Search

The misclassification simulation extrapolation (MC-SIMEX) method proposed by Küchenho et al. is a general method of handling categorical data with measurement error. It consists of two steps, the simulation and extrapolation steps. In the simulation step, it simulates observations with varying degrees of measurement error. Then parameter estimators for varying degrees of measurement error are obtained based on these observations. In the extrapolation step, it uses a parametric extrapolation function to obtain the parameter estimators for data with no measurement error. However, as shown in many studies, the parameter estimators are still biased as a result of the parametric extrapolation function used in the MC-SIMEX method. Therefore, we propose a nonparametric MC-SIMEX method in which we use a nonparametric extrapolation function. It uses the fractional polynomial method with cross-validation to choose the appropriate fractional polynomial terms. An example is provided based on data from the National Health and Nutrition Examination Survey.

In change point problems, there are three main questions that researchers are interested in. First of all, is there a change point or not? Second, when does the change point occur in a time series? Third, how quickly can we detect the change point? In this thesis, we first explain what a change point is, and what a cross-correlation is. We then discuss prior research in this area. Then we discuss and examine a test based on Spearman's rho, introduced by Wied and Dehling (2011), which tests the null hypothesis of no change point, and compare the change point we set with the results from the proposed statistic in simulation. We also use this statistic on data we selected from the U.S. stock market. We conclude with the pros and cons of this statistical method, and how we can detect the change point sensitively using the proposed statistic.