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Bin smoother

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Abstract Bin smoothers, or regressograms, are piecewise constant regression function estimators whose values are averages of the response variable over the sets of a partition of the space of the explanatory variables. First, we review results about bin smoothers whose partition is regular, giving conditions for consistency and for achieving the optimal rate of convergence. Second, we review representative results about bin smoothers whose partition is irregular, again giving conditions for consistency and for achieving the optimal rate of convergence. Third, we give an exposition of recursive partitioning, main examples being greedy partitions and the classification and regression tress (CART) methodology. WIREs Comput Stat 2012 doi: 10.1002/wics.1214 This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Classification and Regression Trees (CART) Statistical and Graphical Methods of Data Analysis > Density Estimation Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

Irregular partitions; (a) A dyadic partition. (b) A CART partition.

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Statistical Learning and Exploratory Methods of the Data Sciences > Classification and Regression Trees (CART)
Statistical and Graphical Methods of Data Analysis > Nonparametric Methods
Statistical and Graphical Methods of Data Analysis > Density Estimation

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