Erratum to: A general result on the uniform in bandwidth consistency of kernel-type function estimators

1 Erratum to: Test (2011) 20:72–94 DOI 10.1007/s11749-010-0188-0

We want to point out the following corrections to the original article:

• 1. Replace “$(\log n) ^{-1}$ ” by “$c\log n/n$” in their Corollaries 1–3 and three lines above Eq. (2.16).

• 2. In Eq. (2.5) replace “$O( \sqrt{b_{n}})$” by “$=O\left( \sqrt{ b_{n}\left( \frac{\left| \log b_{n}\right| }{\log \log n}\vee 1\right) }\right) =o(1)$”.

• 3. In Eqs. (2.6) and (2.7) and in the two lines below their Corollary 2, replace “ $\sqrt{b_{n}\log \log n}$ ” by “ $\sqrt{b_{n}( \log \log n\vee \vert \log b_{n}\vert ) }$” .

• 4. Three lines below Eq. (2.15) replace“ $0<b_{n}<1$ satisfying $b_{n}\ge (\log n) ^{-1}$ and $\sqrt{n} b_{n}/\sqrt{\log \log n}=o(1)$” by“ $b_{n}$ satisfying $b_{n}\ge c\log n/n$ and $b_{n}\rightarrow 0$” .

• 5. In (F.ii) given in the Theorem, $\mathcal {G}$ should be $\mathcal {G}_{\gamma }$.

For more details of corrections 1–4 refer to Corollaries 1.12, 1.13 and 1.14 in Mason and Swanepoel (2013).