Guide in PDF format
Logo

Statistical Inference 2

Code: 104856
Credits: 6
2026/2027
Degree programme Type Course
Applied Statistics OB 2

Contact lecturer

Name :
Alejandra Cabaña Nigro
Email :
anaalejandra.cabana@uab.cat

Teaching staff

Francisco Javier Delgado Vences

Group languages

You can consult this information at the end of the document.

Prerequisites

It is recommended that you are familiar with the contents of Calculus 1 and 2, Probability and Inference-1.

Objectives

In this course we shall stablish the theoretical foundations of the concept of Inference —that is, how Statistics quantifies the uncertainty of the information extracted from data.
The concepts of Modeling, Estimation (both point and interval), and Goodness of Fit will also be established.

The theoretical foundations of different estimation methods will be introduced, especially the Maximum Likelihood Method and the Method of Moments, as well as the fundamental properties of estimators: invariance, sufficiency, efficiency, bias, mean squared error, and asymptotic properties.

The topic of hypothesis testing will be explored in depth, including classical theory (Fisher’s exact tests, optimal theory, asymptotic theory, and non-parametric tests).

Learning outcomes

  • CM08 (Determine the sample size and the sampling strategies required to conduct a specific study in the field of applications.) Determine the sample size and the sampling strategies required to conduct a specific study in the field of applications.
  • KM09 (Discover the fundamental properties of estimators: invariance, sufficiency, efficiency, bias, mean square error and asymptotic properties, in the classical and Bayesian domains.) Discover the fundamental properties of estimators: invariance, sufficiency, efficiency, bias, mean square error and asymptotic properties, in the classical and Bayesian domains.
  • KM11 (Identify exact and asymptotic sampling distributions of different statistics.) Identify exact and asymptotic sampling distributions of different statistics.
  • SM09 (Analyse data through different inference techniques using statistical software.) Analyse data through different inference techniques using statistical software.
  • SM10 (Use different estimation methods depending on the context of application.) Use different estimation methods depending on the context of application.

Contents

Topic 1: Parametric Hypothesis Testing

  • Fisher’s exact theory. Types of error. Null and alternative hypotheses.
  • Neyman–Pearson lemma. Likelihood ratio tests. Asymptotic distribution.
  • Other asymptotic tests based on likelihood (Score and Wald).


Topic 2: Nonparametric Statistics

  • Linear rank tests
  • Permutation tests.
  • Tests based on the empirical distribution function.


Learning activities and methodology

Title Hours ECTS Learning outcomes
Study and think problems 30 1.2
Problems 14 0.56
Theory 26 1.04
Practical work with computer tools 30 1.2
Tutorials 5 0.2
Practices 12 0.48

The course includes theoretical lectures, problem-solving sessions, and practical classes.
New material will be mainly introduced during theoretical lectures, but students are expected to expand on the explanations through autonomous study, supported by the recommended bibliography. Student participation during the professor's presentations will be valued.
A midterm assessment covering theory and problem-solving will be held during the exam week scheduled by the Faculty.
Supplementary review materials will be posted on the Virtual Campus to support the class notes.

The problem-solving classes will be dedicated to guided resolution of selected exercises. Active participation in these sessions will be particularly valued (and graded).

The practical sessions will introduce the use of R software for statistical applications. Both descriptive and inferential methodologies will be covered.

 

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Partial exam 35% 5 0.2 KM09, KM11, SM10
Final exam 35% 8 0.32 CM08, KM09, KM11, SM10
Practical & problems (deliveries, controls) 30% 20 0.8 KM09, KM11, SM09, SM10

Continuous assessment

The course will be assessed through the submission of assignments (exercises, problem sets and/or practical work), some of them to be done during practical sessions and two exams (theory and problems).

To compute the weighted grade for continuous assessment, students must obtain a minimum of 3 out of 10 in each component.

Single assessment

Students who choose the single assessment option will be evaluated based on:

  • A theory exam,
  • A problem-solving test,
  • Submission of the reports for the first and last practical sessions.

The evaluation of submitted reports may require an individual interview with the instructor.

The final grade will be the weighted average of the three components:

  • Exam (theory and problems): 45%
  • Exam (computer solving of excercises): 45%
  • Report submissions: 10%

Resit exam

If the final grade is below 5, students will have another opportunity to pass the course through a resit exam, scheduled by the degree coordinators.

This resit allows recovery of up to 70% of the grade corresponding to theory and problem-solving.

The practical report component is not recoverable.

Use of Artificial Intelligence (AI)

Use of AI technologies is permitted in this course, but only for support tasks, such as:

  • Literature searches,
  • Code or text proofreading,
  • Translations.

Students must clearly identify the parts generated with the help of AI, specify the tools used, and include a critical reflection on how these tools influenced the process and the final result of the activity.

Lack of transparency in the use of AI in assessed activities will be considered academic dishonesty, and may lead to partial or total penalties on the grade, or more severe sanctions in serious cases.


The commission of any irregularity in an assessment activity (academic fraud, plagiarism, or improper use of AI, unless such use is expressly authorized in the course guide) that may lead to a significant change in the grade will result in that assessment being graded 0.

If the course guide stipulates that passing the course requires obtaining a minimum grade in that assessment activity, or if multiple irregularities occur in assessment activities within the same course, the final grade for the course will be 0.

In addition, disciplinary proceedings may be initiated against any student who commits any of these irregularities.

Bibliography

Bibliografía básica

  • Casella, G., & Berger, R. L. (2002). Statistical Inference (2ª ed.). Wadsworth, Belmont, CA.

  • Casella, G., Berger, R. L., & Santana, D. (2002). Solutions Manual for Statistical Inference (2ª ed.).

  • Ruiz Maya Pérez, L., & Martín-Pliego López, F. J. (2006). Estadística II: Inferencia. Editorial AC.

  • Millar, R. B. (2011). Maximum Likelihood Estimation and Inference: With Examples in R, SAS and ADMB. Wiley.

  • Peña, D. (2002). Fundamentos de Estadística. Alianza Editorial.

  • Verzani, J. (2005). Using R for Introductory Statistics. Taylor & Francis.

Bibliografía complementaria

  • DasGupta, A. (2008). Asymptotic Theory of Statistics and Probability. Springer.

  • Rice, J. A. (2007). Mathematical Statistics and Data Analysis (3ª ed.). Duxbury/Thomson.

  • Kendall, M., & Stuart, A. (1983). The Advanced Theory of Statistics. Griffin and Co. Limited, London.

  • Lehmann, E. L., & Romano, J. P. (2005). Testing Statistical Hypotheses (3ª ed.). Springer.

  • Rao, C. R. (1973). Linear Statistical Inference and Its Applications. Wiley, London.

  • Rizzo, M. L. (2007). Statistical Computing with R. Computer Science and Data Analysis Series, Chapman & Hall / CRC.

Software

R Core Team (2025). R: A language and environment for statisticalcomputing. R Foundation for Statistical Computing, Vienna, Austria.

URL https://www.R-project.org/.

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 1 Spanish first semester afternoon
(PAUL) Classroom practices 1 Catalan/Spanish first semester afternoon
(PLAB) Practical laboratories 1 Catalan/Spanish first semester afternoon
(PLAB) Practical laboratories 2 Catalan first semester afternoon