Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are ...Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.展开更多
Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of tw...Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of twoscale asymptotic expansions for solutions to the electrical potential and the displacement in quasi-periodic structure under coupled piezoelectric effect are derived, and the homogenization constants of piezoelectric materials are presented. The coupled twoscale relation between the electrical potential and the displacement is set up, and some improved asymptotic error estimates are analyzed.展开更多
Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS...Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS） were proposed in the different areas. Motivated by K. Chen et al.＇s recent work [J. Amer. Statist. Assoc., 2010, 105： 1104-1112] on the least absolute relative error （LARE） estimation for the accelerated failure time （AFT） model, in this paper, we establish the connection between relative error estimators and the M-estimation in the linear model. This connection allows us to deduce the asymptotic properties of many relative error estimators （e.g., LARE） by the well-developed M-estimation theories. On the other hand, the asymptotic properties of some important estimators （e.g., MRE and RLS） cannot be established directly. In this paper, we propose a general relative error criterion （GREC） for estimating the unknown parameter in the AFT model. Then we develop the approaches to deal with the asymptotic normalities for M-estimators with differentiable loss functions on R or R／{0} in the linear model. The simulation studies are conducted to evaluate the performance of the proposed estimates for the different scenarios. Illustration with a real data example is also provided.展开更多
Though EV model is theoretically more appropriate for applications in which measurement errors exist, people are still more inclined to use the ordinary regression models and the traditional LS method owing to the dif...Though EV model is theoretically more appropriate for applications in which measurement errors exist, people are still more inclined to use the ordinary regression models and the traditional LS method owing to the difficulties of statistical inference and computation. So it is meaningful to study the performance of LS estimate in EV model. In this article we obtain general conditions guaranteeing the asymptotic normality of the estimates of regression coefficients in the linear EV model. It is noticeable that the result is in some way different from the corresponding result in the ordinary regression model.展开更多
This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is e...This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.展开更多
基金Supported by the National Natural Science Foundation of China（60375003） Supported by the Chinese Aviation Foundation（03153059）
文摘Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.
基金supported by the National Natural Science Foundation of China(Grant Nos.10801042,11126132,and 11171257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20104410120001)San Diego supported by China Scholarship Council from July 2012 to July 2013
文摘Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of twoscale asymptotic expansions for solutions to the electrical potential and the displacement in quasi-periodic structure under coupled piezoelectric effect are derived, and the homogenization constants of piezoelectric materials are presented. The coupled twoscale relation between the electrical potential and the displacement is set up, and some improved asymptotic error estimates are analyzed.
文摘Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS） were proposed in the different areas. Motivated by K. Chen et al.＇s recent work [J. Amer. Statist. Assoc., 2010, 105： 1104-1112] on the least absolute relative error （LARE） estimation for the accelerated failure time （AFT） model, in this paper, we establish the connection between relative error estimators and the M-estimation in the linear model. This connection allows us to deduce the asymptotic properties of many relative error estimators （e.g., LARE） by the well-developed M-estimation theories. On the other hand, the asymptotic properties of some important estimators （e.g., MRE and RLS） cannot be established directly. In this paper, we propose a general relative error criterion （GREC） for estimating the unknown parameter in the AFT model. Then we develop the approaches to deal with the asymptotic normalities for M-estimators with differentiable loss functions on R or R／{0} in the linear model. The simulation studies are conducted to evaluate the performance of the proposed estimates for the different scenarios. Illustration with a real data example is also provided.
文摘Though EV model is theoretically more appropriate for applications in which measurement errors exist, people are still more inclined to use the ordinary regression models and the traditional LS method owing to the difficulties of statistical inference and computation. So it is meaningful to study the performance of LS estimate in EV model. In this article we obtain general conditions guaranteeing the asymptotic normality of the estimates of regression coefficients in the linear EV model. It is noticeable that the result is in some way different from the corresponding result in the ordinary regression model.
基金This project is supported by the National Natural Science Foundation of China (No.19631040)
文摘This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.
