Advanced and Robust Regression Models

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Department of Mathematics

Synopsis:

1.Introduction to robust regression - M-estimates, qualitative and quantitative robustness, influential functions, outliers, leverage points.

2.The least median of squares, the trimmed least squares and the least trimmed squares.

3.Weighted least squares and least weighted squares, algorithms, applications.

4.Instrumental weighted variables and their robustification.

5.AR, MA, AR (I) MA, invertibility and stationarity condition. Smoothing of trend using curves, moving averages and exponential. Seasonal and cyclic components, tests of randomness, disturbance (Prais-Winsten, Cochrane-Orcutt).

6.Introduction to mixed linear models, estimation of parameters (ML, REML), generalized mixed linear models.

7.Repeated measurements, Longitudinal data, correlation structure in data.

8.Philosophical debate on mathematical modeling and regression analysis.

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Key references:

[1] Víšek, J. Á., Estimating the Model with Fixed and Random Effects by a Robust Method, Methodology and Computing in Applied Probability 17, 2015

[2] Víšek, J. Á., Representation of the least weighted squares, Advances and Applications in Statistics 47, 2015

Recommended references:

[3] Hardle, W., Applied Nonparametric Regression (1990), ISBN 0-521-42950-1

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Aplikované matematicko-stochastické metody (compulsory elective course)