Optimal confidence bands for shape-restricted curves

Confidence Bands for ROC Curves

We address the problem of comparing the performance of classifiers. In this paper we study techniques for generating and evaluating confidence bands on ROC curves. Historically this has been done using one-dimensional confidence intervals by freezing one variable—the false-positive rate, or threshold on the classification scoring function. We adapt two prior methods and introduce a new radial s...

Polynomial Spline Confidence Bands for Regression Curves

Asymptotically exact and conservative confidence bands are obtained for a nonparametric regression function, using piecewise constant and piecewise linear spline estimation, respectively. Compared to the pointwise confidence interval of Huang (2003), the confidence bands are inflated by a factor proportional to {log (n)}, with the same width order as the Nadaraya-Watson bands of Härdle (1989), ...

REU PROJECT Confidence bands for ROC Curves

Confidence Bands for Convex Median Curves Using Sign-Tests

Suppose that one observes pairs (x1, Y1), (x2, Y2), . . . , (xn, Yn), where x1 ≤ x2 ≤ · · · ≤ xn are fixed numbers, and Y1, Y2, . . . , Yn are independent random variables with unknown distributions. The only assumption is that Median(Yi) = f(xi) for some unknown convex function f . We present a confidence band for this regression function f using suitable multiscale signtests. While the exact ...

Confidence Bands for ROC Curves with Serially Dependent Data

We propose serial correlation robust asymptotic confidence bands for the receiver operating characteristic (ROC) curves estimated by quasi-maximum likelihood in the binormal model. Our simulation experiments confirm that this new method performs fairly well in finite samples. The conventional procedure is found to be markedly undersized in terms of yielding empirical coverage probabilities lowe...