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programu PMSE

NMST434 Modern statistical methods (official information)

Requirements:

The knowledge of the statistics and probability theory at the level of courses Mathematical Statistics 1 and 2 (NMSA331 and NMSA332), Probability Theory 1 (NMSA333) and Linear regression (NMSA407).

Among others we will use the following concepts: almost sure convergence, convergence in probability, convergence in distribution, law of large numbers and central limit theorem for independent and identically distributed random vectors. A nice overview (in Czech language) of most of the results that are used in the course is available here.

• Asymptotic methods - Delta Theorem
• Theory of maximum likelihood
• Profile, conditional and marginal likelihood
• M-estimators and Z-estimators, Quasi-likelihood, Robust estimation
• Bootstrap
• Quantile regression
• EM-algorithm
• Methods for missing data
• Kernel density estimation
• Kernel nonparametric regression

Exercise classes
Exercise classes accompany the lecture with both theoretical as well as practical examples and illustrations.

• Requirements to get the course credit are explained in detail in this document (pdf).
• Current version of the course notes for this academic year.
• Some information about the exam.
• Homework assignments.
  Datasets for the homework assignments: defects2, random-numbers, foodexp, failures.

• Incosistent MLE - nmst434-E03-incosistent-MLE.R
• Number of boys in large families - nmst434-E03-number-of-males.R.

• nmst434-E06.R
• Dataset - concentration_vs_counts.RData.

• Working script - nmst434-E07.R
• Datasets - IQ-en.RData, Kojeni.csv (the code supposes that datasets are placed in the subdirectory `data' of the working directory)

• Working script - nmst434-E08.R
• Datasets - IQ-en.RData, (the code supposes that datasets are placed in the subdirectory `data' of the working directory)

• Working script - nmst434-E09.R
• Datasets - iq.RData, stillbirth.csv, pribram.csv (the code supposes that datasets are placed in the subdirectory `data' of the working directory).

• Working script - nmst434-E10.R
• AAUP.RData (the working script assumes that datasets are stored in the directory 'data' that is placed in the working directory)

• Working script - nmst434-E11.R

• Working script - nmst434-E12 .R
• Supporting script fctions.R.

• Working script - nmst434-E13.R

• Working script - nmst434-E14.R