Identifying Data 2019/20
Subject (*) Nonparametric Methods Code 614493111
Study programme
Mestrado Universitario en Técnicas Estadísticas (Plan 2019)
Descriptors Cycle Period Year Type Credits
Official Master's Degree 1st four-month period
 First Obligatory 5
Language
Teaching method Face-to-face
Prerequisites
Department Matemáticas
Coordinador
Vilar Fernandez, Jose Antonio
 E-mail
jose.vilarf@udc.es
Lecturers
Vilar Fernandez, Jose Antonio
 E-mail
jose.vilarf@udc.es
Web http://http://dm.udc.es/modes/es/node/45?q=es/node/81&profesorId=10&type=1
General description Se introducen os métodos de estimación non paramétrica da función de distribución de probabilidade, da función de densidade de probabilidade e de modelos de regresión, con especial énfase nas técnicas de suavización tipo núcleo. Tamén se presentan os principais tests non paramétricos de bondade de axuste e de asociación en táboas de continxencia, e tests de localización baseados en rangos para unha, dúas e máis de dúas mostras.

Study programme competencies
Code Study programme competences
A16 CE1 - Coñecer, identificar, modelar, estudar e resolver problemas complexos de estatística e investigación operativa, nun contexto científico, tecnolóxico ou profesional, xurdidos en aplicacións reais.
A17 CE2 – Desenvolver autonomía para a resolución práctica de problemas complexos surdidos en aplicación reais e para a interpretación dos resultados cara á axuda na toma de decisións.
A18 CE3 - Adquirir coñecementos avanzados dos fundamentos teóricos subxacentes ás distintas metodoloxías da estatística e a investigación operativa, que permitan o seu desenvolvemento profesional especializado.
A19 CE4 - Adquirir as destrezas necesarias no manexo teórico-práctico da teoría de probabilidade e as variables aleatorias que permitan o seu desenvolvemento profesional no eido científico/académico, tecnolóxico ou profesional especializado e multidisciplinar.
A20 CE5 - Profundizar no coñecemento dos fundamentos teórico-prácticos especializados de modelado e estudo de distintos tipos de relacións de dependencia entre variables estatísticas.
A21 CE6 - Adquirir coñecementos teórico-prácticos avanzados de distintas técnicas matemáticas, orientadas específicamente á axuda na toma de decisións, e desenvolver a capacidade de reflexión para avaliar e decidir entre distintas perspectivas en contextos complexos.
A23 CE8 - Adquirir coñecementos teórico-prácticos avanzados das técnicas destinadas á realización de inferencias e contrastes relativos a variables e parámetros dun modelo estatístico, e saber aplicalos con autonomía suficiente nun contexto científico, tecnolóxico ou profesional.
B1 CB6 - Posuír e comprender coñecementos que acheguen unha base ou oportunidade de ser orixinais no desenvolvemento e/ou aplicación de ideas, a miúdo nun contexto de investigación
B2 CB7 - Que os estudantes saiban aplicar os coñecementos adquiridos e a súa capacidade de resolución de problemas en ámbitos novos ou pouco coñecidos dentro de contextos máis amplos (ou multidisciplinares) relacionados coa súa área de estudo
B3 CB8 - Que os estudantes sexan capaces de integrar coñecementos e enfrontarse á complexidade de formular xuízos a partir dunha información que, sendo incompleta ou limitada, inclúa reflexións sobre as responsabilidades sociais e éticas vinculadas á aplicación dos seus coñecementos e xuízos
B4 CB9 - Que os estudantes saiban comunicar as súas conclusións e os coñecementos e razóns últimas que as sustentan a públicos especializados e non especializados dun modo claro e sen ambigüidades
B5 CB10 - Que os estudantes posúan as habilidades de aprendizaxe que lles permitan continuar estudando dun modo que haberá de ser en gran medida autodirixido ou autónomo.
B17 CG1 - Coñecer, comprender e saber aplicar os principios, metodoloxías e novas tecnoloxías na estatística e a investigación operativa en contextos científico/académicos, tecnolóxicos ou profesionais especializados e multidisciplinares, así como adquirir as destrezas e competencias descritas nos objectivos generales do título.
B18 CG2 - Desenvolver autonomía para identificar, modelar e resolver problemas complexos da estatística e da investigación operativa en contextos científico/académicos, tecnolóxicos ou profesionais especializados e multidisciplinares.
B19 CG3 - Desenvolver a capacidade para realizar estudos e tarefas de investigación e transmitir os resultados a públicos especializados, académicos e xeneralistas.
B20 CG4 - Integrar coñecementos avanzados e enfrontarse á toma de decisións a partir de información científica e técnica.
B21 CG5 - Desenvolver a capacidade de aplicación de algoritmos e técnicas de resolución de problemas complexos no eido da estatística e a investigación operativa, manexando o software especializado axeitado.
C11 CT1 - Desenvolver firmes capacidades de razoamento, análise crítica e autocrítica, así como de argumentación e de síntese, contextos especializados e multidisciplinais.
C13 CT3 - Ser capaz de resolver problemas complexos en novos escenarios mediante a aplicación integrada dos coñecementos.
C14 CT4 - Desenvolver unha sólida capacidade de organización e planificación do estudo, asumindo a responsabilidade do seu propio desenvovemento profesional, para a realización de traballos en equipo e de xeito autónomo.
C15 CT5 - Desenvolver capacidades para o aprendizaxe e a integración no traballo en equipos multidisciplinais, nos ámbitos científico/académico, tecnolóxico e profesional.

