Nonparametric estimation of conditional densities by generalized random forests
提出一种用广义随机森林估计条件期望，进而构造条件密度指数级数估计量的方法，证明了估计量的一致性和渐近正态性，并给出了标准误公式，适用于经济学等领域的条件密度分析。
.Considering a continuous random variable Y together with a continuous random vector X, I propose a nonparametric estimator f̂(⋅|x) for the conditional density of Y given X = x. This estimator takes the form of an exponential series whose coefficients θ̂x=(θ̂x,1,…,θ̂x,J) are the solution of a system of nonlinear equations that depends on an estimator of the conditional expectation E[ϕ(Y)|X=x], where ϕ is a J-dimensional vector of basis functions. The distinguishing feature of the proposed estimator is that E[ϕ(Y)|X=x] is estimated by generalized random forest (Athey, Tibshirani, and Wager, Annals of Statistics, 2019), targeting the heterogeneity of θ̂x across x. I show that f̂(⋅|x) is uniformly consistent and asymptotically normal, allowing J→∞. I also provide a standard error formula to construct asymptotically valid confidence intervals. Results from Monte Carlo experiments are provided, and an empirical application to U.S. timber auction data illustrates how the proposed estimator can be used to estimate the conditional density of bids given auctioned object characteristics.