论文信息 - Bootstrap Prediction Intervals for Regression

Bootstrap Prediction Intervals for Regression

Abstract Bootstrap prediction intervals provide a nonparametric measure of the probable error of forecasts from a standard linear regression model. These intervals approximate the nominal probability content in small samples without requiring specific assumptions about the sampling distribution. Empirical measures of the prediction error rate motivate the choice of these intervals, which are calculated by an application of the bootstrap. The intervals are contrasted to other nonparametric procedures in several Monte Carlo experiments. Asymptotic invariance properties are also investigated.

R. Stine

[1] J. Tukey. Non-Parametric Estimation II. Statistically Equivalent Blocks and Tolerance Regions--The Continuous Case , 1947 .

[2] K. Sharpe. Robustness of normal tolerance intervals , 1970 .

[3] K. Singh,et al. On the Asymptotic Accuracy of Efron's Bootstrap , 1981 .

[4] B. Efron. Bootstrap Methods: Another Look at the Jackknife , 1979 .

[5] M. R. Mickey,et al. Estimation of Error Rates in Discriminant Analysis , 1968 .

[6] S. S. Wilks. Determination of Sample Sizes for Setting Tolerance Limits , 1941 .

[7] D. Freedman. Bootstrapping Regression Models , 1981 .

[8] B. Efron. Estimating the Error Rate of a Prediction Rule: Improvement on Cross-Validation , 1983 .

[9] Ronald W. Butler,et al. Predictive Intervals Based on Reuse of the Sample , 1980 .

[10] M. Stone. Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[11] W. J. Conover,et al. Practical Nonparametric Statistics , 1972 .

[12] B. Efron. The jackknife, the bootstrap, and other resampling plans , 1987 .

[13] Seymour Geisser,et al. The Predictive Sample Reuse Method with Applications , 1975 .

[14] E. Nadaraya,et al. Some New Estimates for Distribution Functions , 1964 .