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1.
设Y_(n×m)服从矩阵正态分布N(XΘ, σ^2Σ×V),X_(n×k)是一个列满秩的矩阵,n ≥k≥3,σ^2是未知的,σ^(-2)S_p服从自由度为p的χ^2分布。当f(t)是单调非降 可微的函数, 且0≤f(t)≤2(k-2)/m(p+2)时,其列向量为Δ_i(Y)=[I_k- f(V′_iY′(X′Σ^(-1)X)^(-2)YV_iS_p_(-1)S_p (X′Σ^(-1)X)^(-1)/V′_iY′(X′Σ^(-1)X)^(-2)YV_i](X′Σ^(-1)X)^(-1)X′Σ^(-1)Y_i的估计Δ(Y)在风险函数R_1或R_2下是能够改善Θ的极大似然估计(X′Σ^(-1)X)^(-1)X′Σ^(-1)Y.同时得到了Θ和CXΘ的线性可容许估计类.
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2.
1IntroductionInthispapertweconsiderthesemilinearellipticproblemwhereA>oisarealparameter,o2.(a2)5(x)ELCc(R"),Otb(x)3OinRNandb(x)EH'(R"),herep'=the.TheSobolevspaceD3l'(RN)isdefinedasthecompletionofCg(R")intheL'(R")normoflvuI.Suchproblemsoccurinvariousbranchesofmathematicalphysicsandpopulationdynamics,andsublinearanaJoguesorsuperline… 相似文献
3.
Lei g(x,ω) be a stationary weakly conelated process, G(t, x) be the Green's function and G(x) be a function with a smooth one-order derivative. Define stochastic processes ξ(t,ω)=∫01G(t,x)g(x,ω)dx (0≤t≤1) and η(t,ω)=∫0tG(x)g(x,ω)dx (0≤t≤T) In this paper we give the strong approximations of random variables ξ(t) and η(t) to normal variables, and also give a weakly in variance principle for process η(·). 相似文献
4.
最近我做了这样一道题 :例 1 f(x) =loga[( 1a - 2 )x+ 1]在区间[1,2 ]上恒为正 ,求实数a的取值范围 .由于本题中真数含有变量 ,因此要对参数进行多次分类讨论 :(Ⅰ ) 0 &;lt;a &;lt;1时 ,设t(x) =( 1a - 2 )x + 1.( 1) 0 &;lt;a&;lt;12 ,t(x)、f(x)在 [1,2 ]上分别单调递增和递减 ,∴ t( 1) =( 1a - 2 ) &;#215; 1+ 1&;gt;0f( 1) =loga[( 1a - 2 )&;#215; 1+ 1] &;gt;0 a&;gt;12 .此时无解 .( 2 )a =12 时 ,f(x) =0 ,也不合题意 .( 3) 12 &;lt;a &;lt;1时 ,t(x)、f(x)在 [1,2 ]上分别单调递减和递增 ,∴ t( 2 ) =( 1a - 2 ) &;#215; 2 + 1&;gt;0f( 1) =loga[( 1a - 2 ) &;#215; 1+ 1] &;gt;0 0 &;lt;a &;lt;23,∴ 12 &;lt;a &;lt;23.(Ⅱ )a &;gt;1时 ,t(x)、f(x)在区间 [1,2 ]上分别单调递减和递增 ,∴ t( 2 ) =( 1a - 2 )&;#215; 2 + 1&;gt;0 ,f( 1) =loga[( 1... 相似文献
5.
ForanytwoconvexbodiesCandDlntheEuc1ideanspaceR"denotebyd(C,D)theminimalnumberAsuchthatthereexistsanaffineoperatorAwhichsatisfiesA(C)=D=AA(C),whereAA(C)denotesahomotheticcopyofA(C)withhom0thetycentrelnsomepointofA(C).d(C,D)iscalledtheMinkowskid1stancebetweenCandD.JohnL'jprovedthatifCisanellipsoid,thend(C,D)相似文献
6.
