# NMAK20002U Semiparametric Inference

Volume 2022/2023
Education

MSc Programme in Statistics
MSc Programme in Mathematics-Economics

Content
• Hilbert space
• Semi-parametric model
• Parametric submodel
• Efficient influence function
• M-estimators
• Targeted MLE
• Aspects of practical implementation and analysis in R.

Modern statistical methods use semiparametric models to avoid model misspecification, which may be the result of using a purely parametric model in a given context where the parametric assumptions are not satisfied. A semiparametric model consist of a parametric part that typically focuses on what is of primary interest to the investigator. This could be a relative risk if it is of interest to compare the efficacy of two treatments on some given outcome. While this is the key parameter it may not be desirable to specify the rest of the statistical model as this part is of no interest to the investigator. Leaving that part unspecified is a typical example of a semiparametric model. It is of interest to develop efficient estimation of the parametric part of the model, i.e., finding the estimator with the smallest asymptotic variance. A key concept is the so-called influence function related to a given estimator.  Finding the efficient estimator and its influence function in semiparametric models turns out to be possible in many interesting cases using classical geometrical concepts for Hilbert spaces such as finding a projection onto a given subspace (the so-called nuisance tangent space). This technique is extremely useful when faced with a new statistical challenge (model) where it is of interest to develop efficient estimation.

Learning Outcome

Knowledge:
Basic knowledge of the topics covered.

Skills:

• Geometric properties of influence functions
• Discuss and understand issues properties of estimand and associated estimators
• Ability to use R for the analysis of certain semi-parametric models.

Competences:

• Understand interplay with influence functions, score funtions and and the sampling setting.
• Understand properties and limitations for estimation in certain semi-parametric models.

Literature:
A. Tsiatis.  Semiparametric Theory and Missing Data. Springer, 2006.

StatMet and MStat (alternatively MatStat from previous years) or similar.

Academic qualifications equivalent to a BSc degree is recommended.
4 hours of a mixture between lectures and student presentations for 7 weeks.
2 hours of practical for 7 weeks.
• Category
• Hours
• Lectures
• 28
• Preparation
• 84
• Theory exercises
• 14
• Project work
• 40
• Exam
• 40
• Total
• 206
Oral
Collective
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
Practical written examination, 40 hours
Type of assessment details
Written assignment, 40 hours
Aid
All aids allowed
Marking scale