Optimclity in multirariate estimation

多元估计中的最优性

• 批准号: 63460007
• 负责人: SUGIURA Nariaki
• 金额: $ 4.48万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1989
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-63460007/
• 关键词: generalized variance; efuirariant estimator; Wishart matrix; latent root; Boot strup method; Jackkrife estimator; sequential estimation; skewness; 共変推定量; Wishart行列; 固有根; ブ-トストラップ法; ジャックナイフ推定量; 逐次推定; 歪度; Wishart分布; 分散の推定; stein推定量; 超幾何関数

Using Macintosh II with its software "Mathematics" purchased by this fiend, improved estimators for the mean matrix, genemfted variance, covariance matrix, and the latrnt roots in multivariate normal population were investigated. The sharp lower bound of the risk of the equivalent shrinkage estimator for the generalized variance is obtained. Numerical values are computed, using hypergeometric function of matrix arguments and it was seen that the risk of Stein estimator is close to the sharp lower bound when the matrix of noncennhty parameters is not so far from 0. Sequential shrinkage estimation and two-stage shrinkage estimation for the mean vector or covariance matrix are proposed, which are better than the ordinary estimators. It is shown that improved estimators for the common means or the generalized variance are obtained based on Pitman closeness criterion apart from quadratic loss or entropy loss.The locally best invariant test for outliers is derived and the numerical values of … More the power is shown, by simulation, to be larger than those of the ordinary tests . The estimation of the location parameter of the two-sided exponential distribution is considered as a nonregular distribution. It is shown that asymploticauy better estimator than the maximum likelihood estimator can be found within a class of linear combination of order statistics near the sample median, which is an extension of Akahira(1987). By simulation the values of the variance of each estimator are compared, when the sample size, is small. The Piman estimator has the smallest variance. However we were unable to obtain the asymptotic variance. The computing program of zonal polynomials made in this project will be useful for many other problems in multivariate statiidcal analysis. Graphs of the distribution of the laent roots of the bivariate Wishart matrix is obtained based on this program. Each investigator developed his study in his research theme actively and the results are reported to abroad too. Less

使用Macintosh II及其软件的“数学”购买了这位恶魔的“数学”，研究了均值基质，genemft差异，协方差矩阵和多变量正常人群中的LATRNT根的改进。获得了广义方差的等效收缩估计量的急剧下限。使用矩阵参数的超几何函数计算数值值，可以看到，当非中心参数的矩阵与0的矩阵不远时，Stein估计器的风险接近急剧下限。顺序收缩估计和平均载体或共价矩阵的两阶段收缩估计比普通估计更好，这比普通的估计值更好。结果表明，除了二次损失或熵损失外，基于Pitman的紧密标准获得了改进的通用均值或广义方差的估计量。得出了异常值的本地最佳不变测试，并得出了……通过模拟显示的功率比普通测试更大的功率显示。两侧指数分布的位置参数的估计被认为是非规范分布。结果表明，在样本中位数附近的订单统计数据的线性组合中可以找到比最大似然估计器更好的估计器，这是Akahira（1987）的扩展。通过仿真，当样本尺寸小时，比较每个估计器的方差值。 PIMAN估计器的方差最小。但是，我们无法获得不对称的方差。该项目中制作的Zonal多项式计算程序对于多元构成分析中的许多其他问题都是有用的。基于此程序获得了双变量WishArt矩阵的晚期根的分布图。每个研究者都积极地在他的研究主题中开发了自己的研究，结果也报告给国外。较少的

项目成果

杉浦成昭: "Entropy loss and a class of improved estimators for powers of the generalized variance" Sankhya Ser.A.51. (1990)

Nariaki Sugiura：“熵损失和一类改进的广义方差幂估计量”Sankhya Ser.A.51 (1990)。

赤平昌文: "Second order asymptotic optinality of estimators for a density with finite cusps" Ann.Inst.Statist.Math.40. 311-328 (1988)

Masafumi Akahira：“有限尖点密度估计量的二阶渐近最优性”Ann.Inst.Statist.Math.40 (1988)。

赤平昌文,竹内啓: "Third order asymptotic effniency of the sequentol maximum lkelihool entimation proceclure." Sequential Analysis. 8. 333-359 (1989)

Masafumi Akahira、Kei Takeuchi：“序列最大 lkelihool 预测过程的三阶渐近效率。” 8. 333-359 (1989)

Sugirua,N. and Sasamoto,H.(1989): "Locally best invariant test for outliers in a gamma type distribution" Commun. Statist.-Simula. 18 415-427.

苏吉鲁阿，N.

Takaaki,Shiraishi: J.JAPAN STATIST.SOC.18. 37-46 (1988)

Takaaki，Shiraishi：J.JAPAN STATIST.SOC.18。