  For supervised classification problems, this paper considers estimating the
query's label probability through local regression using observed covariates.
Well-known nonparametric kernel smoother and $k$-nearest neighbor ($k$-NN)
estimator, which take label average over a ball around the query, are
consistent but asymptotically biased particularly for a large radius of the
ball. To eradicate such bias, local polynomial regression (LPoR) and multiscale
$k$-NN (MS-$k$-NN) learn the bias term by local regression around the query and
extrapolate it to the query itself. However, their theoretical optimality has
been shown for the limit of the infinite number of training samples. For
correcting the asymptotic bias with fewer observations, this paper proposes a
\emph{local radial regression (LRR)} and its logistic regression variant called
\emph{local radial logistic regression~(LRLR)}, by combining the advantages of
LPoR and MS-$k$-NN. The idea is quite simple: we fit the local regression to
observed labels by taking only the radial distance as the explanatory variable
and then extrapolate the estimated label probability to zero distance. The
usefulness of the proposed method is shown theoretically and experimentally. We
prove the convergence rate of the $L^2$ risk for LRR with reference to
MS-$k$-NN, and our numerical experiments, including real-world datasets of
daily stock indices, demonstrate that LRLR outperforms LPoR and MS-$k$-NN.
