| THE ESTIMATE AND TEST IN THE SYMMETRICAUXILIARY INFORMATION |
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| 作者姓名： | CUI Hengjian YUAN Xiujiu |
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| 作者单位： | Department of Mathematics，Beijing Normal University，Beijing 100875，China |
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| 摘 要： | 1.IntroductionLetX,XI,X2,'lXui.i.d.~FO.TheempiricaldistributionFn=Z::,6x./niswellknowntobethenonparametricmaximumlikelihoodestimateofFObasedonXI,X2,')Xu.Here6:denotesapointmassatx.ThelikelihoodfunctionthatFimaximizesisL(G)=fi:=,G{xi},whereG{xi}istheprobabilityoftheset{xi}underG,xiistheobservedvalueofXiandGisanyprobabilitymeasureonCP.WedefinetheempiricallikelihoodfunctionnL(G)=fiG{xi},whereG<
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THE ESTIMATE AND TEST IN THE SYMMETRICAUXILIARY INFORMATION |
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| CUI Hengjian, YUAN Xiujiu.THE ESTIMATE AND TEST IN THE SYMMETRICAUXILIARY INFORMATION[J].Journal of Systems Science and Complexity,1998(2). |
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| Authors: | CUI Hengjian YUAN Xiujiu |
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| Abstract: | This paper gives an estimate of a symmetric population distribution function Fand a modified K. Pearson statistic in the symmetric auxiliary information. Asymptoticalproperties show that they dominate the usual statistics. The asymptotic distribution ofthe modified K. Pearson statistic under the null hypothesis is derived. The approximateBahadur slope and asymptotic power function of a test based on the modified K. Pearsonstatistic are given. Numerical results show the modified K. Pearson statistic is better thanK. Pearson statistic. |
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| Keywords: | Empirical likelihood K Pearson statistic approximate Bahadur slope powerfunction |
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