Dimension Reduction and Prediction for High-dimensional Regression Models Using the Graphical Lasso

• 발행기관: 한국자료분석학회
• 저자명: Eun Jeong Oh Hakbae Lee
• 간행물 정보: 『Journal of The Korean Data Analysis Society (JKDAS)』Vol.15 No.5, 2321~2332쪽, 전체 12쪽
• 주제분류: 자연과학 > 통계학
• 파일형태: PDF
• 발행일자: 2013.10.30

영문 초록

Deriving reductions from high-dimensional covariates with minimal loss of information is an effective way of reducing covariate dimension and plays a pivotal role in sufficient dimension reduction (SDR). We investigate sufficient dimension reduction in highdimensional regressions by using the graphical lasso method developed by Friedman, Hastie, Tibshirani (2007) even when the sample size n is not sufficiently large compared to the number of predictors p. The key point here is that we consider the model in abundant highdimensional regressions where most of the covariates contribute some information on a response, which differ from sparse regressions. By discovering an intrinsic dimensionality of the data and estimating a sufficient reduction R(X), we improve the prediction of the response, which is our ultimate goal, with a kernel-type estimator. The estimated reductions and predicted values of the response are illustrated through simulation studies and a real data application.

목차

1. Introduction

2. Estimation

3. Graphical lasso

4. Simulation study

5. Real data application

6. Concluding Remarks

References

키워드

Sufficient dimension reduction graphical lasso high dimension low sample size (HDLSS) data abundant regressions