頁籤選單縮合
| 題 名 | Boosting for High-Multivariate Responses in High-Dimensional Linear Regression |
|---|---|
| 作 者 | Lutz, Roman Werner; Bühlmann, Peter; | 書刊名 | Statistica Sinica |
| 卷 期 | 16:2 民95.04 |
| 頁 次 | 頁471-494 |
| 分類號 | 319.9 |
| 關鍵詞 | High-multivariate high-dimensional linear regression; L₂Boosting; Vector AR time series; |
| 語 文 | 英文(English) |
| 英文摘要 | We propose a boosting method, multivariate L₂Boosting, for multivariate linear regression based on some squared error loss for multivariate data. It can be applied to multivariate linear regression with continuous responses and to vector autoregressive time series. We prove, for i.i.d. as well as time series data, that multivariate L₂Boosting can consistently recover spare high-dimensional multivariate linear functions, even when the number of predictor variables p[9061] and the dimension of the response q[9061] grow almost exponentially with sample size n, p[9061] = q[9061] = O (exp(Cn□)) (0 < ζ < 1, 0 < C < ∞), but the ℓ₁–norm of the true underlying function is finite. Our theory seems to be among the first to address the issue of large dimension of the response variable; the relevance of such settings is briefly outlined. We also identify empirically cases where our multivariate L₂Boosting is better than multiple application of univariate methods to single response components, thus demonstrating that the multivariate approach can be very useful. |
本系統中英文摘要資訊取自各篇刊載內容。