本文考虑多维广义线性模型的拟似然方程sum from i=1 to n X_i(y_i-μ(X_i^1β))=0,在一定条件下证明了此方程的解(?)渐近存在,并得到了其收敛速度,即■_n-β_0=O_p(■_n^(-1/2)),其中β_0为参数β的真值,■_n是方阵S_n=sum from i=1 to...本文考虑多维广义线性模型的拟似然方程sum from i=1 to n X_i(y_i-μ(X_i^1β))=0,在一定条件下证明了此方程的解(?)渐近存在,并得到了其收敛速度,即■_n-β_0=O_p(■_n^(-1/2)),其中β_0为参数β的真值,■_n是方阵S_n=sum from i=1 to n X_iX_i^1的最小特征值．展开更多
In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for u...In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . We also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of QMLE is S n ?1 → 0, as the sample size n → ∞.展开更多
In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly...In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.展开更多
In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribu...In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works;(ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution;(iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Holder continuous) and pathdistribution dependent.展开更多
The paper studies a generalized linear model（GLM）yt = h（xt^T β） ＋ εt,t = l,2,...,n,where ε1 = η1,ε1 =ρεt ＋ηt,t = 2,3,...;n,h is a continuous differentiable function,ηt＇s are independent and identically...The paper studies a generalized linear model（GLM）yt = h（xt^T β） ＋ εt,t = l,2,...,n,where ε1 = η1,ε1 =ρεt ＋ηt,t = 2,3,...;n,h is a continuous differentiable function,ηt＇s are independent and identically distributed random errors with zero mean and finite variance σ^2.Firstly,the quasi-maximum likelihood（QML） estimators of β,p and σ^2 are given.Secondly,under mild conditions,the asymptotic properties（including the existence,weak consistency and asymptotic distribution） of the QML estimators are investigated.Lastly,the validity of method is illuminated by a simulation example.展开更多
In many lifetime studies, some of the subjects under study are censored on the righ bya prior censoring time. We observe only the censored data. It is important to estimatethe life characteristics of the subjects. Let...In many lifetime studies, some of the subjects under study are censored on the righ bya prior censoring time. We observe only the censored data. It is important to estimatethe life characteristics of the subjects. Let T<sub>1</sub>, T<sub>2</sub>,…, T<sub>n</sub> be independent and identically dis-tributed nonnegative random variables with common continuous distribution funtion F展开更多
基金partly supported by National Natural Science Foundation of China and President Foundation of GUCAS.
文摘本文考虑多维广义线性模型的拟似然方程sum from i=1 to n X_i(y_i-μ(X_i^1β))=0,在一定条件下证明了此方程的解(?)渐近存在,并得到了其收敛速度,即■_n-β_0=O_p(■_n^(-1/2)),其中β_0为参数β的真值,■_n是方阵S_n=sum from i=1 to n X_iX_i^1的最小特征值．
基金supported by the President Foundation (Grant No. Y1050)the Scientific Research Foundation(Grant No. KYQD200502) of GUCAS
文摘In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . We also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of QMLE is S n ?1 → 0, as the sample size n → ∞.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671012,11871072,11701004 and 11701005)the Natural Science Foundation of Anhui Province(Grant No.1508085J06)+2 种基金the Key Projects for Academic Talent of Anhui Province(Grant No.gxbjZD2016005)the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province(Grant No.2017H123)the Research Teaching Model Curriculum of Anhui University(Grant No.xjyjkc1407)
文摘In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.
文摘In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works;(ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution;(iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Holder continuous) and pathdistribution dependent.
基金Supported by National Natural Science Foundation of China(Grant Nos.11071022,11471105)Science and Technology Research Projects of the Educational Department of Hubei Province(Grant No.Q20132505)
文摘The paper studies a generalized linear model（GLM）yt = h（xt^T β） ＋ εt,t = l,2,...,n,where ε1 = η1,ε1 =ρεt ＋ηt,t = 2,3,...;n,h is a continuous differentiable function,ηt＇s are independent and identically distributed random errors with zero mean and finite variance σ^2.Firstly,the quasi-maximum likelihood（QML） estimators of β,p and σ^2 are given.Secondly,under mild conditions,the asymptotic properties（including the existence,weak consistency and asymptotic distribution） of the QML estimators are investigated.Lastly,the validity of method is illuminated by a simulation example.
基金Project supported by the Doctoral Programme Science Foundation and tbe National Natural Science Foundation of China.
文摘In many lifetime studies, some of the subjects under study are censored on the righ bya prior censoring time. We observe only the censored data. It is important to estimatethe life characteristics of the subjects. Let T<sub>1</sub>, T<sub>2</sub>,…, T<sub>n</sub> be independent and identically dis-tributed nonnegative random variables with common continuous distribution funtion F
