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In many metropolitan areas efforts are made to count the homeless to ensureproper provision of social services. Some areas are very large, which makesspatial sampling a viable alternative to an enumeration of the entire terrain.Counts are observed in sampled regions but must be imputed in unvisited areas.Along with the imputation process, the costs of underestimating andoverestimating may be different. For example, if precise estimation in areaswith large homeless c ounts is critical, then underestimation should bepenalized more than overestimation in the loss function. We analyze data fromthe 2004--2005 Los Angeles County homeless study using an augmentation of $L_1$stochastic gradient boosting that can weight overestimates and underestimatesasymmetrically. We discuss our choice to utilize stochastic gradient boostingover other function estimation procedures. In-sample fitted and out-of-sampleimputed values, as well as relationships between the response and predictors,are analyzed for various cost functions. Practical usage and policyimplications of these results are discussed briefly.

Small area estimation of the homeless in Los Angeles: An application of cost-sensitive stochastic gradient boosting