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A limit process for a sequence of partial sums of residuals of a simple regression on order statistics with Markov-modulated noise

Kovalevskii A., Shatalin E.

Probability and Mathematical Statistics

2016

Vol. 36, Fasc. 1

113--120

We consider a simple regression model where a regressor is composed of order statistics, and a noise is Markov-modulated. We introduce an empirical bridge of regression residuals and prove its weak convergence to a centered Gaussian process. In the proof we use convergence properties of order statistics.