Global statistical inference for the difference between two regression mean curves with covariates possibly partially missing. (English) Zbl 1484.62044
Summary: In two sample problems it is of interest to examine the difference between the two regression curves or to detect whether certain functions are adequate to describe the overall trend of the difference. In this paper, we propose a simultaneous confidence band (SCB) as a global inference method with asymptotically correct coverage probabilities for the difference curve based on the weighted local linear kernel regression estimates in each sample. Our procedure allows for random designs, different sample sizes, heteroscedastic errors, and especially missing covariates. Simulation studies are conducted to investigate the finite sample properties of the new SCB which support our asymptotic theory. The proposed SCB is used to analyze two data sets, one of which is concerned with human event-related potentials data which are fully observed and the other is concerned with the Canada 2010/2011 youth student survey data with partially missing covariates, leading to a number of discoveries.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62G07 | Density estimation |
| 62G15 | Nonparametric tolerance and confidence regions |
| 62G20 | Asymptotic properties of nonparametric inference |
Keywords:
covariates missing at random; Gaussian process; simultaneous confidence band; weighted local linear regressionReferences:
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