In this paper, we consider the location model Y = θ + 6, where θ is an unknown parameter, and e is the error belonging to the interval [a,b]. We assume that θhas the following density function: Then we give the lim...In this paper, we consider the location model Y = θ + 6, where θ is an unknown parameter, and e is the error belonging to the interval [a,b]. We assume that θhas the following density function: Then we give the limiting distribution of MLE θn for 1 < min(α,β) < 2 and consider the Bahadur asymptotic estimator. Since the results depend only on α,β,C1,C2 and are independent of the concrete form of f(x), they have adaptability.展开更多
This paper considers the asymptotic efficiency of the maximum likelihood estimator (MLE) for the Box-Cox transformation model with heteroscedastic disturbances. The MLE under the normality assumption (BC MLE) is a con...This paper considers the asymptotic efficiency of the maximum likelihood estimator (MLE) for the Box-Cox transformation model with heteroscedastic disturbances. The MLE under the normality assumption (BC MLE) is a consistent and asymptotically efficient estimator if the “small ” condition is satisfied and the number of parameters is finite. However, the BC MLE cannot be asymptotically efficient and its rate of convergence is slower than ordinal order when the number of parameters goes to infinity. Anew consistent estimator of order is proposed. One important implication of this study is that estimation methods should be carefully chosen when the model contains many parameters in actual empirical studies.展开更多
In this paper, the optimal convergence rates of point estimators have been found under the irregular truncated distribution family, and corresponding Bahadurtype asymptotic efficiencies have been established. It has b...In this paper, the optimal convergence rates of point estimators have been found under the irregular truncated distribution family, and corresponding Bahadurtype asymptotic efficiencies have been established. It has beed justified that commonly used estimators are all efficient in this sense.展开更多
Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul (t), under some mild conditions the recursi...Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul (t), under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.展开更多
This article concerded with a semiparametric generalized partial linear model (GPLM) with the type Ⅱ censored data. A sieve maximum likelihood estimator (MLE) is proposed to estimate the parameter component, allo...This article concerded with a semiparametric generalized partial linear model (GPLM) with the type Ⅱ censored data. A sieve maximum likelihood estimator (MLE) is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.展开更多
In this paper, it has been studied that the singular perturbations for the higherorder nonlinear boundary value problem of the formε2y(n)=f(t, ε, y. '', y(n-2))pj(ε)y(1)(0, ε)-qj(ε)y(j+1)(0. ε)=Aj(ε) (0...In this paper, it has been studied that the singular perturbations for the higherorder nonlinear boundary value problem of the formε2y(n)=f(t, ε, y. '', y(n-2))pj(ε)y(1)(0, ε)-qj(ε)y(j+1)(0. ε)=Aj(ε) (0≤j≤n-3)a1(ε)u(n-2)(0.ε)-a2(ε)y(n-1)(0, ε)=B(ε)b1(ε)y(n-2)(1, ε)+b2(ε)y(n-1),(1. ε)=C(ε)by the method of higher order differential inequalities and boundary layer corrections.Under some mild conditions, the existence of the perturbed solution is proved and itsuniformly efficient asymptotic expansions up to its n-th order derivative function aregiven out. Hence, the existing results are extended and improved.展开更多
In this paper, the problem of locally optimum detection of weak pulse signals in narrow-band non-Gaussian noise is discussed. A generalized model is proposed for locally optimum detectors (LOD) and the corresponding p...In this paper, the problem of locally optimum detection of weak pulse signals in narrow-band non-Gaussian noise is discussed. A generalized model is proposed for locally optimum detectors (LOD) and the corresponding physical meaning is explained. On the basis of this generalized model, the LOD structures are derived for detecting both coherent- and incoherent-pulse signals in narrow-band non-Gaussian noise. The asymptotic relative efficiency (ARE) due to Pitman is used to evaluate the performance of these LODs. Finally, numerical calculations are carried out for the AREs of these LODs and some valuable results are obtained.展开更多
Consider the model Y=Xτβ+g(T)+ε. Here g is a smooth but unknown function, β is a k×1 parameter vector to be estimated and ε, is an random error with mean 0 and variance σ2. The asymptotically efficient esti...Consider the model Y=Xτβ+g(T)+ε. Here g is a smooth but unknown function, β is a k×1 parameter vector to be estimated and ε, is an random error with mean 0 and variance σ2. The asymptotically efficient estimator of β is constructed on the basis of the model Yi=Xτiβ+g(Ti)+εi, i=1,…,n, when the density functions of (X,T) and ε are known or unknown.Finally, an asymptotically normal estimator of σ2 is given.展开更多
This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary...This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.展开更多
This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalizatio...This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.展开更多
文摘In this paper, we consider the location model Y = θ + 6, where θ is an unknown parameter, and e is the error belonging to the interval [a,b]. We assume that θhas the following density function: Then we give the limiting distribution of MLE θn for 1 < min(α,β) < 2 and consider the Bahadur asymptotic estimator. Since the results depend only on α,β,C1,C2 and are independent of the concrete form of f(x), they have adaptability.
