Refereed) Published
Abstract [en]

An estimator is proposed for semiparametric linear regression models with left truncated and right censored dependent variables. The estimator is derived from a moment condition following the principles of Newey [Newey, W.K., 2001. Conditional moment restrictions in censored and truncated regression models. Econometric Theory 17, 863–888] on conditional moment conditions. Consistency of the estimator is shown and simulation is used for illustration of the small sample properties.

Place, publisher, year, edition, pages
Elsevier, 2008
Identifiers
urn:nbn:se:umu:diva-4606 (URN)10.1016/j.spl.2008.06.009 (DOI)
Note
Ändrat till publicerad artikel 21/8-09Available from: 2005-05-16 Created: 2005-05-16 Last updated: 2009-08-21Bibliographically approved
4. Analysis of interpurchase intervals of cars using truncated and censored data
Open this publication in new window or tab >>Analysis of interpurchase intervals of cars using truncated and censored data
2005 (English)Report (Other academic)
Abstract [en]

Knowledge of consumer behaviour is important to companies and governmental authorities for, e.g, planning purposes. In this paper the relationship between interpurchase intervals of  cars and demographic and economic characteristics of the car owners are analysed. Data was collected within a panel study of households in Sweden. Due to the study design, data is left truncated and right censored. The degree of censoring was almost 80 percent which made estimation of the models challenging. Results show that income and age of the car owners are important for the length of the interpurchase intervals of cars. Moreover, the results imply that models recommended for interpurchase intervals of durable goods in general might be inappropriate for interpurchase intervals of cars. A generalized gamma distribution, which embeds several distributions, is used to model interpurchase intervals. Semiparametric models are also considered.

National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-4607 (URN)
Note

Ändrat till publicerad 21/8-09

Available from: 2005-05-16 Created: 2005-05-16 Last updated: 2016-12-01Bibliographically approved

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