Varying coefficient models
| Thesis title in Czech: | Modely s proměnlivými koeficienty |
|---|---|
| Thesis title in English: | Varying coefficient models |
| Key words: | modely s proměnlivými koeficienty, jádrová regrese, polynomiální regrese, splinová regrese; |
| English key words: | varying coefficient models, kernel regression, polynomial regression, spline regression; |
| Academic year of topic announcement: | 2015/2016 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. RNDr. Matúš Maciak, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 06.12.2015 |
| Date of assignment: | 24.02.2016 |
| Confirmed by Study dept. on: | 07.03.2016 |
| Date and time of defence: | 13.09.2017 00:00 |
| Date of electronic submission: | 20.07.2017 |
| Date of submission of printed version: | 21.07.2017 |
| Date of proceeded defence: | 13.09.2017 |
| Opponents: | doc. RNDr. Arnošt Komárek, Ph.D. |
| Guidelines |
| One option to increase an overall flexibility of parametric regression models is to assume varying coefficient models instead. The model parameters are not some fixed unknown numbers but rather some smooth functions while their specific values usually depend on some other covariate(s). These models gained a lot of popularity especially due to some recent developments in algorithmic computations, fast computers and quite complex datasets which are of interest.
The aim of this thesis is to gain some knowledge about the varying-coefficient models and to provide some brief summary of existing methods and fitting algorithms. Basic statistical properties should be discussed and some modifications and model extensions can be further pursued. The finite sample performance should be investigated using some simulations and a real data example. |
| References |
| [1] Hastie, T. and Tibshirani, R. (1993). Varying-coefficient models. Journal of the Royal Statistical Society B, Vol.55, No.4, 757-796.
[2] Fan, J. and Zhang, W. (2008). Statistical methods with varying coefficient models. Statistics and its Interface, Vol.1, 179–195. [3] Cai, Z., Fan, J., and Li, R. (2000). Efficient Estimation and Inferences for Varying-Coefficient Models. Journal of the American Statistical Association, Vol.95, No.451, 888-902. [4] Nicholls, D.F. and Pagan, A.R. (1985). Varying Coefficient Regression. Handbook of Statistics, Vol.5, 413-449. |