To tackle multi collinearity or ill-conditioned design matrices in linear models, adaptive biased estimators such as the time-honored Stein estimator, the ridge and the principal component estimators have been studied...To tackle multi collinearity or ill-conditioned design matrices in linear models, adaptive biased estimators such as the time-honored Stein estimator, the ridge and the principal component estimators have been studied intensively. To study when a biased estimator uniformly outperforms the least squares estimator, some sufficient conditions are proposed in the literature. In this paper, we propose a unified framework to formulate a class of adaptive biased estimators. This class includes all existing biased estimators and some new ones. A sufficient condition for outperforming the least squares estimator is proposed. In terms of selecting parameters in the condition, we can obtain all double-type conditions in the literature.展开更多
In this article, we study a least squares estimator （LSE） of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt＋dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain...In this article, we study a least squares estimator （LSE） of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt＋dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.展开更多
We study the parameter estimation in a nonlinear regression model with a general error's structure,strong consistency and strong consistency rate of the least squares estimator are obtained.
Consider the linear model Y=Xβ+e; e～N(0, σ~2I). (1) where X is a known n×p matrix of rank p【n; β∈R^p and σ】0 are parameters. Assume that prior information about β in the form U=Hβ+ε (2) is available. H...Consider the linear model Y=Xβ+e; e～N(0, σ~2I). (1) where X is a known n×p matrix of rank p【n; β∈R^p and σ】0 are parameters. Assume that prior information about β in the form U=Hβ+ε (2) is available. Here H is a known k×p matrix. and H≠0; ε～N(0, W); W is known and positive definite symmetric. Assume also that e and ε are independent.展开更多
基金Supported by a grant from The Research Grants Council of Hong Kong HKU7181/02H.The authors wishes to thank the referees for the constructive comments
文摘To tackle multi collinearity or ill-conditioned design matrices in linear models, adaptive biased estimators such as the time-honored Stein estimator, the ridge and the principal component estimators have been studied intensively. To study when a biased estimator uniformly outperforms the least squares estimator, some sufficient conditions are proposed in the literature. In this paper, we propose a unified framework to formulate a class of adaptive biased estimators. This class includes all existing biased estimators and some new ones. A sufficient condition for outperforming the least squares estimator is proposed. In terms of selecting parameters in the condition, we can obtain all double-type conditions in the literature.
基金supported by the National Natural Science Foundation of China(11271020)the Distinguished Young Scholars Foundation of Anhui Province(1608085J06)supported by the National Natural Science Foundation of China(11171062)
文摘In this article, we study a least squares estimator （LSE） of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt＋dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19971001).
文摘We study the parameter estimation in a nonlinear regression model with a general error's structure,strong consistency and strong consistency rate of the least squares estimator are obtained.
基金Research supported by the National Natural Science Foundation of China.
文摘Consider the linear model Y=Xβ+e; e～N(0, σ~2I). (1) where X is a known n×p matrix of rank p【n; β∈R^p and σ】0 are parameters. Assume that prior information about β in the form U=Hβ+ε (2) is available. Here H is a known k×p matrix. and H≠0; ε～N(0, W); W is known and positive definite symmetric. Assume also that e and ε are independent.
