Bayesian and non-Bayesian contributions to fuzzy regression analysis

Date

2009-12-02T20:02:37Z

Authors

Feng, Hui

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Abstract

In this dissertation, the performance of the newly developed Fuzzy Regression analysis is explored in various ways. First, the Fuzzy Regression model is compared with the popular nonlinear Self-Exciting Threshold Autoregressive (SETAR) model for forecasting high frequency financial data. Second, we develop Bayesian Fuzzy Regression by using Bayesian Posterior Odds analysis to determine the number of clusters for the fuzzy regression, and fitting Bayesian regressions over each cluster. A careful Monte Carlo experiment indicates that the use of Bayesian Posterior Odds in the context of Fuzzy Regression performs extremely well. Both small sample applications and a large cross sectional case study of the South African equivalence scales then provide strong support to this Bayesian Fuzzy Regression analysis. The advantages of using the Bayesian Fuzzy Regression include its ability to capture nonlinearities in the data in a flexible semi-parametric way, while avoiding the "curse of dimensionality" associated with nonparametric kernel regression.

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Keywords

econometrics, Bayesian statistical decision theory

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