MX002 Goodness-of-fit tests for regression models

Faculty of Science
Spring 2010
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Type of Completion: z (credit).
Teacher(s)
Wenceslao González-Manteiga (lecturer), prof. RNDr. Ivanka Horová, CSc. (deputy)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Course Enrolment Limitations
The course is offered to students of any study field.
Syllabus
  • Contents
  • 1. Introduction .
  • 1.1. Motivation .
  • 1.2. The distribution case .
  • 1.3. Parametric models.
  • 2. Tests based on the estimation of the regression function.
  • 2.1. An example for fixed design.
  • 2.2. An example for random design.
  • 2.3. The generalized likelihood ratio tests.
  • 2.4. Other approaches.
  • 2.5. Bootstrap approximations.
  • 2.6. Connections with the F test and with the log-likelihood ratio test
  • 2.7. Discussion about the power.
  • 3. Tests based on the estimation of the integrated regression function.
  • 3.1. The integrated regression function.
  • 3.2. The marked empirical process.
  • 3.3. Bootstrap approximations.
  • 4. Related setups, extensions and open problems.
  • 4.1. Testing the equality of regression curves.
  • 4.2. Testing partial linearity .
  • 4.3. Generalized linear regression models.
  • 4.4. Significance tests.
  • 4.5. Testing in additive models.
  • 4.6. Goodness-of-fit for regressions models with incomplete data.
  • 4.7. Tests with dependent data.
  • 4.8. Tests based on empirical likelihood.
  • 4.9. Tests based on the empirical distribution of the residuals.
  • 4.10. Tests for directional data.
  • 4.11. Tests for functional data.
Language of instruction
English
Further Comments
Study Materials
The course is taught only once.
The course is taught in blocks.
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