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.