Simple and Honest Confidence Intervals in Nonparametric Regression

Supplemental Appendix for SIMPLE AND HONEST CONFIDENCE INTERVALS IN NONPARAMETRIC REGRESSION

SIMPLE AND HONEST CONFIDENCE INTERVALS IN NONPARAMETRIC REGRESSION By

We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive and tabulate novel critical values that take into account the possible bias of the estimator upon which the CIs are ba...

Supplemental Materials for “Simple and Honest Confidence Intervals in Nonparametric Regression”

We verify the conditions (1), (5) and (7) in some applications. Section C.1 shows that these conditions hold in the Gaussian white noise model under a mild extension of conditions in Donoho and Low (1992). Thus, the results apply to estimating, among other things, a function or one of its derivatives evaluated at a given point, when the function is observed in the white noise model. By equivale...

Nonparametric Regression, Confidence Regions and Regularization

In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region An which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically centre on certain simplest functions in An where simplicity can be defined in term...

Confidence Intervals for Lower Quantiles Based on Two-Sample Scheme

In this paper, a new two-sampling scheme is proposed to construct appropriate confidence intervals for the lower population quantiles. The confidence intervals are determined in the parametric and nonparametric set up and the optimality problem is discussed in each case. Finally, the proposed procedure is illustrated via a real data set.