Open Access
2019 Estimating transformation function
Yunyi Zhang, Jiazheng Liu, Zexin Pan, Dimitris N. Politis
Electron. J. Statist. 13(2): 3095-3119 (2019). DOI: 10.1214/19-EJS1603


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.


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Yunyi Zhang. Jiazheng Liu. Zexin Pan. Dimitris N. Politis. "Estimating transformation function." Electron. J. Statist. 13 (2) 3095 - 3119, 2019.


Received: 1 January 2019; Published: 2019
First available in Project Euclid: 24 September 2019

zbMATH: 07113713
MathSciNet: MR4010594
Digital Object Identifier: 10.1214/19-EJS1603

Primary: 62G05 , 62G09 , 62G10

Keywords: quantile process , resampling method , Transformation function

Vol.13 • No. 2 • 2019
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