Learning aims
Learning outcomes Study programme competences
To become familiar with basic techniques of nonparametric estimation of the probability distribution function, the probability density function and the regression function. AC18
AC19
AC20
AC21
AC23
 BJ1
BJ3
BJ5
BJ20
BJ21
 CJ13
Get the know-how to apply the main nonparamteric tests for goodness-of-fit and association. AC18
AC19
AC20
AC21
AC23
 BJ1
BJ3
BJ5
BJ20
BJ21
 CJ13
Get thorough knowledge about strengths and weaknesses of the nonparametric approach in data analysis. AC16
AC17
AC19
AC21
AC23
 BJ2
BJ17
BJ20
BJ21
 CJ11
CJ13
Develop autonomus competence to apply nonparametric tools in data analysis, in complex and/or multidisciplinary scenarios. AC17
 BJ18
 CJ14
CJ15
To know how present data analysis based on nonparametric techniques to both specialized and non-specialized audience. BJ4
BJ19

Contents
Topic Sub-topic
Nonparametric distribution estimation
 The empirical distribution. Properties. Moments and quantiles estimation.
Classical one-sample nonparametric tests. Goodness-of-fit tests: Kolmogorov-Smirnov test.
Normality analysis: Q-Q plot, Lilliefors test, Shapiro-Wilk test, transformations for normality.
One-sample location tests: sign test, Wilcoxon signed-rank test.
Two-sample tests.
 Two-sample comparison: Kolmogorv-Smirnov test for two-samples, Mann-Whitney-Wilcoxon test.
Extensions for three or more samples: Kruskal-Wallis test, Friedman test.
Tests based on contingency tables. Contingency tables analysis. Chi-squared tests for goodness-of-fit, homogeneity and independence on contingency tables.
Smoothing methods: nonparametric density estimation. The histogram. Kernel density estimation. Assessment of density estimators. Smoothing parameter selectors in kernel density estimation: cross-validation and plug-in approaches. Multivariate kernel density estimation.
Nonparametric regression estimation. Kernel regression. Local polynomial regression. k-nearest neighbor regression. Smoothing parameter selectors in kernel regression estimation: cross-validation and plug-in approaches. Loess algorithm. Spline regression: a brief introduction.

Planning
Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours
Guest lecture / keynote speech A16 A18 A21 A23 B1 B3 B17 B20 C13 C11 20 15 35
Seminar A16 A17 A19 A20 A21 A23 B2 B3 B5 B17 B18 B19 B20 B21 C11 C13 7 5.25 12.25
ICT practicals A17 A19 A20 A21 A23 B2 B5 B18 B19 7 5.25 12.25
Problem solving A16 A17 A19 A23 B2 B3 B5 B18 B19 B20 B21 C11 C13 C14 C15 0 28.5 28.5
Case study A16 A17 A19 A21 A23 B2 B3 B4 B5 B18 B19 B20 B21 C13 C14 C15 0 21 21
Supervised projects A17 A19 A21 A23 B2 B4 B5 B18 B19 B20 B21 C11 C13 C14 C15 0 9.5 9.5
Workshop A17 A16 B2 B3 B4 B17 B18 B19 C11 C13 C14 C15 1 2.5 3.5
Objective test A16 A17 A18 A19 A20 A21 A23 B20 B21 C11 C13 0 3 3
 
Personalized attention 0 0
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies Description
Guest lecture / keynote speech The theoretical principles of the nonparametric tools and procedures for their application in practice will be introduced. Their interest in applications will be illustrated by using specific real examples from different disciplines, highlighting advantages and limitations. Students participation will be strongly encouraged.
Seminar Specific problems and suitable approaches to get them solved will be presented in seminars. The main objective is to show how the concepts and algorithms exposed in the keynote speechs are useful to face these problems.
ICT practicals Interactive sessions addressed to solve specific exercises by using scripts with free code from R software. The lecturer will support and supervise the right application of the knowledge and skills gathered by the students.
Problem solving Issues, exercises and examples that can be addressed by using nonparametric techniques of inference and modeling will be provided to be individually solved by students.
Case study Specific study cases will be proposed to be solved in group and/or individually.
Supervised projects Solutions for exercises and study case will be supervised by the lecturer.
Workshop Case study analyzed in detail by students will be presented and discussed.
Objective test Written examination to assess the the acquisition of knowledge.

