In dealing with nonparametric regression the GAM procedure is the most versatile of several new procedures. The terminology behind this procedure is more flexible than traditional parametric modeling tools. It relaxes...In dealing with nonparametric regression the GAM procedure is the most versatile of several new procedures. The terminology behind this procedure is more flexible than traditional parametric modeling tools. It relaxes the usual assumptions of parametric model and enables us to uncover structure to establish the relationship between independent variables and dependent variable in exponential family that may not be obvious otherwise. In this paper, we discussed two methods of fitting generalized additive logistic regression model, one based on Newton Raphson method and another based on iterative weighted least square method for first and second order Taylor series expansion. The use of the GAM procedure with the specified set of weights, using local scoring algorithm, was applied to real life data sets. The cubic spline smoother is applied to the independent variables. Based on nonparametric regression and smoothing techniques, this procedure provides powerful tools for data analysis.展开更多
The one-sided and two-sided hypotheses about the parametric component in partially linear model are considered in this paper. Generalized p-values are proposed based on fiducial method for testing the two hypotheses a...The one-sided and two-sided hypotheses about the parametric component in partially linear model are considered in this paper. Generalized p-values are proposed based on fiducial method for testing the two hypotheses at the presence of nonparametric nuisance parameter. Note that the nonparametric component can be approximated by a linear combination of some known functions, thus, the partially linear model can be approximated by a linear model. Thereby, generalized p-values for a linear model are studied first, and then the results are extended to the situation of partially linear model. Small sample frequency properties are analyzed theoretically. Meanwhile, simulations are conducted to assess the finite sample performance of the tests based on the proposed p-values.展开更多
Single-index varying-coefficient models (SIVCMs) are very useful in multivariate nonparametric regression.However,there has less attention focused on inferences of the SIVCMs.Using the local linear method,we propose e...Single-index varying-coefficient models (SIVCMs) are very useful in multivariate nonparametric regression.However,there has less attention focused on inferences of the SIVCMs.Using the local linear method,we propose estimates of the unknowns in the SIVCMs.In this article,our main purpose is to examine whether the generalized likelihood ratio (GLR) tests are applicable to the testing problem for the index parameter in the SIVCMs.Under the null hypothesis our proposed GLR statistic follows the chi-squared distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters or functions,which is called as Wilks' phenomenon (see Fan et al.,2001).A simulation study is conducted to illustrate the proposed methodology.展开更多
文摘In dealing with nonparametric regression the GAM procedure is the most versatile of several new procedures. The terminology behind this procedure is more flexible than traditional parametric modeling tools. It relaxes the usual assumptions of parametric model and enables us to uncover structure to establish the relationship between independent variables and dependent variable in exponential family that may not be obvious otherwise. In this paper, we discussed two methods of fitting generalized additive logistic regression model, one based on Newton Raphson method and another based on iterative weighted least square method for first and second order Taylor series expansion. The use of the GAM procedure with the specified set of weights, using local scoring algorithm, was applied to real life data sets. The cubic spline smoother is applied to the independent variables. Based on nonparametric regression and smoothing techniques, this procedure provides powerful tools for data analysis.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 10771015 and the Start-Up Funds for Doctoral Scientific Research of Shandong University of Finance.
文摘The one-sided and two-sided hypotheses about the parametric component in partially linear model are considered in this paper. Generalized p-values are proposed based on fiducial method for testing the two hypotheses at the presence of nonparametric nuisance parameter. Note that the nonparametric component can be approximated by a linear combination of some known functions, thus, the partially linear model can be approximated by a linear model. Thereby, generalized p-values for a linear model are studied first, and then the results are extended to the situation of partially linear model. Small sample frequency properties are analyzed theoretically. Meanwhile, simulations are conducted to assess the finite sample performance of the tests based on the proposed p-values.
基金supported by National Natural Science Foundation of China (Grant Nos.10871072,11101114 and 11171112)PhD Program Foundation of Ministry of Education of China (Grant No.20090076110001)
文摘Single-index varying-coefficient models (SIVCMs) are very useful in multivariate nonparametric regression.However,there has less attention focused on inferences of the SIVCMs.Using the local linear method,we propose estimates of the unknowns in the SIVCMs.In this article,our main purpose is to examine whether the generalized likelihood ratio (GLR) tests are applicable to the testing problem for the index parameter in the SIVCMs.Under the null hypothesis our proposed GLR statistic follows the chi-squared distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters or functions,which is called as Wilks' phenomenon (see Fan et al.,2001).A simulation study is conducted to illustrate the proposed methodology.