解不等式的基本思想是化归转化 ,其理论依据是不等式的性质 .要熟练掌握以下几类不等式的解法 :1)一元一次、一元二次不等式的求解要准确、熟练、迅速 ,这是解其他不等式的基础 .2 )关于一元高次不等式 ,一般应先分解因式 ,再利用序轴法求解 .3)关于分式不等式 ,可先化为 f(x)g(x) >0或f(x)g(x) <0 ,再转化为整式不等式求解 :f(x)g(x) >0 f(x)·g(x) >0 ,f(x)g(x) <0 f(x)·g(x) <0 .4 )关于无理不等式 ,应转化为有理不等式求解 .f(x) >g (x ) g(x)≥ 0 ,f(x) >g2 (x) 或g(x) <0 ,f(x)≥ 0 .f(x… 相似文献
7.
In this paper we study the oscillation of the retarded differential equation x′(t)+∫abp(t,ξ)x[g(t,ξ)]dσ(ξ)=0 (b>a) (1)and the advanced differential equation x′(t)-∫abp(t,ξ)x[g(t,ξ)]dσ(ξ)=0 (b>a) (2) We improved the main results of [1-4]. 相似文献
8.
赵增勤 《数学物理学报(A辑)》2005,25(3):393-403
设(i) f(t,u): (0,1)×(0,+∞)→[0,+∞)连续,关于u 单调增加; (ii) 存在函数g:[1,+∞)→(0,+∞),g(b)0,G(t,s)是相应问题的Green函数。 相似文献
9.
文 [1 ]就方程ax =x根的分布情形作了讨论 ,本文把方程ax =x变形为a=x1 x(x>0 ) ,通过函数f(x) =x1x 性质的讨论也可得出方程ax=x根的分布规律 .函数f(x) =x1x(x>0 )有如下性质 :( 1 )当 0 <x<e时 ,f(x)递增 ;当x>e时f(x)递减 .( 2 )在x =e处f(x)取最大值e1e.( 3)limx ∞f(x) =1 ,limx 0 f(x) =0 ,证 ( 1 )因为f′(x) =x1x1 -lnxx2 ,显然0 <x <e时 ,f′(x) >0 ,f′(x) >e时 ,f′(x) <0 .所以当 0 <x <e时 ,f(x)递增 ,x>e时 ,f(x)递减 .( 2 )据 ( 1 )的结… 相似文献
10.
仅考虑简单图.设G是一个图,g(x)和f(x)是定义在V(G)上的整数值函数,且对任意的x∈V(G),设g(x)≤f(x),H是G的一个子图,F={F1,F2,…,Ft}是G的一个因子分解,如果对所有的1≤i≤t, |E(G)∩E(Fi)|=1,则称F与H正交.证明了:设G是一个(mg(x)+k,mf(x)-k)-图,其中对任意的x∈V(G),g(x)≥1或f(x)≥5是定义在V(G)上的整数值函数,1≤k<m,则存在一个子图R满足对G的任意子图H,|E(H)|=k,R有(g,f)-因子分解与H正交. 相似文献
11.
GUIQing-ming DUANQing-tang GUOJian-feng ZHOUQiao-yun 《数学季刊》2003,18(1):82-87
In this paper,a class of new biased estimators for linear model is proposed by modifying the singular values of the design matrix so as to directly overcome the difficulties caused by ill-conditioning in the design matrix.Some important properties of these new estimators are obtained.By appropriate choices of the biased parameters,we construct many useful and important estimators.An application of these new estimators in three-dimensional position adjustment by distance in a spatial coordiate surveys is given.The results show that the proposed biased estimators can effectively overcome ill-conditioning and their numerical stabilities are preferable to ordinary least square estimation. 相似文献
12.