文摘This paper considers the asymptotic efficiency of the maximum likelihood estimator (MLE) for the Box-Cox transformation model with heteroscedastic disturbances. The MLE under the normality assumption (BC MLE) is a consistent and asymptotically efficient estimator if the “small ” condition is satisfied and the number of parameters is finite. However, the BC MLE cannot be asymptotically efficient and its rate of convergence is slower than ordinal order when the number of parameters goes to infinity. Anew consistent estimator of order is proposed. One important implication of this study is that estimation methods should be carefully chosen when the model contains many parameters in actual empirical studies.
文摘In this paper, the optimal convergence rates of point estimators have been found under the irregular truncated distribution family, and corresponding Bahadurtype asymptotic efficiencies have been established. It has beed justified that commonly used estimators are all efficient in this sense.
基金supported by the Natural Sciences and Engineering Research Council of Canadathe National Natural Science Foundation of China+2 种基金the Doctorial Fund of Education Ministry of Chinasupported by the Natural Sciences and Engineering Research Council of Canadasupported by the National Natural Science Foundation of China
文摘Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul (t), under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.
基金The talent research fund launched (3004-893325) of Dalian University of Technologythe NNSF (10271049) of China.
文摘This article concerded with a semiparametric generalized partial linear model (GPLM) with the type Ⅱ censored data. A sieve maximum likelihood estimator (MLE) is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.
文摘In this paper, it has been studied that the singular perturbations for the higherorder nonlinear boundary value problem of the formε2y(n)=f(t, ε, y. '', y(n-2))pj(ε)y(1)(0, ε)-qj(ε)y(j+1)(0. ε)=Aj(ε) (0≤j≤n-3)a1(ε)u(n-2)(0.ε)-a2(ε)y(n-1)(0, ε)=B(ε)b1(ε)y(n-2)(1, ε)+b2(ε)y(n-1),(1. ε)=C(ε)by the method of higher order differential inequalities and boundary layer corrections.Under some mild conditions, the existence of the perturbed solution is proved and itsuniformly efficient asymptotic expansions up to its n-th order derivative function aregiven out. Hence, the existing results are extended and improved.
文摘In this paper, the problem of locally optimum detection of weak pulse signals in narrow-band non-Gaussian noise is discussed. A generalized model is proposed for locally optimum detectors (LOD) and the corresponding physical meaning is explained. On the basis of this generalized model, the LOD structures are derived for detecting both coherent- and incoherent-pulse signals in narrow-band non-Gaussian noise. The asymptotic relative efficiency (ARE) due to Pitman is used to evaluate the performance of these LODs. Finally, numerical calculations are carried out for the AREs of these LODs and some valuable results are obtained.
文摘Consider the model Y=Xτβ+g(T)+ε. Here g is a smooth but unknown function, β is a k×1 parameter vector to be estimated and ε, is an random error with mean 0 and variance σ2. The asymptotically efficient estimator of β is constructed on the basis of the model Yi=Xτiβ+g(Ti)+εi, i=1,…,n, when the density functions of (X,T) and ε are known or unknown.Finally, an asymptotically normal estimator of σ2 is given.
基金Supported by National Natural Science Foundation of China (Grant Nos.10771017,10971015,10901020)Key Project of MOE,PRC (Grant No.309007)
文摘This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.
基金Supported by the National Natural Science Foundation of China(No.10771017,No.10231030)Key Project of Ministry of Education,PRC(No.309007)
文摘This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.