کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1154882 958419 2012 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Prior influence in linear regression when the number of covariates increases to infinity
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آمار و احتمال
پیش نمایش صفحه اول مقاله
Prior influence in linear regression when the number of covariates increases to infinity
چکیده انگلیسی
It is becoming more typical in regression problems today to have the situation where “p>n”, that is, where the number of covariates is greater than the number of observations. Approaches to this problem include such strategies as model selection and dimension reduction, and, of course, a Bayesian approach. However, the discrepancy between p and n can be so large, especially in genomic data, that examining the limiting case where p→∞ can be a relevant calculation. Here we look at the effect of a prior distribution on the coefficients, and in particular characterize the conditions under which, as p→∞, the prior does not overwhelm the data. Specifically, we find that the prior variance on the growing number of covariates must approach zero at rate 1/p, otherwise the prior will overwhelm the data and the posterior distribution of the regression coefficient will equal the prior distribution.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistics & Probability Letters - Volume 82, Issue 3, March 2012, Pages 438-445
نویسندگان
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