线性模型参数的稳健化有偏估计 总被引:1,自引:1,他引:0
本文讨论复共线性和粗差同时存在时线性模型的参数估计问题,基于等价权原理提出了一个稳健有偏估计类(稳健压缩估计),并且建立了稳健压缩估计的计算方法,为了满足实际问题的需要,构造了许多很有意义的稳健有偏估计,例如稳健岭估计、稳健主成分估计,稳健组合主成估计、稳健单参数主成分估计、稳健根方估计等等,最后通过一个算例表明,本文提出的稳健有偏估计具有既可克服复共线性影响又可抵抗粗差干扰的良好性质。 相似文献
13.
Adaptive Unified Biased Estimators of Parameters in Linear Model 总被引:1,自引:0,他引:1
HuYang Li-xingZhu 《应用数学学报(英文版)》2004,20(3):425-432
To tackle multi collinearity or ill-conditioned design matrices in linear models,adaptive biasedestimators such as the time-honored Stein estimator,the ridge and the principal component estimators havebeen 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 toformulate a class of adaptive biased estimators.This class includes all existing biased estimators and some newones.A sufficient condition for outperforming the least squares estimator is proposed.In terms of selectingparameters in the condition,we can obtain all double-type conditions in the literature. 相似文献
14.
AClassofLinearBiasedEstimatorsofRegressionParameterMatrixintheGrowthCurveModel¥GuiQingming(ZhengzhouInstituteofSurveyingandMa... 相似文献
15.
Francisco Cribari-Neto Maria da Glória A. Lima 《Annals of the Institute of Statistical Mathematics》2010,62(6):1053-1082
The linear regression model is commonly used by practitioners to model the relationship between the variable of interest and
a set of explanatory variables. The assumption that all error variances are the same, known as homoskedasticity, is oftentimes
violated when cross sectional data are used. Consistent standard errors for the ordinary least squares estimators of the regression
parameters can be computed following the approach proposed by White (Econometrica 48:817–838, 1980). Such standard errors,
however, are considerably biased in samples of typical sizes. An improved covariance matrix estimator was proposed by Qian
and Wang (J Stat Comput Simul 70:161–174, 2001). In this paper, we improve upon the Qian–Wang estimator by defining a sequence
of bias-adjusted estimators with increasing accuracy. The numerical results show that the Qian–Wang estimator is typically
much less biased than the estimator proposed by Halbert White and that our correction to the former can be quite effective
in small samples. Finally, we show that the Qian–Wang estimator can be generalized into a broad class of heteroskedasticity-consistent
covariance matrix estimators, and our results can be easily extended to such a class of estimators. 相似文献
16.
本文基于最优线性最小偏差估计的谱分解,定义了秩亏线性模型未知参数的一个新的线性有偏估计类,并讨论了它的许多重要性质,通过选取偏参数的适当形式,构造了许多很有意义的线性有偏估计,最后,给出了一个算例。 相似文献
17.
In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations. 相似文献
18.
Ridge regression is an important approach in linear regression when explanatory variables are highly correlated. Although expressions of estimators of ridge regression parameters have been successfully obtained via matrix operation after observed data are standardized, they cannot be used to big data since it is impossible to load the entire data set to the memory of a single computer and it is hard to standardize the original observed data. To overcome these difficulties, the present article proposes new methods and algorithms. The basic idea is to compute a matrix of sufficient statistics by rows. Once the matrix is derived, it is not necessary to use the original data again. Since the entire data set is only scanned once, the proposed methods and algorithms can be extremely efficient in the computation of estimates of ridge regression parameters. It is expected that the basic knowledge gained in this article will have a great impact on statistical approaches to big data. 相似文献
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20.
半参数回归模型的几乎无偏岭估计 总被引:2,自引:0,他引:2
提出了半参数回归模型的几乎无偏岭估计,并与岭估计进行了比较,在均方误差意义下,几乎无偏岭估计优于岭估计. 然后讨论了有偏参数的选取问题. 最后,用模拟算例和实际应用说明了几乎无偏岭估计的有效性和可行性. 相似文献