This paper deals with the regressi on optimality of combining ridge and prinapal components estimator.It is proved that the combining ridge and principal compenents estimator of regression coefficient has several type...This paper deals with the regressi on optimality of combining ridge and prinapal components estimator.It is proved that the combining ridge and principal compenents estimator of regression coefficient has several types of minimum—Variance preperties.Some results of the paper[2] are the special cases of this paper.We also compare the combining ridge and principal components estimator with the principal components esti- mator in several senses.展开更多
The problem of two-dimensional direction of arrival(2D-DOA)estimation for uniform planar arrays(UPAs)is investigated by employing the reduced-dimensional(RD)polynomial root finding technique and 2D multiple signal cla...The problem of two-dimensional direction of arrival(2D-DOA)estimation for uniform planar arrays(UPAs)is investigated by employing the reduced-dimensional(RD)polynomial root finding technique and 2D multiple signal classification(2D-MUSIC)algorithm.Specifically,based on the relationship between the noise subspace and steering vectors,we first construct 2D root polynomial for 2D-DOA estimates and then prove that the 2D polynomial function has infinitely many solutions.In particular,we propose a computationally efficient algorithm,termed RD-ROOT-MUSIC algorithm,to obtain the true solutions corresponding to targets by RD technique,where the 2D root-finding problem is substituted by two one-dimensional(1D)root-finding operations.Finally,accurate 2DDOA estimates can be obtained by a sample pairing approach.In addition,numerical simulation results are given to corroborate the advantages of the proposed algorithm.展开更多
In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the r...In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of Gaussian random matrices by obtaining the optimal estimate of the erasure ratio for a small given norm distortion rate. As a consequence, we establish the robustness property of Johnson-Lindenstrauss lemma and the robustness property of restricted isometry property with corruption for Gaussian random matrices. Secondly, we obtain a sharp estimate for the optimal lower and upper bounds of norm distortion rates of Gaussian random matrices under a given erasure ratio. This allows us to establish the strong restricted isometry property with the almost optimal restricted isometry property(RIP) constants, which plays a central role in the study of phaseless compressed sensing. As a byproduct of our results, we also establish the robustness property of Gaussian random finite frames under erasure.展开更多
文摘This paper deals with the regressi on optimality of combining ridge and prinapal components estimator.It is proved that the combining ridge and principal compenents estimator of regression coefficient has several types of minimum—Variance preperties.Some results of the paper[2] are the special cases of this paper.We also compare the combining ridge and principal components estimator with the principal components esti- mator in several senses.
基金supported by the National Natural Science Foundation of China(Nos.61631020,61971218,61601167,61371169)。
文摘The problem of two-dimensional direction of arrival(2D-DOA)estimation for uniform planar arrays(UPAs)is investigated by employing the reduced-dimensional(RD)polynomial root finding technique and 2D multiple signal classification(2D-MUSIC)algorithm.Specifically,based on the relationship between the noise subspace and steering vectors,we first construct 2D root polynomial for 2D-DOA estimates and then prove that the 2D polynomial function has infinitely many solutions.In particular,we propose a computationally efficient algorithm,termed RD-ROOT-MUSIC algorithm,to obtain the true solutions corresponding to targets by RD technique,where the 2D root-finding problem is substituted by two one-dimensional(1D)root-finding operations.Finally,accurate 2DDOA estimates can be obtained by a sample pairing approach.In addition,numerical simulation results are given to corroborate the advantages of the proposed algorithm.
基金supported by Natural Sciences and Engineering Research Council of Canada (Grant No. 05865)Zhiqiang Xu was supported by National Natural Science Foundation of China (Grant Nos. 11422113, 91630203, 11021101 and 11331012)National Basic Research Program of China (973 Program) (Grant No. 2015CB856000)
文摘In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of Gaussian random matrices by obtaining the optimal estimate of the erasure ratio for a small given norm distortion rate. As a consequence, we establish the robustness property of Johnson-Lindenstrauss lemma and the robustness property of restricted isometry property with corruption for Gaussian random matrices. Secondly, we obtain a sharp estimate for the optimal lower and upper bounds of norm distortion rates of Gaussian random matrices under a given erasure ratio. This allows us to establish the strong restricted isometry property with the almost optimal restricted isometry property(RIP) constants, which plays a central role in the study of phaseless compressed sensing. As a byproduct of our results, we also establish the robustness property of Gaussian random finite frames under erasure.
