caa a22 4500 477062679 CHVBK 20180405111405.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF00049292 doi (NATIONALLICENCE)springer-10.1007/BF00049292 Fuzzy weighted scaled coefficients in semi-parametric model [Elektronische Daten] [Jong-Wuu Wu, Jiahn-Bang Jang, Tzong-Ru Tsai] In general, the regressor variables are stochastic, Duan and Li (1987, J. Econometrics, 35, 25-35), Li and Duan (1989, Ann. Statist., 17, 1009-1052) have been shown that under very general design conditions, the least squares method can still be useful in estimating the scaled regression coefficients of the semi-parametric model Y i =Q 1(α+βX i ;ɛ i , i+ 1,2,...,n. Here α is a constant, β is a 1×p row vector, X i is a p×1 column vector of explanatory variables, ɛ i is an unobserved random error and Q 1 is an arbitrary unknown function. When the data set (X i , Y i ),i=1, 2, ..., n, contains one or several outliers, the least squares method can not provide a consistent estimator of the scaled coefficients β. Therefore, we suggest the "fuzzy” weighted least squares method to estimate the scaled coefficients β for the data set with one or several outliers. It will be shown that the proposed "fuzzy” weighted least squares estimators are % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaakaaabaGaamOBaaWcbeaaaaa!3D3C!\[\sqrt n \] and asymptotically normal under very general design condition. Consistent measurement of the precision for the estimator is also given. Moreover, a limited Monte Carlo simulation and an example are used to study the practical performance of the procedures. The Institute of Statistical Mathematics, 1996 Least squares estimator nationallicence semi-parametric model nationallicence outlier nationallicence asymptotic normality nationallicence fuzzy weighted least squares estimator nationallicence Monte Carlo simulation nationallicence Wu Jong-Wuu Department of Statistics, Tamkang University, Tamsui, 25137, Taipei, Taiwan, R.O.C. aut Jang Jiahn-Bang Graduate School of Statistics, National Chengchi University, 64, 2nd Section, Chi-nan Rd., 11623, Taipei, Taiwan, R.O.C. aut Tsai Tzong-Ru Graduate School of Statistics, National Chengchi University, 64, 2nd Section, Chi-nan Rd., 11623, Taipei, Taiwan, R.O.C. aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/1(1996-03-01), 97-110 0020-3157 48:1<97 1996 48 10463 https://doi.org/10.1007/BF00049292 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00049292 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wu Jong-Wuu Department of Statistics, Tamkang University, Tamsui, 25137, Taipei, Taiwan, R.O.C aut NATIONALLICENCE 700 1- Jang Jiahn-Bang Graduate School of Statistics, National Chengchi University, 64, 2nd Section, Chi-nan Rd., 11623, Taipei, Taiwan, R.O.C aut NATIONALLICENCE 700 1- Tsai Tzong-Ru Graduate School of Statistics, National Chengchi University, 64, 2nd Section, Chi-nan Rd., 11623, Taipei, Taiwan, R.O.C aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/1(1996-03-01), 97-110 0020-3157 48:1<97 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer