Nonparametric and Robust Methods

Study Course Description

Course Description Statuss:Approved

Course Description Version:3.00

Study Course Accepted:26.01.2021 12:28:27

Study Course Information
Course Code:		SL_116		LQF level:		Level 7
Credit Points:		4.00		ECTS:		6.00
Branch of Science:		Mathematics; Theory of Probability and Mathematical Statistics		Target Audience:		Life Science
Study Course Supervisor
Course Supervisor:		Jānis Valeinis
Study Course Implementer
Structural Unit:		Statistics Unit
The Head of Structural Unit:
Contacts:		23 Kapselu street, 2nd floor, Riga, statistikarsu[pnkts]lv, +371 67060897
Study Course Planning
Full-Time - Semester No.1
Lectures (count)		14	Lecture Length (academic hours)		2	Total Contact Hours of Lectures		28
Classes (count)		14	Class Length (academic hours)		2	Total Contact Hours of Classes		28
Total Contact Hours								56
Part-Time - Semester No.1
Lectures (count)		14	Lecture Length (academic hours)		1	Total Contact Hours of Lectures		14
Classes (count)		14	Class Length (academic hours)		2	Total Contact Hours of Classes		28
Total Contact Hours								42
Study course description
Preliminary Knowledge:
• Familiarity with probability theory and mathematical statistics. • Basic knowledge in R is required.
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.
Topic Layout (Full-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Basic concepts of nonparametric statistics: definitions and examples. Testing normality and other assumptions for classical parametric procedures. Transformations of data.			Lectures		1.00	auditorium
2	Testing normality, homogeneity and other assumptions in classical statistical procedures using simulated and real datasets in R.			Classes		1.00	computer room
3	Classical nonparametric tests: basic concepts. Sing test and Wilcoxon test for the one-sample case.			Lectures		1.00	auditorium
4	Comparison of t-test, sign test and Wilcoxon test for the one-sample case in R. Confidence procedures and power simulations.			Classes		1.00	computer room
5	Wilcoxon rank-sum test and Wilcoxon signed-rank test in the two-sample case.			Lectures		1.00	auditorium
6	Wilcoxon rank-sum test and Wilcoxon signed-rank tests in R.			Classes		1.00	computer room
7	Nonparametric one and two-way ANOVA procedures. Friedman and Kruskal-Wallis tests. Post-hoc procedures.			Lectures		1.00	auditorium
8	Dataset analysis in program R using both parametric and nonparametric ANOVA procedures.			Classes		1.00	computer room
9	General smoothing concepts. Histogram and binwidth parameter selection.			Lectures		1.00	auditorium
10	Histogram and binwidth parameter selection in R.			Classes		1.00	computer room
11	Nonparametric density estimation. Bandwidth parameter selection using crossvalidation.			Lectures		1.00	auditorium
12	Nonparametric density estimation in R.			Classes		1.00	computer room
13	Nonparametric regression: Nadaraya-Watson kernel regression, local polynomial regression.			Lectures		1.00	auditorium
14	Nonparametric regression in R.			Classes		1.00	computer room
15	Generalized additive models GAM.			Lectures		1.00	auditorium
16	Generalized additive models in R.			Classes		1.00	computer room
17	Introduction to data resampling methods: Jackknife and Bootstrap methods. Bootstrap method for confidence intervals. Permutation tests.			Lectures		1.00	auditorium
18	Data resampling methods in R. Bootstrap method for confidence intervals and permutation testing examples in R.			Classes		1.00	computer room
19	Robust inference. Basic definition and examples. M-estimators. Robust location and scale estimation.			Lectures		1.00	auditorium
20	Robust location and scale estimation in R.			Classes		1.00	computer room
21	Robust confidence intervals and statistical tests.			Lectures		1.00	auditorium
22	Robust confidence intervals and tests in R. Comparison with classical methods.			Classes		1.00	computer room
23	Robust ANOVA methods in simple one-way and two-way designs.			Lectures		1.00	auditorium
24	Robust ANOVA methods in R. Comparison with parametric procedures.			Classes		1.00	computer room
25	Robust regression.			Lectures		1.00	auditorium
