رسالة جامعية
Quantile regression in heteroscedastic varying coefficient models: testing and variable selection
| العنوان: | Quantile regression in heteroscedastic varying coefficient models: testing and variable selection |
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| المؤلفون: | Ibrahim, Mohammed Abdulkerim |
| المساهمون: | Verhasselt, Anneleen, Gijbels, Irène |
| سنة النشر: | 2018 |
| المجموعة: | Document Server@UHasselt (Universiteit Hasselt) |
| مصطلحات موضوعية: | adaptive lasso, heteroscedasticity, likelihood-ratio test, non-negative garrote, penalized splines, qualitative shape testing, quantile regression, varying coefficient models |
| الوصف: | In this dissertation, quantile regression in varying coefficient models using a nonparametric technique called P-splines is investigated. In mean regression, we study the influence of the covariates on the conditional mean of the response. An alternative way to study the central location is median regression which is robust to heavy-tailed distributions. Quantile regression is a generalization of median regression to investigate the influence of the covariates on the quantiles/percentiles (entire distribution) of the response. It allows for a wide range of applications. For instance, investigating the 25th percentile of the response (e.g. weight of the child) might be of interest in studying severe malnutrition in children. In order to find the estimates, we need to minimize a quantile objective function. In contrast to that of mean regression, the objective function for quantile regression is not differentiable everywhere. Hence, the coefficient estimates have no explicit expression. A varying coefficient model is an extension of a classical linear regression model, where each coefficient is varying with another variable. This model is important when we have a complex data setting like longitudinal data. In such data scheme, it is intuitive to allow the coefficients to vary with `time'. We consider, in particular, a location-scale varying coefficient model. The key statistical tools are introduced in Chapter 1. Population conditional quantiles cannot cross for different quantile levels (percentiles). However, individual conditional quantile estimators can cross each other. To avoid these crossings, we use an approach called `AHe' (based on two assumptions). This approach enables us to estimate the scale (variability function), and by doing so estimate several quantiles with less computational time. In Chapter 2, we show the consistency of the proposed estimator theoretically and illustrate it in a simulation study. Since estimation of the quantiles other than the median relies on the variability function, it is ... |
| نوع الوثيقة: | doctoral or postdoctoral thesis |
| وصف الملف: | application/pdf |
| اللغة: | English |
| العلاقة: | http://hdl.handle.net/1942/26069Test |
| الإتاحة: | https://doi.org/10.1007/s00362-016-0847-7Test http://hdl.handle.net/1942/26069Test |
| حقوق: | info:eu-repo/semantics/embargoedAccess |
| رقم الانضمام: | edsbas.71D9D957 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |