OBJECTIVE:To optimize the vinegar-steaming process of Wuweizi(Fructus Schisandrae Chinensis)using the response surface method(RSM)based on the Box-Behnken design.METHODS:A regression model was constructed with the res...OBJECTIVE:To optimize the vinegar-steaming process of Wuweizi(Fructus Schisandrae Chinensis)using the response surface method(RSM)based on the Box-Behnken design.METHODS:A regression model was constructed with the response variables,the content of Deoxyschizandrin,and the three explanatory factors:length of steaming time,the quantity of vinegar and length of moistening time to evaluate the effects on the processing of Wuweizi(Fructus SchisandraeChinensis).RESULTS:There was a linear relationship between the content of Deoxyschizandrin and the three explanatory factors.When the steaming time was5.49 h,with 2.365 g of vinegar added and a moistening time of 4.13 h,the content of Deoxyschizandrin reached the maximum predicted value of0.1076%,and under the conditions the average content of Deoxyschizandrin was 0.1058%.CONCLUSION:The correlation coefficient of thenonlinear mathematical model was relatively high and the model matched the data well,potentially providing a method for the study of the steaming process.展开更多
In this paper we investigate the robust estimation of generalized varying coefficient models in which the unknown regression coefficients may change with different explanatory variables. Based on the B-spline series a...In this paper we investigate the robust estimation of generalized varying coefficient models in which the unknown regression coefficients may change with different explanatory variables. Based on the B-spline series approximation and Walsh-average technique we develop an initial estimator for the unknown regression coefficient functions. By virtue of the initial estimator, the generalized varying coefficient model is reduced to a univariate nonparametric regression model. Then combining the local linear smooth and Walsh average technique we further propose a two-stage local linear Walsh-average estimator for the unknown regression coefficient functions. Under mild assumptions, we establish the large sample theory of the proposed estimators by utilizing the results of U-statistics and shows that the two-stage local linear Walsh-average estimator own an oracle property, namely the asymptotic normality of the two-stage local linear Walsh-average estimator of each coefficient function is not affected by other unknown coefficient functions. Extensive simulation studies are conducted to assess the finite sample performance, and a real example is analyzed to illustrate the proposed method.展开更多
基金Supported by Scientific Research Foundation of Health Department of Shaanxi Province(2012D14),China
文摘OBJECTIVE:To optimize the vinegar-steaming process of Wuweizi(Fructus Schisandrae Chinensis)using the response surface method(RSM)based on the Box-Behnken design.METHODS:A regression model was constructed with the response variables,the content of Deoxyschizandrin,and the three explanatory factors:length of steaming time,the quantity of vinegar and length of moistening time to evaluate the effects on the processing of Wuweizi(Fructus SchisandraeChinensis).RESULTS:There was a linear relationship between the content of Deoxyschizandrin and the three explanatory factors.When the steaming time was5.49 h,with 2.365 g of vinegar added and a moistening time of 4.13 h,the content of Deoxyschizandrin reached the maximum predicted value of0.1076%,and under the conditions the average content of Deoxyschizandrin was 0.1058%.CONCLUSION:The correlation coefficient of thenonlinear mathematical model was relatively high and the model matched the data well,potentially providing a method for the study of the steaming process.
基金Supported by the National Natural Science Foundation of China(NSFC)(No.11471203)the Graduate Innovation Fund of Shanghai University of Finance and Economics(CXJJ-2013-459)
文摘In this paper we investigate the robust estimation of generalized varying coefficient models in which the unknown regression coefficients may change with different explanatory variables. Based on the B-spline series approximation and Walsh-average technique we develop an initial estimator for the unknown regression coefficient functions. By virtue of the initial estimator, the generalized varying coefficient model is reduced to a univariate nonparametric regression model. Then combining the local linear smooth and Walsh average technique we further propose a two-stage local linear Walsh-average estimator for the unknown regression coefficient functions. Under mild assumptions, we establish the large sample theory of the proposed estimators by utilizing the results of U-statistics and shows that the two-stage local linear Walsh-average estimator own an oracle property, namely the asymptotic normality of the two-stage local linear Walsh-average estimator of each coefficient function is not affected by other unknown coefficient functions. Extensive simulation studies are conducted to assess the finite sample performance, and a real example is analyzed to illustrate the proposed method.
