By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral dela...By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.展开更多
Partly linear regression model is useful in practice, but littleis investigated in the literature to adapt it to the real data which are dependent and conditionally heteroscedastic. In this paper, the estimators of th...Partly linear regression model is useful in practice, but littleis investigated in the literature to adapt it to the real data which are dependent and conditionally heteroscedastic. In this paper, the estimators of the regression components are constructed via local polynomial fitting and the large sample properties are explored. Under certain mild regularities, the conditions are obtained to ensure that the estimators of the nonparametric component and its derivatives are consistent up to the convergence rates which are optimal in the i.i.d. case, and the estimator of the parametric component is root-n consistent with the same rate as for parametric model. The technique adopted in the proof differs from that used and corrects the errors in the reference by Hamilton and Truong under i.i.d. samples.展开更多
文摘By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No.79930900) the Belgian Government's "Projet d'Actions de Recherche Concertees" (PARC No. 93/98-164) China Educational Ministry's Research Fund for Retur
文摘Partly linear regression model is useful in practice, but littleis investigated in the literature to adapt it to the real data which are dependent and conditionally heteroscedastic. In this paper, the estimators of the regression components are constructed via local polynomial fitting and the large sample properties are explored. Under certain mild regularities, the conditions are obtained to ensure that the estimators of the nonparametric component and its derivatives are consistent up to the convergence rates which are optimal in the i.i.d. case, and the estimator of the parametric component is root-n consistent with the same rate as for parametric model. The technique adopted in the proof differs from that used and corrects the errors in the reference by Hamilton and Truong under i.i.d. samples.
