Thesis (M.Sc.) - Cairo University - Institute of Statistical Studies and Research - Department of Statistics and Econometrics

This thesis is concerned mainly with lack of fit tests. A presentation of existing tests is given. All mentioned tests in the literature is going to be reviewed. This thesis contributes in two directions. First, we introduced local linear kernel estimator by assuming that the third derivative of the regression function exists then, approximating the regre- ssion function locally by using a second-degree polynomial for Li (2005) test. Secondly, a comparative study between two non replicated lack of fit tests called the Rainbow (1982) and Burn and Ryan (1983) tests will be considered by using R language. The two tests are compared with various parameters and data generating for different types of alternative one-variable models. The comparative will be depend on the second and the third order of polynomial models containing the case of hierarchical models with (without) constant, also the case of non hierarchical models. In addition to three different types of sinusoidal models. For third order polynomial models, the case to fit the highest degree of the models, and to fit the second degree of the models will be introduced. The comparative study is depending on normal distributions of the errors with different parameters. The power of the tests will be used as the criterion to evaluate the performance of the tests and based on 5000 simulated. The simulation studies indicate that the best power of the Rainbow (1982) and Burn and Ryan (1983) tests for polynomial models, when fitting the highest degree of the model.

Issued also as CD