26	Robust regression in R. Comparison with linear and nonparametric regressions.			Classes		1.00	computer room
27	Insight in nonparametric and robust procedures in different areas of statistical applications.			Lectures		1.00	auditorium
28	Different R packages for other nonparametric and robust methods.			Classes		1.00	computer room
Topic Layout (Part-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Basic concepts of nonparametric statistics: definitions and examples. Testing normality and other assumptions for classical parametric procedures. Transformations of data.			Lectures		1.00	auditorium
2	Testing normality, homogeneity and other assumptions in classical statistical procedures using simulated and real datasets in R.			Classes		1.00	computer room
3	Classical nonparametric tests: basic concepts. Sing test and Wilcoxon test for the one-sample case.			Lectures		1.00	auditorium
4	Comparison of t-test, sign test and Wilcoxon test for the one-sample case in R. Confidence procedures and power simulations.			Classes		1.00	computer room
5	Wilcoxon rank-sum test and Wilcoxon signed-rank test in the two-sample case.			Lectures		1.00	auditorium
6	Wilcoxon rank-sum test and Wilcoxon signed-rank tests in R.			Classes		1.00	computer room
7	Nonparametric one and two-way ANOVA procedures. Friedman and Kruskal-Wallis tests. Post-hoc procedures.			Lectures		1.00	auditorium
8	Dataset analysis in program R using both parametric and nonparametric ANOVA procedures.			Classes		1.00	computer room
9	General smoothing concepts. Histogram and binwidth parameter selection.			Lectures		1.00	auditorium
10	Histogram and binwidth parameter selection in R.			Classes		1.00	computer room
11	Nonparametric density estimation. Bandwidth parameter selection using crossvalidation.			Lectures		1.00	auditorium
12	Nonparametric density estimation in R.			Classes		1.00	computer room
13	Nonparametric regression: Nadaraya-Watson kernel regression, local polynomial regression.			Lectures		1.00	auditorium
14	Nonparametric regression in R.			Classes		1.00	computer room
15	Generalized additive models GAM.			Lectures		1.00	auditorium
16	Generalized additive models in R.			Classes		1.00	computer room
17	Introduction to data resampling methods: Jackknife and Bootstrap methods. Bootstrap method for confidence intervals. Permutation tests.			Lectures		1.00	auditorium
18	Data resampling methods in R. Bootstrap method for confidence intervals and permutation testing examples in R.			Classes		1.00	computer room
19	Robust inference. Basic definition and examples. M-estimators. Robust location and scale estimation.			Lectures		1.00	auditorium
20	Robust location and scale estimation in R.			Classes		1.00	computer room
21	Robust confidence intervals and statistical tests.			Lectures		1.00	auditorium
22	Robust confidence intervals and tests in R. Comparison with classical methods.			Classes		1.00	computer room
23	Robust ANOVA methods in simple one-way and two-way designs.			Lectures		1.00	auditorium
24	Robust ANOVA methods in R. Comparison with parametric procedures.			Classes		1.00	computer room
25	Robust regression.			Lectures		1.00	auditorium
26	Robust regression in R. Comparison with linear and nonparametric regressions.			Classes		1.00	computer room
27	Insight in nonparametric and robust procedures in different areas of statistical applications.			Lectures		1.00	auditorium
28	Different R packages for other nonparametric and robust methods.			Classes		1.00	computer room
Assessment
Unaided 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.
Assessment Criteria:
Assessment on the 10-point scale according to the RSU Educational Order: • Homeworks of practical classes – 50%. • Final written exam – 50%.
Final Examination (Full-Time):		Exam (Written)
Final Examination (Part-Time):		Exam (Written)
Learning Outcomes
Knowledge:		• 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:		• 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.
Competencies:		• 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
Bibliography
No.	Reference
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.