The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0...The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.展开更多
We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is c...We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler(KL)-divergence term for the Poisson noise and a total variation(TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers(ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock's first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.展开更多
This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {Xt} be a linear process defined by Xt =∑k=0^∞ψ kεt-k, where {ψk, k ≥...This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {Xt} be a linear process defined by Xt =∑k=0^∞ψ kεt-k, where {ψk, k ≥ 0} is a sequence of real numbers and {εk, k = 0, ±1, ±2,...} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {εk, k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent （ALNQD） random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d, innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter a when {εk, k ≥ 1} is a sequence of negatively associated （NA） random variables, and ψ0 = 1, ψk = 0, k ≥ 1.展开更多
This paper considers the problem of estimating the finite population total in two-phase sampling when some information on auxiliary variable is available. The authors employ an informationtheoretic approach which make...This paper considers the problem of estimating the finite population total in two-phase sampling when some information on auxiliary variable is available. The authors employ an informationtheoretic approach which makes use of effective distance between the estimated probabilities and the empirical frequencies. It is shown that the proposed cross-entropy minimization estimator is more efficient than the usual estimator and has some desirable large sample properties. With some necessary modifications, the method can be applied to two-phase sampling for stratification and non-response. A simulation study is presented to assess the finite sample performance of the proposed estimator.展开更多
文摘The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.
基金supported by National Natural Science Foundation of China(Grant Nos.1136103011271049 and 11271049)+5 种基金the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry(Grant Nos.CUHK400412HKBU502814211911and 12302714)Hong Kong Research Grants Council(Grant No.Ao E/M-05/12)FRGs of Hong Kong Baptist University
文摘We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler(KL)-divergence term for the Poisson noise and a total variation(TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers(ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock's first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.
基金supported by the National Natural Science Foundation of China under Grant Nos.10971081 and 11001104985 Project of Jilin University
文摘This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {Xt} be a linear process defined by Xt =∑k=0^∞ψ kεt-k, where {ψk, k ≥ 0} is a sequence of real numbers and {εk, k = 0, ±1, ±2,...} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {εk, k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent （ALNQD） random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d, innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter a when {εk, k ≥ 1} is a sequence of negatively associated （NA） random variables, and ψ0 = 1, ψk = 0, k ≥ 1.
基金supported by the National Natural Science Foundation of China under Grant No.61070236
文摘This paper considers the problem of estimating the finite population total in two-phase sampling when some information on auxiliary variable is available. The authors employ an informationtheoretic approach which makes use of effective distance between the estimated probabilities and the empirical frequencies. It is shown that the proposed cross-entropy minimization estimator is more efficient than the usual estimator and has some desirable large sample properties. With some necessary modifications, the method can be applied to two-phase sampling for stratification and non-response. A simulation study is presented to assess the finite sample performance of the proposed estimator.
