| Summary: | 碩士 === 國立政治大學 === 統計研究所 === 100 === In this thesis, we consider the problem of estimating a regression function assuming the regression function is unimodal. The proposed method is to model the regression function as linear combination of B-spline basis functions with equally spaced knots, and the number of knots is determined using AIC (Akaike information criterion). Specific constraints are placed on the coefficients of basis functions to ensure that estimated regression function is unimodal. The coefficients are estimated using least square method.
The proposed method is refered as RSPL and is compared with two other methods: SPL and CSPL, where SPL is similar to RSPL except that the coefficients of basis functions are estimated without any constraints, and CSPL gives concave regression function estimates. Simulation results show that RSPL outperforms SPL and CSPL when the true regression function is unimodal but not concave, and CSPL outperforms RSPL and SPL when the true regression function is concave. Also, RSPL is applied to temperature data to estimate temperature trend within one year.
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