文章基本信息

标题：Estimating transformation function
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作者：Yunyi Zhang ; Jiazheng Liu ; Zexin Pan 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2019
卷号：13
期号：2
页码：3095-3119
DOI：10.1214/19-EJS1603
语种：English
出版社：Institute of Mathematical Statistics
摘要：In this paper, we propose an estimator for $g(x)$ under the model $Y_{i}=g(Z_{i}),\ i=1,2,...,n$ where $Z_{i},\ i=1,2,...$ are random variables with known distribution but unknown observed values, $Y_{i},\ i=1,2,...$ are observed data and $g(x)$ is an unknown strictly monotonically increasing function (we call $g(x)$ transformation function). We prove the almost sure convergence of the estimator and construct confidence intervals and bands when $Z_{i},i=1,2,...$ are i.i.d data based on their asymptotic distribution. Corresponding case when $Z_{i}$ being linear process is handled by resampling method. We also design the hypothesis test regarding whether $g(x)$ equals an expected transformation function or not. The finite sample performance is evaluated by applying the method to simulated data and an urban waste water treatment plant’s dataset.
关键词：Transformation function; quantile process; resampling method