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91.
E. Demidenko 《Journal of Optimization Theory and Applications》2008,136(3):375-395
We develop criteria for the existence and uniqueness of the global minima of a continuous bounded function on a noncompact
set. Special attention is given to the problem of parameter estimation via minimization of the sum of squares in nonlinear
regression and maximum likelihood. Definitions of local convexity and unimodality are given using the level set. A fundamental
theorem of nonconvex optimization is formulated: If a function approaches the minimal limiting value at the boundary of the
optimization domain from below and its Hessian matrix is positive definite at the point where the gradient vanishes, then
the function has a unique minimum. It is shown that the local convexity level of the sum of squares is equal to the minimal
squared radius of the regression curvature. A new multimodal function is introduced, the decomposition function, which can
be represented as the composition of a convex function and a nonlinear function from the argument space to a space of larger
dimension. Several general global criteria based on majorization and minorization functions are formulated. 相似文献
92.
In this paper, a theorem on the moderate deviation principle for random arrays under m-dependence with unbounded m is established. This partially extends the results of Chen (Stat. Probab. Lett. 35:123–134, 1997). As an application, the moderate deviation principle for the truncation estimator of the variance in the analysis of time
series is obtained.
相似文献
93.
刘湘蓉 《高校应用数学学报(A辑)》2008,23(4)
对于线性模型y=Xθ ε,ε服从椭球等高单峰分布,未知参数θ满足不等式约束a′θ≥0,证明了在参数估计优良性的集中概率准则下,θ的约束最小二乘估计θ~*优于最小二乘估计θ. 相似文献
94.
拟似然非线性模型中最大拟似然估计的强相合性 总被引:2,自引:0,他引:2
This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation (MQLE) in quasi-likelihood nonlinear models (QLNM). Our results may be regarded as a further generalization of the relevant results in Ref. [4]. 相似文献
95.
96.
97.
Yutaka Kano 《Annals of the Institute of Statistical Mathematics》1986,38(1):57-68
Summary This paper is concerned with the consistency of estimators in a single common factor analysis model when the dimension of
the observed vector is not fixed. In the model several conditions on the sample sizen and the dimensionp are established for the least squares estimator (L.S.E.) to be consistent. Under some assumptions,p/n→0 is a necessary and sufficient condition that the L.S.E. converges in probability to the true value. A sufficient condition
for almost sure convergence is also given. 相似文献
98.
§ 1.Introduction and Notations In this paper,for any given matrices A and B,A B denotes the Kronecker productof A and B,A is a vector formed by stacking the columns of A under each other,μ(A)is a space generated by the columns of A,and PA=A(A′A) - A′. Fourthmore,if A andB are square matrices,then A>B and A≥ B mean that A-B is a symmetrical positiveand nonnegative matrix,respectively,andλi(A) is the i-th largest eigenvalue of A. Consider general multivariate linear modelY … 相似文献
99.
Let X,Y be Banach spaces and M a linear manifold in X×Y={{x,y}∣x∈X,y∈Y}. The central problem which motivates many of the concepts and results of this paper is the problem of characterization and construction of all extremal solutions of a linear inclusion y∈M(x). First of all, concept of metric operator parts and metric generalized inverses for linear manifolds are introduced and investigated, and then, characterizations of the set of all extremal or least extremal solutions in terms of metric operator parts and metric generalized inverses of linear manifolds are given by the methods of geometry of Banach spaces. The principal tool in this paper is the generalized orthogonal decomposition theorem in Banach spaces. 相似文献
100.
We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov
transform for the the two-parameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity
theory.
相似文献