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单调连续处理效应曲线的双重稳健逐点置信区间AI 解读

We study nonparametric inference for the causal dose–response curve when the treatment variable is continuous rather than discrete. We develop doubly robust confidence intervals for the continuous treatment effect curve (at a fixed point) under the assumption that it is monotonic, based on inverting a likelihood ratio-type test. Monotonicity of the treatment effect curve is often a very natural assumption, and this assumption removes the need to choose a smoothing or tuning…

连续处理效应的非参数双重稳健检验AI 解读

The vast majority of literature on evaluating the significance of a treatment effect based on observational data has been confined to discrete treatments. These methods are not applicable to drawing inference for a continuous treatment, which arises in many important applications. To adjust for confounders when evaluating a continuous treatment, existing inference methods often rely on discretizing the treatment or using (possibly misspecified) parametric models for the…

对数凹密度众数的统计推断AI 解读

We study a likelihood ratio test for the location of the mode of a log-concave density. Our test is based on comparison of the log-likelihoods corresponding to the unconstrained maximum likelihood estimator of a log-concave density and the constrained maximum likelihood estimator where the constraint is that the mode of the density is fixed, say at $m$. The constrained estimation problem is studied in detail in Doss and Wellner (2018). Here, the results of that paper are…

对数凹与 s 凹密度极大似然估计的全局收敛速率AI 解读

We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and $s$-concave densities on $\mathbb{R}$. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than $n^{-2/5}$ when $-1<s<\infty$ where $s=0$ corresponds to the log-concave case. We also show that the MLE does not exist for the classes of $s$-concave densities with $s<-1$.