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We study a multi-armed bandit problem in a setting where covariates are available. We take a nonparametric approach to estimate the functional relationship between the response (reward) and the covariates. The estimated relationships and appropriate randomization are used to select a good arm to play for a greater expected reward. Randomization helps(More)
It is well known that AIC and BIC have different properties in model selection. BIC is consistent in the sense that if the true model is among the candidates, the probability of selecting the true model approaches 1. On the other hand, AIC is minimax-rate optimal for both parametric and nonparametric cases for estimating the regression function. There are(More)
Adaptation over diierent procedures is of practical importance. Diierent procedures perform well under diierent conditions. In many practical situations, it is rather hard to assess which conditions are (approximately) satissed so as to identify the best procedure for the data at hand. Thus automatic adaptation over various scenarios is desirable. A(More)
Risk bounds are derived for regression estimation based on model selection over a unrestricted number of models. While a large list of models provides more exibility, sig-niicant selection bias may occur with bias-correction based model selection criteria like AIC. We incorporate a model complexity penalty term in AIC to handle the selection bias. Resulting(More)
This paper looks into the issue of evaluating forecast accuracy measures. In the theoretical direction, for comparing two forecasters, only when the errors are stochastically ordered, the ranking of the forecasts is basically independent of the form of the chosen measure. We propose well-motivated Kullback-Leibler Divergence based accuracy measures. In the(More)