Details

Autor(en) / Beteiligte

• Dümbgen, Lutz

Titel

Confidence Bands for Convex Median Curves Using Sign-Tests

Ist Teil von

• Lecture notes-monograph series, 2007-01, Vol.55, p.85-100

Ort / Verlag

Institute of Mathematical Statistics

Erscheinungsjahr

2007

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Suppose that one observes pairs (x₁, Y₁), (x₂, Y₂),..., ($x_{n}$,$Y_{n}$), where$x_{1}\leq x_{2}\leq \cdots \leq x_{n}$are fixed numbers, and Y₁, Y₂,...,$Y_{n}$are independent random variables with unknown distributions. The only assumption is that$\text{Median}(Y_{i})=f(x_{i})$for some unknown convex function f. We present a confidence band for this regression function f using suitable multiscale signtests. While the exact computation of this band requires O(n⁴) steps, good approximations can be obtained in O(n²) steps. In addition the confidence band is shown to have desirable asymptotic properties as the sample size n tends to infinity.