Personalized attention
Methodologies
ICT practicals
Supervised projects
Description



The ICT practicals will be conducted to solve exercises by using scripts with free code from R software. This way, students must thoroughly understand the used R-packages, particularly the main functions and the type of generated outputs. To reach this objective as soon as possible, personalized attention is desirable and will be provided during the session.




Every student must complete, properly supervised, a specific project involving real data and using techniques and skills developed throughout the course. Personalized attention will consist in monitoring the different stages of the project at succesive working meetings.

Assessment
Methodologies Competencies Description Qualification
Workshop A17 A16 B2 B3 B4 B17 B18 B19 C11 C13 C14 C15 The defence in the workshop of a supervised work is worth 5% of the global mark. 5
Objective test A16 A17 A18 A19 A20 A21 A23 B20 B21 C11 C13 The final objective test is a written exam consisting of several theoretical-practical questions on the key contents of the subject, including proper interpretation of the results obtained from the R software. This exam is mandatory and the attained mark is worth up to 70% of the global qualification. 70
Problem solving A16 A17 A19 A23 B2 B3 B5 B18 B19 B20 B21 C11 C13 C14 C15 Solving and timely delivery of exercises proposed during the course will be part of the continuous evaluation. Correct answers in this item is worth up to 7.5% of the global qualification. 7.5
Case study A16 A17 A19 A21 A23 B2 B3 B4 B5 B18 B19 B20 B21 C13 C14 C15 Solving and timely delivery of case study proposed during the course will be part of the continuous evaluation. Correct answers in this item is worth up to 7.5% of the global qualification. 7.5
Supervised projects A17 A19 A21 A23 B2 B4 B5 B18 B19 B20 B21 C11 C13 C14 C15 A detailed development of the proposed study case, completed either individually or in group, is worth up to 10% of the global qualification. 10
 
Assessment comments

Presentación á avaliación: Considérase que un estudante concurre a unha convocatoria cando participa en actividades que lle permiten obter cando menos un 50% da avaliación final. A cualificación obtida conservarase entre as oportunidades (ordinaria e extraordinaria) dentro da convocatoria de cada curso.

Oportunidade extraordinaria de recuperación (proba de xullo): O peso da avaliación continua na oportunidade extraordinaria de recuperación (proba de xullo) será o mesmo que na avaliación ordinaria. Na segunda oportunidade de avaliación (recuperación), realizarase un exame e a nota final será o máximo de tres cantidades: a nota da avaliación ordinaria, a nota do novo exame e a media ponderada do novo exame e a avaliación continua.

Sources of information
Basic
  • Fan J., Gijbels I. (1996) Local polynomial modelling and its applications. Monographs on Statistics and Applied Probability 66. Chapman & Hall/CRC.
  • Gibbons J.D, Chakraborti S. (2010) Nonparametric Statistical Inference (5th edition). Statistics: Textbooks and Monographs. Chapman & Hall/CRC.
  • Hollander M., Wolfe D.A., Chicken E. (2014) Nonparametric Statistical Methods (3rd edition). Wiley Series in Probability and Statistics, Wiley.
  • Silverman, B. W. (1986) Density Estimation for Statistics and Data Analysis. Monographs on Statisticsand Applied Probability 26. Chapman & Hall/CRC. 
  • Wand M.P., Jones M.C. (1995) Kernel smoothing. Monographs on Statistics and Applied Probability 60. Chapman & Hall/CRC.
Complementary
  • Bowman A.W., Azzalini A. (1997) Applied Smoothing Techniques for Data Analysis. Oxford: Oxford University Press.
  • McKean J.W., Kloke J. (2014) Nonparametric Statistical Methods using R. The R Series. Chapman and Hall/CRC.
  • Simonoff J.S. (1996) Smoothing methods in statistics. Springer Series in Statistics. New York: Springer.
  • Smeeton N.C, Sprent P. (2007) Applied Nonparametric Statistical Methods (4th edition) Chapman & Hall/CRC Texts in Statistical Science. Chapman & Hall/CRC.
  • Wasserman L. (2006) All of Nonparametric Statistics. Springer Texts in Statistics. New York: Springer.

Recommendations
Subjects that it is recommended to have taken before

Subjects that are recommended to be taken simultaneously

Subjects that continue the syllabus

Other comments

It is advisable that students have basic notions on probability calculus and statistic. Also it is desirable to posses regular skills to manage computers, and particularly knowledge of statistical software. To be able of understanding the practical sense of the learnt methods will allow to improve the learning process.


(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.