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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 36, Fasc. 1,
pages 113 - 120
 

A LIMIT PROCESS FOR A SEQUENCE OF PARTIAL SUMS OF RESIDUALS OF A SIMPLE REGRESSION ON ORDER STATISTICS WITH MARKOV-MODULATED NOISE

Artyom Kovalevskii
Evgeny Shatalin

Abstract: 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.

2000 AMS Mathematics Subject Classification: Primary: 60F17; Secondary: 62J05.

Keywords and phrases: Simple regression model, order statistics, Markov-modulated noise, regression residuals, empirical bridge.

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