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Estimation and Inference for Quantile Regression of Longitudinal Data: With Applications in Biostatistics
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science.ORCID iD: 0000-0003-3691-8326
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of four papers dealing with estimation and inference for quantile regression of longitudinal data, with an emphasis on nonlinear models.

The first paper extends the idea of quantile regression estimation from the case of cross-sectional data with independent errors to the case of linear or nonlinear longitudinal data with dependent errors, using a weighted estimator. The performance of different weights is evaluated, and a comparison is also made with the corresponding mean regression estimator using the same weights.

The second paper examines the use of bootstrapping for bias correction and calculations of confidence intervals for parameters of the quantile regression estimator when longitudinal data are used. Different weights, bootstrap methods, and confidence interval methods are used.

The third paper is devoted to evaluating bootstrap methods for constructing hypothesis tests for parameters of the quantile regression estimator using longitudinal data. The focus is on testing the equality between two groups of one or all of the parameters in a regression model for some quantile using single or joint restrictions. The tests are evaluated regarding both their significance level and their power.

The fourth paper analyzes seven longitudinal data sets from different parts of the biostatistics area by quantile regression methods in order to demonstrate how new insights can emerge on the properties of longitudinal data from using quantile regression methods. The quantile regression estimates are also compared and contrasted with the least squares mean regression estimates for the same data set. In addition to looking at the estimates, confidence intervals and hypothesis testing procedures are examined.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2006. , p. 36
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 18
Keywords [en]
Statistics, Bias correction, Bootstrap, Dependent errors, Hypothesis testing, Nonlinear model, Simulation study
Keywords [sv]
Statistik
Identifiers
URN: urn:nbn:se:uu:diva-7186ISBN: 91-554-6678-8 (print)OAI: oai:DiVA.org:uu-7186DiVA, id: diva2:169006
Public defence
2006-11-10, Hörsal 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, 13:15
Opponent
Supervisors
Available from: 2006-10-19 Created: 2006-10-19 Last updated: 2013-06-20Bibliographically approved
List of papers
1. Nonlinear quantile regression estimation of longitudinal data
Open this publication in new window or tab >>Nonlinear quantile regression estimation of longitudinal data
2008 (English)In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 37, no 1, p. 114-131Article in journal (Refereed) Published
Abstract [en]

This article examines a weighted version of the quantile regression estimator as defined by Koenker and Bassett (1978), adjusted to the case of nonlinear longitudinal data. Using a four-parameter logistic growth function and error terms following an AR(1) model, different weights are used and compared in a simulation study. The findings indicate that the nonlinear quantile regression estimator is performing well, especially for the median regression case, that the differences between the weights are small, and that the estimator performs better when the correlation in the AR(1) model increases. A comparison is also made with the corresponding mean regression estimator, which is found to be less robust. Finally, the estimator is applied to a data set with growth patterns of two genotypes of soybean, which gives some insights into how the quantile regressions provide a more complete picture of the data than the mean regression.

Keywords
dependent errors, median regression, repeated measures, simulation study
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-94965 (URN)10.1080/03610910701723963 (DOI)000252321400009 ()
Available from: 2006-10-19 Created: 2006-10-19 Last updated: 2017-12-14Bibliographically approved
2. Bootstrap Methods for Bias Correction and Confidence Interval Estimation for Nonlinear Quantile Regression of Longitudinal Data
Open this publication in new window or tab >>Bootstrap Methods for Bias Correction and Confidence Interval Estimation for Nonlinear Quantile Regression of Longitudinal Data
2009 (English)In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 79, no 10, p. 1205-1218Article in journal (Refereed) Published
Abstract [en]

This paper examines the use of bootstrapping for bias correction and   calculation of confidence intervals (CIs) for a weighted nonlinear   quantile regression estimator adjusted to the case of longitudinal   data. Different weights and types of CIs are used and compared by   computer simulation using a logistic growth function and error terms   following an AR(1) model. The results indicate that bias correction   reduces the bias of a point estimator but fails for CI calculations. A   bootstrap percentile method and a normal approximation method perform   well for two weights when used without bias correction. Taking both   coverage and lengths of CIs into consideration, a non-bias-corrected   percentile method with an unweighted estimator performs best.

Keywords
autocorrelated errors, bias reduction, dependent errors, median regression, panel data, repeated measurements
National Category
Computer and Information Sciences
Identifiers
urn:nbn:se:uu:diva-94966 (URN)10.1080/00949650802221180 (DOI)000270155800003 ()
Available from: 2006-10-19 Created: 2006-10-19 Last updated: 2018-01-13Bibliographically approved
3. Bootstrap-Based Hypothesis Tests for Nonlinear Quantile Regression of Longitudinal Data
Open this publication in new window or tab >>Bootstrap-Based Hypothesis Tests for Nonlinear Quantile Regression of Longitudinal Data
(English)Manuscript (Other academic)
National Category
Social Sciences
Identifiers
urn:nbn:se:uu:diva-94967 (URN)
Available from: 2006-10-19 Created: 2006-10-19 Last updated: 2013-06-20Bibliographically approved
4. New Insights on Longitudinal Biostatistics Data from Using Quantile Regressions
Open this publication in new window or tab >>New Insights on Longitudinal Biostatistics Data from Using Quantile Regressions
(English)Manuscript (Other academic)
National Category
Social Sciences
Identifiers
urn:nbn:se:uu:diva-94968 (URN)
Available from: 2006-10-19 Created: 2006-10-19 Last updated: 2013-06-20Bibliographically approved

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