This study tackles the issue of chloramphenicol(CAP)in wastewater by exploring its removal using rattan waste-based metal functionalized carbon(RMFC).The study provides new insights into the adsorption mechanism by in...This study tackles the issue of chloramphenicol(CAP)in wastewater by exploring its removal using rattan waste-based metal functionalized carbon(RMFC).The study provides new insights into the adsorption mechanism by investigating the role of Cu^(2+)functionalization in enhancing CAP uptake through ion-dipole andπ-πinteractions.The RMFC surface was enriched with Cu^(2+)ions through modification with CuN_(2)O_(6),resulting in the production of copper-enriched RMFC(Cu^(2+)-RMFC).The conditions for preparing Cu^(2+)-RMFC were optimized through response surface methodology(RSM).Following this,an F-test was conducted to evaluate the differences in variance distinguishing linear from non-linear ap-proaches pertaining to isotherm together with kinetic models,with the null hypothesis proposing that these variances are the same.The adsorption capacities of CAP by pristine RMFC and Cu^(2+)-RMFC were 53.69 mg/g and 77.14 mg/g,respectively,indicating a 30.40%increase.Besides hydrogen bonds,dipole-dipole bonds,andπ-πinteractions,the enhanced CAP removal by Cu^(2+)-RMFC was attributed to the ion-dipole interaction between Cu^(2+)ions and more electronegative oxygen(O)atoms in CAP molecules.The RSM identified the optimal conditions as 660 W,8.07 min,and a metal loading ratio(MLR)of 0.47 g/g in relation to radiation power,duration of radiation,and MLR,correspondingly.These circumstances brought about predicted CAP uptake values of 76.15 mg/g(actual:77.14 mg/g;error:1.28%)and a Cu^(2+)-RMFC yield of 31.54%(actual:32.36%;error:2.53%).The adsorption process was well represented by the non-linear Freundlich and non-linear pseudo-first-order(PFO)models.The adsorption capacity of the Langmuir monolayer(Q_(m))was 101.01 mg/g for the linear model and 108.00 mg/g for the non-linear model.The F-test results indicated that for all isotherm models studied,the F value was smaller than the F-critical value,leading to the acceptance of the null hypothesis.In contrast,the F values for all ki-netic models exceeded the F-critical value,resulting in the refusal of the null hypothesis.展开更多
In linear regression model, the influence on the regression coefficients has beed paid great attention and other aspects such as the influence on confidence regions have also been studied. However, influence on F-test...In linear regression model, the influence on the regression coefficients has beed paid great attention and other aspects such as the influence on confidence regions have also been studied. However, influence on F-test in linear regression model received few consideration. This paper examines the local influence of small perturbations on Fstatistic. The diagnostic results permit one to check the sensitivity of F-statistic to the exact perturbations of error variance, explanatory variables and response variables. This method is applied to testing problem of transformation parameter in transformation model.Diagnostics are illustrated with two examples and compared with standard method.展开更多
This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown ...This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown nonlinear component by some nonparametric methods and then generalize the F-statistic to test the regression coefficients under some regular conditions. During this procedure, the estimation of the nonlinear component brings much challenge to explore the properties of generalized F-test. The authors obtain some asymptotic properties of the generalized F-test in more general cases,including the asymptotic normality and the power of this test with p/n ∈(0, 1) without normality assumption. The asymptotic result is general and by adding some constraint conditions we can obtain the similar conclusions in high dimensional linear models. Through simulation studies, the authors demonstrate good finite-sample performance of the proposed test in comparison with the theoretical results. The practical utility of our method is illustrated by a real data example.展开更多
F-test is the most popular test in the general linear model. However, there is few discussions on the robustness of F-test under the singular linear model. In this paper, the necessary and sufficient conditions of rob...F-test is the most popular test in the general linear model. However, there is few discussions on the robustness of F-test under the singular linear model. In this paper, the necessary and sufficient conditions of robust F-test statistic are given under the general linear models or their partition models, which allows that the design matrix has deficient rank and the covariance matrix of error is a nonnegative definite matrix with parameters. The main results obtained in this paper include the existing findings of the general linear model under the definite covariance matrix. The usage of the theorems is illustrated by an example.展开更多
The usual F--test has been used to test a general linear hypothesis for a two--stage least squaresmethod in a system of economic equations. However, we find that this F--test is actuallyasymptotically invalid. Some su...The usual F--test has been used to test a general linear hypothesis for a two--stage least squaresmethod in a system of economic equations. However, we find that this F--test is actuallyasymptotically invalid. Some suggestions are given for testing a general linear hypothesis in thissituation.展开更多
基金Deanship of Research and Graduate Studies at King Khalid University for generously supporting this study through the Large Research Projects grant, awarded under grant number RGP2/563/45.
