کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10525770 | 958224 | 2005 | 24 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Asymptotics of cross-validated risk estimation in estimator selection and performance assessment
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کلمات کلیدی
Asymptotic linearityPerformance assessment - ارزیابی عملکردCross-validation - اعتبار سنجی متقابلModel selection - انتخاب مدلDensity estimation - برآورد تراکمAsymptotic optimality - بهینه بودن همبستگیQuadratic loss function - تابع افت زاویه ایLoss function - تابع افتادنGeneralization error - خطای عمومیRisk - خطرRegression - رگرسیونClassification - طبقه بندیconfidence interval - فاصله اطمینانPrediction - پیش بینی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آمار و احتمال
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Risk estimation is an important statistical question for the purposes of selecting a good estimator (i.e., model selection) and assessing its performance (i.e., estimating generalization error). This article introduces a general framework for cross-validation and derives distributional properties of cross-validated risk estimators in the context of estimator selection and performance assessment. Arbitrary classes of estimators are considered, including density estimators and predictors for both continuous and polychotomous outcomes. Results are provided for general full data loss functions (e.g., absolute and squared error, indicator, negative log density). A broad definition of cross-validation is used in order to cover leave-one-out cross-validation, V-fold cross-validation, Monte Carlo cross-validation, and bootstrap procedures. For estimator selection, finite sample risk bounds are derived and applied to establish the asymptotic optimality of cross-validation, in the sense that a selector based on a cross-validated risk estimator performs asymptotically as well as an optimal oracle selector based on the risk under the true, unknown data generating distribution. The asymptotic results are derived under the assumption that the size of the validation sets converges to infinity and hence do not cover leave-one-out cross-validation. For performance assessment, cross-validated risk estimators are shown to be consistent and asymptotically linear for the risk under the true data generating distribution and confidence intervals are derived for this unknown risk. Unlike previously published results, the theorems derived in this and our related articles apply to general data generating distributions, loss functions (i.e., parameters), estimators, and cross-validation procedures.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistical Methodology - Volume 2, Issue 2, July 2005, Pages 131-154
Journal: Statistical Methodology - Volume 2, Issue 2, July 2005, Pages 131-154
نویسندگان
Sandrine Dudoit, Mark J. van der Laan,