On the existence of maximum likelihood estimates for weighted logistic regression

被引：11

作者：

Zeng, Guoping ^{[1
]}

机构：

[1] Elevate, Risk Management, 5080 Spectrum Dr, Addison, TX 75001 USA

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2017年 / 46卷 / 22期

关键词：

Complete separation; Logistic regression; Maximum likelihood estimate; Overlap; Quasicomplete separation; Weighted logistic regression; MODELS;

D O I：

10.1080/03610926.2016.1260742

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The problems of existence and uniqueness of maximum likelihood estimates for logistic regression were completely solved by Silvapulle in 1981 and Albert and Anderson in 1984. In this paper, we extend the well- known results by Silvapulle and by Albert and Anderson to weighted logistic regression. We analytically prove the equivalence between the overlap condition used by Albert and Anderson and that used by Silvapulle. We show that the maximum likelihood estimate of weighted logistic regression does not exist if there is a complete separation or a quasicomplete separation of the data points, and exists and is unique if there is an overlap of data points. Our proofs and results for weighted logistic apply to unweighted logistic regression.

引用

页码：11194 / 11203

页数：10

共 50 条

[1] ON THE EXISTENCE OF MAXIMUM-LIKELIHOOD ESTIMATES IN LOGISTIC-REGRESSION MODELS
ALBERT, A
ANDERSON, JA
[J]. BIOMETRIKA, 1984, 71 (01) : 1 - 10
[2] CONDITIONS FOR THE EXISTENCE OF MAXIMUM-LIKELIHOOD-ESTIMATES IN LOGISTIC-REGRESSION MODELS
SANTNER, TJ
DUFFY, DE
[J]. BIOMETRIKA, 1986, 73 (03) : 755 - 758
[3] On the existence of the maximum likelihood estimates in Poisson regression
Silva, J. M. C. Santos
Tenreyro, Silvana
[J]. ECONOMICS LETTERS, 2010, 107 (02) : 310 - 312
[4] NORMAL MAXIMUM LIKELIHOOD, WEIGHTED LEAST SQUARES, AND RIDGE REGRESSION ESTIMATES
Withers, Christopher S.
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[J]. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 2012, 32 (01): : 11 - 24
[5] The existence of maximum likelihood estimates in location and dispersion regression models with censored data
Li, Jihong
Wang, Yu
[J]. DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES B-APPLICATIONS & ALGORITHMS, 2007, 14 : 402 - 405
[6] THE PHASE TRANSITION FOR THE EXISTENCE OF THE MAXIMUM LIKELIHOOD ESTIMATE IN HIGH-DIMENSIONAL LOGISTIC REGRESSION
Candes, Emmanuel J.
Sur, Pragya
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[7] Weighted likelihood, pseudo-likelihood and maximum likelihood methods for logistic regression analysis of two-stage data
Breslow, NE
Holubkov, R
[J]. STATISTICS IN MEDICINE, 1997, 16 (1-3) : 103 - 116
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King, EN
Ryan, TP
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[10] EXISTENCE OF MAXIMUM-LIKELIHOOD-ESTIMATES IN REGRESSION-MODELS FOR GROUPED AND UNGROUPED DATA
SILVAPULLE, MJ
BURRIDGE, J
[J]. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL, 1986, 48 (01): : 100 - 106

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