管中閔Kuan, Chung-Ming臺灣大學:經濟學研究所林子期Lin, Tzu-ChiTzu-ChiLin2010-05-052018-06-282010-05-052018-06-282009U0001-0907200901040000http://ntur.lib.ntu.edu.tw//handle/246246/179479New data-driven smooth tests are proposed in this thesis. The new testsre proposed to eschew the downward weighting problem of the traditionalmnibus tests, and the new tests are constructed based on the componentsf Karhunen-Lo′eve expansion of limiting process. As examples, we constructests for the null hypothesis of stationarity, coefficient stability, symmetricynamics of quantile autoregressive model, and bivariate independence.imulation results show that, new tests have moderate size control and niceower performance for a wide range of alternatives. In contrast to traditionalmnibus tests, new tests are more robust to complex models and perform wellnder high-frequency alternatives.Contents Introduction 1 Literature Review 3.1 The Smooth Test of Neyman (1937) . . . . . . . . . . . . . . . 4.2 Relationship Between Neyman’s Smooth Test and Rao’s Scoreest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Applications of Neyman’s Test . . . . . . . . . . . . . . . . . . 9.3.1 Orthogonal Polynomials and Smooth Test in Regression 9.3.2 Rank Tests for Independence . . . . . . . . . . . . . . 12 Karhunen-Lo′eve Expansion and the Deficiency of the CvMorm 14 New Tests 20.1 Testing Stationarity . . . . . . . . . . . . . . . . . . . . . . . . 20.2 Testing Coefficient Stability . . . . . . . . . . . . . . . . . . . 22.3 Testing Symmetric Dynamics of Quantile Autoregressive Model 24.4 Testing Bivariate Independence . . . . . . . . . . . . . . . . . 26 Monte Carlo Simulation 30.1 Block 1: Benchmark . . . . . . . . . . . . . . . . . . . . . . . 32.2 Block 2: Uncorrelated but Dependent Random Variables . . . 34 Conclusion 35ppendix: Mathematical Proof 36eferences 41ist of Figures Block1.BN: blue - smooth; pink - Hoeff; red - TOR ; green -RB; yellow - CvM . . . . . . . . . . . . . . . . . . . . . . . . 48 Block1.Morgen: blue - smooth; pink - Hoeff; red - TOR ; green SRB; yellow - CvM . . . . . . . . . . . . . . . . . . . . . . . 48 Block1.Plack: blue - smooth; pink - Hoeff; red - TOR ; green SRB; yellow - CvM . . . . . . . . . . . . . . . . . . . . . . . 49 Block1.Gunbel: blue - smooth; pink - Hoeff; red - TOR ; green SRB; yellow - CvM . . . . . . . . . . . . . . . . . . . . . . . 49 Block1.Clay: blue - smooth; pink - Hoeff; red - TOR ; green -RB; yellow - CvM . . . . . . . . . . . . . . . . . . . . . . . . 50 Block2.Linear: blue - smooth; pink - Hoeff; red - TOR ,green SRB; yellow - CvM . . . . . . . . . . . . . . . . . . . . . . . 50 Block2.Exp: blue - smooth; pink - Hoeff; red - TOR ; green -RB; yellow - CvM . . . . . . . . . . . . . . . . . . . . . . . . 51 Block2.Tan: blue - smooth; pink - Hoeff; red - TOR ; green -RB; yellow - CvM . . . . . . . . . . . . . . . . . . . . . . . . 51 Block2.SIRV: blue - smooth; pink - Hoeff; red - TOR ; green SRB; yellow - CvM . . . . . . . . . . . . . . . . . . . . . . . 520 Block2.IRV: blue - smooth; pink - Hoeff; red - TOR ; green -RB; yellow - CvM . . . . . . . . . . . . . . . . . . . . . . . . 52application/pdf356902 bytesapplication/pdfen-US尼曼平滑檢定Karhunen-Loeve 展開式結構轉變定態；Cramer-von Mises testKarhunen-Loeve ExpansionNeyman smooth testorthonormal polynomialintegral equationstationaritystructural changequantile autoregressivebivariate independencethesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/179479/1/ntu-98-R96323032-1.pdf