Electronic Journal of Statistics

Goodness-of-fit testing the error distribution in multivariate indirect regression

Justin Chown, Nicolai Bissantz, and Holger Dette

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We propose a goodness-of-fit test for the distribution of errors from a multivariate indirect regression model, which we assume belongs to a location-scale family under the null hypothesis. The test statistic is based on the Khmaladze transformation of the empirical process of standardized residuals. This goodness-of-fit test is consistent at the root-$n$ rate of convergence, and the test can maintain power against local alternatives converging to the null at a root-$n$ rate.

Article information

Electron. J. Statist., Volume 13, Number 2 (2019), 2658-2685.

Received: December 2018
First available in Project Euclid: 14 August 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing 62G30: Order statistics; empirical distribution functions
Secondary: 62G05: Estimation 62G08: Nonparametric regression

Hypothesis testing indirect regression inverse problems multivariate regression regularization

Creative Commons Attribution 4.0 International License.


Chown, Justin; Bissantz, Nicolai; Dette, Holger. Goodness-of-fit testing the error distribution in multivariate indirect regression. Electron. J. Statist. 13 (2019), no. 2, 2658--2685. doi:10.1214/19-EJS1591. https://projecteuclid.org/euclid.ejs/1565748204

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