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For supervised classification problems, this paper considers estimating thequery'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, areconsistent but asymptotically biased particularly for a large radius of theball. 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 andextrapolate it to the query itself. However, their theoretical optimality hasbeen shown for the limit of the infinite number of training samples. Forcorrecting 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 ofLPoR and MS-$k$-NN. The idea is quite simple: we fit the local regression toobserved labels by taking only the radial distance as the explanatory variableand then extrapolate the estimated label probability to zero distance. Theusefulness of the proposed method is shown theoretically and experimentally. Weprove the convergence rate of the $L^2$ risk for LRR with reference toMS-$k$-NN, and our numerical experiments, including real-world datasets ofdaily stock indices, demonstrate that LRLR outperforms LPoR and MS-$k$-NN.

Improving Nonparametric Classification via Local Radial Regression with an Application to Stock Prediction