文摘This study tackles the issue of chloramphenicol(CAP)in wastewater by exploring its removal using rattan waste-based metal functionalized carbon(RMFC).The study provides new insights into the adsorption mechanism by investigating the role of Cu^(2+)functionalization in enhancing CAP uptake through ion-dipole andπ-πinteractions.The RMFC surface was enriched with Cu^(2+)ions through modification with CuN_(2)O_(6),resulting in the production of copper-enriched RMFC(Cu^(2+)-RMFC).The conditions for preparing Cu^(2+)-RMFC were optimized through response surface methodology(RSM).Following this,an F-test was conducted to evaluate the differences in variance distinguishing linear from non-linear ap-proaches pertaining to isotherm together with kinetic models,with the null hypothesis proposing that these variances are the same.The adsorption capacities of CAP by pristine RMFC and Cu^(2+)-RMFC were 53.69 mg/g and 77.14 mg/g,respectively,indicating a 30.40%increase.Besides hydrogen bonds,dipole-dipole bonds,andπ-πinteractions,the enhanced CAP removal by Cu^(2+)-RMFC was attributed to the ion-dipole interaction between Cu^(2+)ions and more electronegative oxygen(O)atoms in CAP molecules.The RSM identified the optimal conditions as 660 W,8.07 min,and a metal loading ratio(MLR)of 0.47 g/g in relation to radiation power,duration of radiation,and MLR,correspondingly.These circumstances brought about predicted CAP uptake values of 76.15 mg/g(actual:77.14 mg/g;error:1.28%)and a Cu^(2+)-RMFC yield of 31.54%(actual:32.36%;error:2.53%).The adsorption process was well represented by the non-linear Freundlich and non-linear pseudo-first-order(PFO)models.The adsorption capacity of the Langmuir monolayer(Q_(m))was 101.01 mg/g for the linear model and 108.00 mg/g for the non-linear model.The F-test results indicated that for all isotherm models studied,the F value was smaller than the F-critical value,leading to the acceptance of the null hypothesis.In contrast,the F values for all ki-netic models exceeded the F-critical value,resulting in the refusal of the null hypothesis.
文摘In linear regression model, the influence on the regression coefficients has beed paid great attention and other aspects such as the influence on confidence regions have also been studied. However, influence on F-test in linear regression model received few consideration. This paper examines the local influence of small perturbations on Fstatistic. The diagnostic results permit one to check the sensitivity of F-statistic to the exact perturbations of error variance, explanatory variables and response variables. This method is applied to testing problem of transformation parameter in transformation model.Diagnostics are illustrated with two examples and compared with standard method.
基金supported by the Natural Science Foundation of China under Grant Nos.11231010,11471223,11501586BCMIIS and Key Project of Beijing Municipal Educational Commission under Grant No.KZ201410028030
文摘This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown nonlinear component by some nonparametric methods and then generalize the F-statistic to test the regression coefficients under some regular conditions. During this procedure, the estimation of the nonlinear component brings much challenge to explore the properties of generalized F-test. The authors obtain some asymptotic properties of the generalized F-test in more general cases,including the asymptotic normality and the power of this test with p/n ∈(0, 1) without normality assumption. The asymptotic result is general and by adding some constraint conditions we can obtain the similar conclusions in high dimensional linear models. Through simulation studies, the authors demonstrate good finite-sample performance of the proposed test in comparison with the theoretical results. The practical utility of our method is illustrated by a real data example.
基金Supported by National Social Science Foundation of China(Grant No.13CTJ012)National Natural Science Foundation of China(Grant No.11171058)+2 种基金Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ13A010002)Guangdong Provincial Natural Science Foundation of China(Grant No.S2012040007622)he National Statistical Science Research Project(Grant No.2012LY129)
文摘F-test is the most popular test in the general linear model. However, there is few discussions on the robustness of F-test under the singular linear model. In this paper, the necessary and sufficient conditions of robust F-test statistic are given under the general linear models or their partition models, which allows that the design matrix has deficient rank and the covariance matrix of error is a nonnegative definite matrix with parameters. The main results obtained in this paper include the existing findings of the general linear model under the definite covariance matrix. The usage of the theorems is illustrated by an example.
文摘The usual F--test has been used to test a general linear hypothesis for a two--stage least squaresmethod in a system of economic equations. However, we find that this F--test is actuallyasymptotically invalid. Some suggestions are given for testing a general linear hypothesis in thissituation.
