Selection of variables and estimation of regression coefficients in datasets with the number of variables exceeding the number of observations consti- tutes an often discussed topic in modern statistics. Today the maximum penalized likelihood method with an appropriately selected function of the parameter as the penalty is used for solving this problem. The penalty should evaluate the benefit of the variable and possibly mitigate or nullify the re- spective regression coefficient. The SCAD and LASSO penalty functions are popular for their ability to choose appropriate regressors and at the same time estimate the parameters in a model. This thesis presents an overview of up to date results in the area of characteristics of estimates obtained by using these two methods for both small number of regressors and multidimensional datasets in a normal linear model. Due to the fact that the amount of pe- nalty and therefore also the choice of the model is heavily influenced by the tuning parameter, this thesis further discusses its selection. The behavior of the LASSO and SCAD penalty functions for different values and possibili- ties for selection of the tuning parameter is tested with various numbers of regressors on simulated datasets.
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:347986 |
| Date | January 2016 |
| Creators | Chlubnová, Tereza |
| Contributors | Kulich, Michal, Maciak, Matúš |
| Source Sets | Czech ETDs |
| Language | Czech |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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