Reweighted nonparametric likelihood inference for linear functionals

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY
Karun Adusumilli, Taisuke Otsu, Chen Qiu
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引用次数: 0

Abstract

This paper is concerned with inference on finite dimensional parameters in semiparametric moment condition models, where the moment functionals are linear with respect to unknown nuisance functions. By exploiting this linearity, we reformulate the inference problem via the Riesz representer, and develop a general inference procedure based on nonparametric likelihood. For treatment effect or missing data analysis, the Riesz representer is typically associated with the inverse propensity score even though the scope of our framework is much wider. In particular, we propose a two-step procedure, where the first step computes the projection weights to approximate the Riesz representer, and the second step reweights the moment conditions so that the likelihood increment admits an asymptotically pivotal chi-square calibration. Our reweighting method is naturally extended to inference on missing data, treatment effects, and data combination models, and other semiparametric problems. Simulation and real data examples illustrate usefulness of the proposed method. We note that our reweighting method and theoretical results are limited to linear functionals.
线性泛函的重加权非参数似然推理
研究了半参数矩条件模型有限维参数的推理问题,其中矩函数对未知扰函数是线性的。通过利用这种线性,我们通过Riesz表示重新表述了推理问题,并开发了基于非参数似然的一般推理过程。对于治疗效果或缺失数据分析,Riesz代表通常与反向倾向得分相关联,尽管我们的框架范围要宽得多。特别是,我们提出了一个两步过程,其中第一步计算投影权重以近似Riesz表示,第二步重新加权矩条件,使似然增量允许渐近枢纽卡方校准。我们的重权方法可以很自然地扩展到对缺失数据、处理效果、数据组合模型和其他半参数问题的推断。仿真和实际数据实例验证了该方法的有效性。我们注意到,我们的重权方法和理论结果仅限于线性泛函。
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来源期刊
Electronic Journal of Statistics
Electronic Journal of Statistics STATISTICS & PROBABILITY-
CiteScore
1.80
自引率
9.10%
发文量
100
审稿时长
3 months
期刊介绍: The Electronic Journal of Statistics (EJS) publishes research articles and short notes on theoretical, computational and applied statistics. The journal is open access. Articles are refereed and are held to the same standard as articles in other IMS journals. Articles become publicly available shortly after they are accepted.
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