多元统计分析新观点:点估计

摘要/Abstract

摘要：

在科学研究中，经常利用观测到的数据对复杂系统的某些客观对象进行估计，这实际上是科学的一个最基础问题，在统计科学之中也是一个最基本的问题，称为：点估计.对点估计的优良性研究文章众多，但是由于东西方认知世界的哲学思想不同，所以历史上东西方对点估计的计算和论证方法有着相当大的差异.该文通过对东西方点估计的计算方法进行模拟比较，说明东方象数学的多元统计分析点估计的计算方法具有再现性，而西方多元统计分析点估计的计算方法不具有再现性.从再现性的观点来看，东方象数学的点估计的计算方法科学性更强.

关键词: 点估计, 象数学点估计, 再现性

Abstract:

In scientific research, often using the observed data of some objective object for complex systems, estimates that this is actually one of the most basic problems with the scientific, in statistical science is one of the most basic problem, known as the point estimate, of point estimate optimal benign numerous research articles. But because cognitive world philosophy east and west is different, so the history of east and west point estimate calculation and reasoning methods have quite big difference. In this paper, through the comparison of the calculation method of east and west point estimation, illustrate the east as the calculation method of the point estimation in image mathematics has reproducibility, and the west as the calculation method of the point estimation of multivariate statistical analysis has not reproducibility. Reproducibility from the point of view, the oriental image mathematical point estimation method is more scientific.

Key words: Point estimation, Image mathematical point estimation, Reproducibility

中图分类号:

O212.6

张燕,杨林,廖靖宇,张应山. 多元统计分析新观点:点估计[J]. 数学物理学报, 2019, 39(4): 971-992.

Yan Zhang,Lin Yang,Jingyu Liao,Yingshan Zhang. New View: Point Estimation of Multivariate Statistical Analysis[J]. Acta mathematica scientia,Series A, 2019, 39(4): 971-992.

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MEANX($\mu$)
3.66	34.11	10.01
XTAU($\alpha_i$)
-2.16	-20.61	0.09
0.85	0.15	-0.04
1.32	20.45	-0.06

VARXTAU($Var(\tau_{x_0})$)
2.38	23.88	-0.1
23.88	281	-1.03
-0.1	-1.03	0
EEE($Var(\varepsilon)$)
2.55	2.55	-1.99
2.55	53.1	-5.92
-1.99	-5.92	4.05

	K($K=(k_1, k_2, k_3)$)
	1 7 12
	W($\bar W$)= 0.4087302
TRACEVARXTAU($aa$)	TRACEEEE($bb$)	SUM($aa+bb$)
94.46	19.9	114.36
RXTAU($r_{\tau_{x_0}}$)	REPSILON($r_{\varepsilon}$)	RF($\frac{r_{\tau_{x_0}}}{r_{\varepsilon}}$)
0.83	0.17	4.88

RFa	aaa	bbb
0.97	0	0

	XTAU0($\alpha_{i0}$)
	2 20 0
	0 0 0
	-2 -20 0
	MU0($\mu_0$)
	4 50 10
LAMBDAMU($\lambda_{\mu}$)	LAMBDAALPHA($\lambda_{\alpha}$)	FE$f_e$
7.34	0.82	17