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

MO Xiao-Hu

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《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

Abstract
HTML
Reference
Related

PDF

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

[1]

. D'Agostini G. Nucl. Instrum. Methods, 1994, A346: 3062. Takeuchi T. Prog. Thero. Phys., 1996, 123(Suppl.): 2473. MO X H, ZHU Y S. HEP NP, 2003, 27: 371(in Chinese)(莫晓虎，朱永生.高能物理.与核物理, 2003, 27: 371)4. MO X H. HEP NP, 2006, 30: 140-146(in Chinese)(莫晓虎.高能物理与核物理，2006, 30: 140-146)5. MO X H, ZHU Y S. HEP NP, 2003, 27: 747(in Chinese)(莫晓虎，朱永生.高能物理与核物理，2003, 27: 747)6. Bartel W et al(JADE Collab.). Phys. Lett., 1983, B129:1457. BAI J Z et al(BES Collab.). Phys. Rev. Lett., 2000, 84:5948. BAI J Z et al(BES Collab.). Phys. Rev. Lett., 2002, 88:1018029. Siegrist J L et al. Phys. Rev., 1982, D26: 969-99010. CERN Library. MINUIT Reference Manual, version 92.1,March 1992

[1]	PING Rong-Gang , MO Xiao-Hu , DU Shu-Xian , LIU Jing , MA Lian-Liang , SHEN Cheng-Ping , WANG Zhi-Yong , YUAN Chang-Zheng . Extract Signals by Fitting χ² Distribution of the Kinematic Fit. Chinese Physics C, 2007, 31(3): 229-231.
[2]	LIU Ye , GAO Yuan-Ning . An Unbiased Estimator of Poisson Statistics. Chinese Physics C, 2007, 31(7): 660-663.
[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.
[5]	MO Xiao-Hu , ZHU Yong-Sheng . Correlated Data Fitting and Error Analysis in ψ(2S) Scan Experiment. Chinese Physics C, 2003, 27(6): 474-478.
[6]	MO Xiao-Hu , ZHU Yong-Sheng . Different χ² Forms for Correlated Data and Their Properties. Chinese Physics C, 2003, 27(9): 747-753.
[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.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(3516)
PDF Downloads(598)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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.