Veidlapa Nr. M-3 (8)
Study Course Description
Nonparametric and Robust Methods
Course Code
SL_116
Branch of Science
Mathematics; Theory of probability and mathematical statistics
ECTS
6.00
Target Audience
Life Science
LQF
Level 7
Study Type And Form
Full-Time; Part-Time
Study Course Implementer
Course Supervisor
Jānis Valeinis
Structure Unit Manager
Andrejs Ivanovs
Structural Unit
Statistics Unit
Contacts
23 Kapselu street, 2nd floor, Riga, statistika@rsu.lv, +371 67060897
About Study Course
Objective
The objective of this course is to give students the in-depth knowledge of nonparametric and robust methods in mathematical statistics. In biostatistical applications it is common that the sample sizes are small and the normality of data is questionable. Moreover, the classical t-test and ANOVA procedure require additionally homogeneity condition which is often violated. Nonparametric and robust procedures often are used in those situations. Classical linear regression also requires normality assumption and is limited to describe only the linear dependence. Nonparametric smoothing techniques allow to estimate the regression function in a very general way. Resampling methods are popular especially for deriving confidence intervals. The software package R will be used for computation and case study applications.
Preliminary Knowledge
• Familiarity with probability theory and mathematical statistics.
• Basic knowledge in R is required.
Learning Outcomes
Knowledge
1.• understand knowledge of and are able to define concepts and procedures of nonparametric and robust statistical procedures. • are acquainted with and are able to choose nonparametric and robust statistical procedures in program R.
Skills
1.• Perform nonparametric testing in R and interpret the results. • Use and apply smoothing techniques for density and regression function estimation. • Be able to perform data resampling methods. • Apply robust procedures for different statistical data problems.
Competences
1.• Understand and support the importance of assumptions made in standard statistical methods. • Be able to make justified decisions between parametric, nonparametric and robust procedures for practical data analysis, demonstrate understanding and ethical responsibility for the potential impact of scientific results on the environment and society. • Independently develop a correct statistical model, critically interpret and present the obtained results, if necessary, further analysis will be performed
Assessment
Individual work
|
Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Individual work |
-
|
-
|
|
1. Individual work with the course material in preparation to lectures according to plan.
2. Independently prepare homeworks after all practical classes practicing the concepts studied in the course.
|
||
Examination
|
Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Examination |
-
|
-
|
|
Assessment on the 10-point scale according to the RSU Educational Order:
• Homeworks of practical classes – 50%.
• Final written exam – 50%.
|
||
Study Course Theme Plan
FULL-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Basic concepts of nonparametric statistics: definitions and examples. Testing normality and other assumptions for classical parametric procedures. Transformations of data.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Testing normality, homogeneity and other assumptions in classical statistical procedures using simulated and real datasets in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Classical nonparametric tests: basic concepts. Sing test and Wilcoxon test for the one-sample case.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Comparison of t-test, sign test and Wilcoxon test for the one-sample case in R. Confidence procedures and power simulations.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Wilcoxon rank-sum test and Wilcoxon signed-rank test in the two-sample case.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Wilcoxon rank-sum test and Wilcoxon signed-rank tests in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Nonparametric one and two-way ANOVA procedures. Friedman and Kruskal-Wallis tests. Post-hoc procedures.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Dataset analysis in program R using both parametric and nonparametric ANOVA procedures.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
General smoothing concepts. Histogram and binwidth parameter selection.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Histogram and binwidth parameter selection in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Nonparametric density estimation. Bandwidth parameter selection using crossvalidation.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Nonparametric density estimation in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Nonparametric regression: Nadaraya-Watson kernel regression, local polynomial regression.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Nonparametric regression in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Generalized additive models GAM.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Generalized additive models in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Introduction to data resampling methods: Jackknife and Bootstrap methods. Bootstrap method for confidence intervals. Permutation tests.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Data resampling methods in R. Bootstrap method for confidence intervals and permutation testing examples in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Robust inference. Basic definition and examples. M-estimators. Robust location and scale estimation.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Robust location and scale estimation in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Robust confidence intervals and statistical tests.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Robust confidence intervals and tests in R. Comparison with classical methods.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Robust ANOVA methods in simple one-way and two-way designs.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Robust ANOVA methods in R. Comparison with parametric procedures.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Robust regression.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Robust regression in R. Comparison with linear and nonparametric regressions.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Insight in nonparametric and robust procedures in different areas of statistical applications.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Different R packages for other nonparametric and robust methods.
|
Total ECTS (Creditpoints):
6.00
Contact hours:
56 Academic Hours
Final Examination:
Exam (Written)
PART-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Basic concepts of nonparametric statistics: definitions and examples. Testing normality and other assumptions for classical parametric procedures. Transformations of data.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Testing normality, homogeneity and other assumptions in classical statistical procedures using simulated and real datasets in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Classical nonparametric tests: basic concepts. Sing test and Wilcoxon test for the one-sample case.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Comparison of t-test, sign test and Wilcoxon test for the one-sample case in R. Confidence procedures and power simulations.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Wilcoxon rank-sum test and Wilcoxon signed-rank test in the two-sample case.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Wilcoxon rank-sum test and Wilcoxon signed-rank tests in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Nonparametric one and two-way ANOVA procedures. Friedman and Kruskal-Wallis tests. Post-hoc procedures.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Dataset analysis in program R using both parametric and nonparametric ANOVA procedures.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
General smoothing concepts. Histogram and binwidth parameter selection.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Histogram and binwidth parameter selection in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Nonparametric density estimation. Bandwidth parameter selection using crossvalidation.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Nonparametric density estimation in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Nonparametric regression: Nadaraya-Watson kernel regression, local polynomial regression.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Nonparametric regression in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Generalized additive models GAM.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Generalized additive models in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Introduction to data resampling methods: Jackknife and Bootstrap methods. Bootstrap method for confidence intervals. Permutation tests.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Data resampling methods in R. Bootstrap method for confidence intervals and permutation testing examples in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Robust inference. Basic definition and examples. M-estimators. Robust location and scale estimation.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Robust location and scale estimation in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Robust confidence intervals and statistical tests.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Robust confidence intervals and tests in R. Comparison with classical methods.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Robust ANOVA methods in simple one-way and two-way designs.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Robust ANOVA methods in R. Comparison with parametric procedures.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Robust regression.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Robust regression in R. Comparison with linear and nonparametric regressions.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Insight in nonparametric and robust procedures in different areas of statistical applications.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Different R packages for other nonparametric and robust methods.
|
Total ECTS (Creditpoints):
6.00
Contact hours:
42 Academic Hours
Final Examination:
Exam (Written)
Bibliography
Required Reading
1.
Lehmann, Erich Leo, and Howard J. D'Abrera. Nonparametrics: statistical methods based on ranks. Holden-Day. 1975.
2.
Wasserman, Larry. All of nonparametric statistics. Springer Science & Business Media. 2006.
3.
Maronna, R. A., Martin, R. D., Yohai, V. J., & Salibián-Barrera, M. Robust statistics: theory and methods (with R). John Wiley & Sons. 2019.
Additional Reading
1.
Agresti, A., Franklin, C. A. Statistics: The Art and Science of Learning from Data (3rd ed.), Pearson Education. 2013
2.
Chan, Bertram KC. Biostatistics for epidemiology and public health using R. Springer Publishing Company. 2015.
3.
DasGupta, Anirban. Asymptotic theory of statistics and probability. Springer Science & Business Media. 2008.