A viable method for goodness-of-fit test in maximum likelihood fit

ZHANG Feng; GAO Yuan-Ning; HUO Lei

doi:10.1088/1674-1137/35/6/014

Chinese Physics C> 2011, Vol. 35> Issue(6) : 580-584 DOI: 10.1088/1674-1137/35/6/014

A viable method for goodness-of-fit test in maximum likelihood fit

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Abstract：
A test statistic is proposed to perform the goodness-of-fit test in the unbinned maximum likelihood fit. Without using a detailed expression of the efficiency function, the test statistic is found to be strongly correlated with the maximum likelihood function if the efficiency function varies smoothly. We point out that the correlation coefficient can be estimated by the Monte Carlo technique. With the established method, two examples are given to illustrate the performance of the test statistic.

References

[1]

Hoel P G. Ann. Math. Stat., 1938, 9: 1582 Baker S, Cousins R D. Nucl. Instrum. Methods, 1984, 221: 4373 Cowen G. Statistical Data Analysis. Oxford: Clarendon Press, 1998. 894 ZHANG Feng, GAO Yuan-Ning, HUO Lei. Phys. Lett. B, 2009, 681: 2375 Amsler C et al. (Particle Data Group). Phys. Lett. B, 2008, 667: 16 Ablikim M et al. (BES collaboration). Phys. Lett. B, 2006, 632: 181

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ZHANG Feng, GAO Yuan-Ning and HUO Lei. A viable method for goodness-of-fit test in maximum likelihood fit[J]. Chinese Physics C, 2011, 35(6): 580-584. doi: 10.1088/1674-1137/35/6/014

ZHANG Feng, GAO Yuan-Ning and HUO Lei. A viable method for goodness-of-fit test in maximum likelihood fit[J]. Chinese Physics C, 2011, 35(6): 580-584. doi: 10.1088/1674-1137/35/6/014 shu

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Received: 2010-09-07
Revised: 2010-11-22

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沈阳化工大学材料科学与工程学院沈阳 110142

A viable method for goodness-of-fit test in maximum likelihood fit

Received Date: 2010-09-07
Accepted Date: 2010-11-22
Available Online: 2011-06-05

Abstract: A test statistic is proposed to perform the goodness-of-fit test in the unbinned maximum likelihood fit. Without using a detailed expression of the efficiency function, the test statistic is found to be strongly correlated with the maximum likelihood function if the efficiency function varies smoothly. We point out that the correlation coefficient can be estimated by the Monte Carlo technique. With the established method, two examples are given to illustrate the performance of the test statistic.