Abstract
Curse of dimensionality is a big obstacle for constructing efficient goodness-of-fit tests for regression models with large or moderate number of covariates. To alleviate this difficulty, numerous efforts have been devoted in the last two decades. This review intends to collect and comment on the developments in this aspect. To make the paper self-contained, basic ideas on goodness-of-fit testing for regression models are also briefly reviewed, and the main classes of methods and their advantages and disadvantages are presented. Further, the difficulty caused by the dimensionality (number of covariates) is then discussed. The relevant dimension reduction methodologies are presented. Further, as a dedication to Stute's 70th birthday, we also include a section to summarize his great contributions other than the results in dimension reduction-based tests.
| Original language | English |
|---|---|
| Title of host publication | From Statistics to Mathematical Finance |
| Subtitle of host publication | Festschrift in Honour of Winfried Stute |
| Editors | Dietmar Ferger, Wenceslao González Manteiga, Thorsten Schmidt, Jane-Ling Wang |
| Publisher | Springer Cham |
| Pages | 105-125 |
| Number of pages | 21 |
| Edition | 1st |
| ISBN (Electronic) | 9783319509860 |
| ISBN (Print) | 9783319509853, 9783319845388 |
| DOIs | |
| Publication status | Published - 29 Oct 2017 |
Scopus Subject Areas
- General Mathematics
- General Medicine
- Economics, Econometrics and Finance(all)
- General Business,Management and Accounting
User-Defined Keywords
- Curse of dimensionality
- Dimension reduction
- Goodness-of-fit
- Model checking
- Parametric regression models
- Projection pursuit