• 论文 • 上一篇    下一篇

测量误差为Laplace分布的非线性统计推断

史建红1 ,宋卫星2   

  1. 1.山西师范大学数学与计算机科学学院, 临汾 041004; 2.Department of Statistics, Kansas State University, Manhattan, KS 66503
  • 出版日期:2015-12-25 发布日期:2016-01-12

史建红,宋卫星. 测量误差为Laplace分布的非线性统计推断[J]. 系统科学与数学, 2015, 35(12): 1510-1528.

SHI Jianhong,SONG Weixing. NONLINEAR STATISTICAL INFERENCES WITH LAPLACE MEASUREMENT ERROR[J]. Journal of Systems Science and Mathematical Sciences, 2015, 35(12): 1510-1528.

NONLINEAR STATISTICAL INFERENCES WITH LAPLACE MEASUREMENT ERROR

SHI Jianhong1 ,SONG Weixing2   

  1. 1.School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004; 2.Department of Statistics, Kansas State University, Manhattan, KS 66503
  • Online:2015-12-25 Published:2016-01-12

当$p$-维参数$\theta$通过矩条件$Em(X,\theta)=0$定义, 且$X$带有Laplace测量误差时,即我们只能观测到$Z=X+U$, 文献中提出了一种基于无条件期望关系 $Em(X,\theta)=EH(Z,\theta)$的估计方法,其中$H$ 为某个 形式已知的函数.然而该方法仅适用于$U$的各分量服从Laplace分布 且相互独立的情况.文章将介绍一种一般的多元Laplace分布, 并将基于无条件期望的估计方法推广到具有这种多元Laplace分布的测量 误差模型中. 另外,基于无条件期望关系的估计方法对一些统计推 断问题并不适用. 文章将构造一种基于条件期望 $E[m(X,\theta)|Z]$ 的估计方法. 当$X$为一维时,我们对这些估计的大样本性质进行了讨论.

When a $p$-dimensional parameter $\theta$ is defined through the moment condition $Em(X,\theta)=0$, a simple estimation procedure of $\theta$ was proposed in literature based on the unconditional expectation $Em(X,\theta)=EH(Z,\theta)$ for some function $H$, when X, a $k$-dimensional random vector, are contaminated with Laplace measurement error $U$, that is, only $Z=X+U$ can be observed. However, the estimation procedure was designed particularly for the cases where the components of the measurement error vector $U$ are independent. In this paper, we first introduce a general multivariate Laplace distribution, then extend the existing method to the general multivariate scenario. However, an example shows that the estimation procedure based on the unconditional expectation does not work in some cases. In this paper, we will propose an estimation procedure based on the condition expectation $E(m(X,\theta)|Z)$. Large sample properties of the proposed estimation procedure when $X$ is one-dimensional are discussed.

MR(2010)主题分类: 

()
[1] 张赛茵,梁华. 部分线性回归模型的加权似然推断[J]. 系统科学与数学, 2015, 35(12): 1501-1509.
[2] 徐家杰. 双阀值LSTAR模型及其在人民币汇率预测中的应用[J]. 系统科学与数学, 2013, 33(3): 264-275.
[3] 魏传华;吴喜之. 部分线性变系数模型的Profile Lagrange乘子检验[J]. 系统科学与数学, 2008, 28(4): 416-424.
[4] 孟洁;王惠文;黄海军;苏建宁. 基于样条变换的PLS回归的非线性结构分析[J]. 系统科学与数学, 2008, 28(2): 243-250.
阅读次数
全文


摘要