Unbiased χ<SUP>2</SUP> Estimator for Linear Function Fit Involving Correlated Data

MO Xiao-Hu

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2007, Vol. 31> Issue(8) : 745-749

Unbiased χ² Estimator for Linear Function Fit Involving Correlated Data

MO Xiao-Hu ^,

Institute of High Energy Physics, CAS, Beijing 100049, China

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Abstract：
An unbiased factorized chi-square estimator is constructed to deal with the correlated data for linear function fit. The difference between the biased and unbiased chi-square fitting is expounded. In addition, the simplified R-value measurement is quoted to test the conclusion quantitatively.

References

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[3]	ZHAO Zhen-Tang , JIANG Bo-Cheng . Longitudinal Coupled Bunch Instability in Fractionally Filled Storage Rings. Chinese Physics C, 2004, 28(11): 1209-1213.
[4]	FU Cheng-Dong , MO Xiao-Hu , ZHANG Jia-Wen , ZHU Yong-Sheng , YUAN Chang-Zheng , DONG Xin , DONG Liao-Yuan . Fast Reconstruction of ψ(2S) Data and Corresponding Quality Supervision. Chinese Physics C, 2003, 27(8): 653-658.
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[7]	CUI XiangZong , GU YiFan , LI XinHua , HAN ShiWen . Measurement of Integrated Luminosity at ψ(2S) by Wide-Angle Bhabha Scattering. Chinese Physics C, 2000, 24(1): 4-10.
[8]	Yao Xueyi , Chen Guoming , Chen Gang , Chen Hesheng , Tang Xiaowei . Measurement of Structure Function of τ→π^±2π⁰v. Chinese Physics C, 1999, 23(1): 10-16.
[9]	Hui Ping . Fifth Order Approximate Analytic Calculation of (2+1)-D SU(2) Vacuum Wavefunction. Chinese Physics C, 1998, 22(4): 322-325.
[10]	Mao Zepu , Wang Jun , Ye Shizhang , Lan Huibin , Sun Shijun , Liu Huaimin , Liu Qi , Liu Jing , Li Weiguo , Li Peiqin , Chen Shaomin , Chen Guangpei , Qiu Jinfa , Shong Xiaofei , Fang Xiaoling , Zhou Li , Rong Gang , Zhang Shaoqiog , Zhang Jiawen , Han Ying , Xue Shengtian , Pan linajun . BES Data Off-line Calibration. Chinese Physics C, 1996, 20(12): 1073-1081.
[11]	Zheng Taiyu , Li Changsong . Internal Massive Fermion Loop Contribution to Casimir Force in Two-Dimensions. Chinese Physics C, 1996, 20(3): 211-215.
[12]	Chen Qizhou , Li Lei , Li Zhibing , Guo Shuohong . Vacuum Wave Function Study of 2+1 Dimensional SU(2) Gauge Field. Chinese Physics C, 1994, 18(5): 417-423.
[13]	Chen Qizhou , Li Zhibing , Li Lei , Guo Shuohong . Infrared Vacuum Wavefunction of (2+1)-Dimensional SU(2) Gauge Field. Chinese Physics C, 1994, 18(1): 37-42.
[14]	Xu Jianming . Study on the Output from Programs in Calculating Lattice with Tranverse Coupling. Chinese Physics C, 1994, 18(10): 955-960.
[15]	HOU Bo-Yu , SHI Kang-Jie , YUE Rui-Hong . The Crossing Matrices and Correlation Function in Nonunitary SU_K(2) Wess-Zumino-Witten Model. Chinese Physics C, 1992, 16(5): 414-422.
[16]	YANG Ze-Sen (Tse Sen Yang) . THE SU₂×SU₂ BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEM AND THE TRACELESS BOSON OPERATORS(Ⅲ). Chinese Physics C, 1983, 7(4): 489-499.
[17]	YANG Ze-Sen (Tse-sen Yang) . THE SU₂×SU₂BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEMS AND THE TRACELESS BOSON OPERATORS (Ⅱ). Chinese Physics C, 1983, 7(2): 245-256.
[18]	YANG ZE-SEN , TSE-SEN YANG . THE SU₂×SU₂BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEMS AND THE TRACELESS BOSON OPERATORS (Ⅰ). Chinese Physics C, 1982, 6(5): 630-641.
[19]	HOU BO-YU , HOU BO-YUAN . STATICAL SPHEROSYMMETRICAL SOURCELESS SOLUTION OF SU(2) GAUGE FIELD——THE SELFDUALITY,UNIQUENESS AND THE SELF INDUCED CHARGE CURRENT. Chinese Physics C, 1979, 3(3): 225-265.
[20]	WANG YUN-KONG , CHANG KUO-TIU , HOU BO-YU . A SERIES OF SOURCELESS SOLUTION OF SU(2) GAUGE FIELDS——THE SU(2) AND U(1) POTENTIAL OF STATIC MONOPOLE SYSTEMS. Chinese Physics C, 1978, 2(4): 368-370.

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MO Xiao-Hu. Unbiased χ² Estimator for Linear Function Fit Involving Correlated Data[J]. Chinese Physics C, 2007, 31(8): 745-749.

MO Xiao-Hu. Unbiased χ² Estimator for Linear Function Fit Involving Correlated Data[J]. Chinese Physics C, 2007, 31(8): 745-749. shu

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Received: 2006-10-09
Revised: 2006-11-29

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沈阳化工大学材料科学与工程学院沈阳 110142

Unbiased χ² Estimator for Linear Function Fit Involving Correlated Data

MO Xiao-Hu ^,

Corresponding author: MO Xiao-Hu,

Institute of High Energy Physics, CAS, Beijing 100049, China

Received Date: 2006-10-09
Accepted Date: 2006-11-29
Available Online: 2007-08-05

Abstract: An unbiased factorized chi-square estimator is constructed to deal with the correlated data for linear function fit. The difference between the biased and unbiased chi-square fitting is expounded. In addition, the simplified R-value measurement is quoted to test the conclusion quantitatively.