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Analysis of contingency tables
Kalina, Jan
The paper compares asymptotic, exact conditional and exact unconditional tests for the evaluation of contingency tables. Relationship of asymptotic methods with generalized linear models is studied. The work focuses on exact methods, which yield promising results in the analysis of data with small samples. Some of the methods are alternatively derived in the context of logistic and Poisson regression.
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On Heteroscedasticity in Robust Regression
Kalina, Jan
This work studies the phenomenon of heteroscedasticity and its consequences for various methods of linear regression, including the least squares, least weighted squares and regression quantiles. We focus on hypothesis tests for these regression methods. The new approach consists in deriving asymptotic heteroscedasticity tests for robust regression, which are asymptotically equivalent to standard tests computed for the least squares regression. One approach to modeling heteroscedasticity assumes a prior knowledge or specific model for the variability of random regression errors. Another (and more general) approach does not assume a specific form of heteroscedasticity. The paper also describes heteroscedastic regression, which is a tool to incorporate heteroscedasticity to the model. This allows us to define the heteroscedastic least weighted squares regression.
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Some models for categorical data
Kalina, Jan
The work investigates connections between log-linear and logit models, which are two special cases of generalized linear models, suitable for statistical modeling of categorical data. Further the Markov-McNemar test is described, which is a test of homogeneity of limit marginal probabilities originally proposed for evaluating DNA sequences.
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Classification analysis
Kalina, Jan
The paper compares properties of methods, which are commonly used for the task of classification analysis in both statistics and informatics. Some relationships are derived concerning the usage of classification methods for such data, which do not fit fulfill usual assumptions.
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