多重共线性存在下二元逻辑回归的一般限制估计

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Gargi Tyagi, S. Chandra
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引用次数: 0

摘要

多重共线性的存在严重影响了逻辑回归模型中最大似然估计量的推理性质。这是一个公认的事实,使用限制降低了多重共线性的影响。在本文中,通过将精确的先验信息组合到逻辑r - k类(Lrk)估计器中,引入了ML估计器的替代方法。该估计量被命名为逻辑受限r - k类估计量。作为LRrk估计量的一种特殊情况,我们还开发了另一种估计量——logistic限制性PCR估计量。研究了估计量的渐近均方误差(MSE)矩阵性质,得到了估计量的渐近均方误差的充要条件。此外,进行了蒙特卡罗模拟研究,以比较估计器在标量MSE和预测MSE方面的性能。研究发现,在大多数情况下,所提出的估计器比现有的估计器性能更好。此外,还给出了一个数值例子来比较估计器的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A general restricted estimator in binary logistic regression in the presence of multicollinearity
The presence of multicollinearity adversely affects the inferential properties of the maximum likelihood (ML) estimator in logistic regression model. It is a well established fact that the use of restrictions lowers the effect of multicollinearity. In this article, an alternative to the ML estimator has been introduced by combining the exact prior information into the logistic r − k class (Lrk) estimator. The estimator is named a logistic restricted r − k class estimator. Another estimator, logistic restricted PCR estimator, is also developed as a special case of the LRrk estimator. The asymptotic mean squared error (MSE) matrix properties of the estimators are studied and necessary and sufficient conditions are derived. Further, a Monte Carlo simulation study is performed to compare the performance of the estimators in terms of the scalar MSE and the prediction MSE. It is found that the proposed estimators perform better than the existing estimators in most of the cases considered. Moreover, a numerical example has also been presented for comparing the performance of the estimators.
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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