Admissible and Optimal Confidence Bands in Simple Linear Regression

Comparison Of Hyperbolic And Constant Width Simultaneous Confidence Bands in Multiple Linear Regression Under MVCS Criterion

‎A simultaneous confidence band gives useful information on the reasonable range of the unknown regression model‎. ‎In this note‎, ‎when the predictor variables are constrained to a special ellipsoidal region‎, ‎hyperbolic and constant width confidence bonds for a multiple linear regression model are compared under the minimum volome confidence set (MVCS) criterion‎. ‎The size of one speical an...

Simultaneous confidence bands for a percentile line in linear regression

Construction of simultaneous confidence bands for a percentile line in linear regression has been considered by several authors. But only conservative symmetric bands, which use critical constants over the whole covariate range (−∞, ∞), are available in the literature. New methods allow the construction of exact symmetric bands for a percentile line over a finite interval of the covariate x. Th...

Bootstrap Partial Linear Quantile Regression and Confidence Bands∗

In this paper uniform confidence bands are constructed for nonparametric quantile estimates of regression functions. The method is based on the bootstrap, where resampling is done from a suitably estimated empirical density function (edf) for residuals. It is known that the approximation error for the uniform confidence band by the asymptotic Gumbel distribution is logarithmically slow. It is p...

Confidence Bands in Nonparametric Time Series Regression

We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct. The imposed dependence structure allows applications in many linear and nonlinear auto-regressive processes. The results are appli...

Adjusted Confidence Bands in Nonparametric Regression