多元统计分析新观点:点估计

Abstract

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

CLC Number:

O212.6

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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Figures/Tables 27

References 14

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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

New View: Point Estimation of Multivariate Statistical Analysis

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		C		T2	F	FA
		3.34		42.62	12.54	3.29
N	K			B	JYMU
20	1	7	12	3	4	50	10
					3.66	34.11	10.01
					0.000	0.000	0.000
					0.001	0.001	0.001

			C	T2	F	FA
			3.34	0.064	0.02	3.29
N	K			B	JYALPHA1
20	1	7	12	3	-2	-20	0
					-2.16	-20.61	0.09
					0.997	0.997	0.997
					0.947	0.947	0.947

			C	T2	F	FA
			3.34	0.07	0.02	3.29
N	K			B	JYALPHA2
20	1	7	12	3	0	0	0
					0.85	0.15	-0.04
					0.70	0.70	0.70
					0.87	0.87	0.87

			C	T2	F	FA
			3.34	0.22	0.06	3.29
N	K			B	JYALPHA3
20	1	7	12	3	2	20	0
					1.32	20.45	-0.06
					0.79	0.79	0.79
					0.89	0.89	0.89

MEANX($\mu^{\sigma}$)
1.21	4.68	1.47
XTAU($\alpha_i^{\sigma}$)
-1.01	-3.92	-1.36
0.37	1.46	0.97
0.64	2.45	0.39

VARXTAU($Var(\tau_{x_0}^{\sigma})$)
0.52	2.02	0.66
2.02	7.83	2.57
0.66	2.57	0.98
EEE($Var(\varepsilon^{\sigma})$)
1.55	-2.01	0.14
-2.01	32.17	0.48
0.14	0.48	1.48

	K($K=(k_1, k_2, k_3)$)
	1 7 12
	W ($\bar W$)= 0.4087302
TRACEVARXTAU($aa^{\sigma}$)	TRACEEEE($bb^{\sigma}$)	SUM($aa^{\sigma}+bb^{\sigma}$)
3.11	11.73	14.84
RXTAU($r_{\tau_{x_0}^{\sigma}}$)	REPSILON($r_{\varepsilon^{\sigma}}$)	RF($\frac{r_{\tau_{x_0}^{\sigma}}}{r_{\tau_{x_0}^{\sigma}}}$)
0.21	0.79	0.27

XTAU0($\alpha_{i0}^{\sigma}$)
0 0 0
0 0 0
0 0 0
MU0 ($\mu_0^{\sigma}$)
1.7 6.5 2
LAMBDAMU ($\lambda_{\mu}$)		FE($f_e$)
20		19

		C		T2	F	FA
		3.28		0.02	0.01	3.2
N	K			B	JYMU
20	1	7	12	3	1.7	6.5	2
					1.67	6.47	1.97
					1	1	1
					0.95	0.95	0.95

		C		T2	F	FA
		3.28		9.77	2.91	3.2
N	K			B	JYMU
20	1	7	12	3	4	50	10
					4.64	45.4	9.965
					0.065	0.065	0.065
					0.362	0.362	0.362

西方误差方差估计结论eee
2.88	10.01	-1.81
10.01	199.79	-5.64
-1.81	-5.64	3.63
误差方差平均迹为$trace(EEE/p)= 68.77$,
自由度参数$lambdamu=20, fe=19$

		C		T2	F	FA
		3.28		11.5	3.43	3.2
N	K			B	JYMU
20	1	7	12	3	1.7	6.5	2
					1.63	13.93	1.97
					0.04	0.04	0.04
					0.28	0.28	0.28

			C	T2		F	FA
			2.82	1.52		0.5	2.64
	N	K			B	JYMU
均值:	300	275	15	10	3	4		50	10
						2.37		31.67	9.83
						0		0	0
						0		0	0
			C	T2		F	FA
			2.82	19.39		6.42	2.64
	N	K			B	JYMU
标准差:	300	275	15	10	3	1.7		6.5	2
						1.86		8.73	1.9
						0		0	0
						0.03		0.03	0.03

			C		T2	F	FA
			2.82		1.52	0.5	2.64
	N	K			B	JYMU
均值:	300	275	15	10	3	4		50	10
						3.83		49.16	10.03
						0.68		0.68	0.68
						0.85		0.85	0.85
			C	T2		F	FA
			2.82	3.87		1.28	2.64
	N	K			B	JYMU
标准差:	300	275	15	10	3	1.7		6.5	2
						1.79		6.14	1.91
						0.28		0.28	0.28
						0.66		0.66	0.66

		K
		1 7 12
		W= 0.4087302
TRACEVARXTAU		TRACEEEE		SUM
94.46		19.9		114.36
RXTAU	REPSILON	RF	RFa	aaa	bbb
0.83	0.17	4.88	0.97	0	0

象数学误差方差估计结论EEEx
2.55	2.55	-1.99
2.55	53.1	-5.92
-1.99	-5.92	4.05
误差方差平均迹为$trace(EEEx/p)=19.9$,
自由度参数$lambdamu=7.34, lambdaalpha=0.82, fe=17$

	XTAU0($\alpha_{i0}$)				XTAU0($\alpha_{i0}^{\sigma}$)
考虑均值原假设:	2	20	0	考虑标准差原假设:	0	0	0
	0	0	0		0	0	0
	-2	-20	0		0	0	0
	MU0($\mu_0$)				MU0 ($\mu_0^{\sigma}$)
	4	50	10		1.7	6.5	2

			C	T2		F	FA
			2.82	100		33.11	2.64
	N	K			B	JYMU
均值:	300	10	165	125	3	4		50	10
						5.07		58.67	9.83
						0		0	0
						0		0	0
			C	T2		F	FA
			2.82	100		33.11	2.64
	N	K			B	JYMU
标准差:	300	10	165	125	3	1.7		6.50	2
						2.08		14.01	1.9
						0		0	0
						0		0	0