Stochastic equicontinuity and weak convergence of unbounded sequential empirical processes

34 Pages·1994·0.85 MB·English

by  Bai, Jushan

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STOCHASTIC EQUICONTINUITY AND WEAK CONVERGENCE
OF UNBOUNDED SEQUENTIAL EMPIRICAL PROCESES
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139

STOCHASTIC EQUICONTINUITY AND WEAK CONVERGENCE
OF UNBOUNDED SEQUENTIAL EMPIRICAL PROCESES
Jushan Bai
94-7 Jan. 1993
Abstract
This note explains why sequential empirical processes arise naturally in the context of
structural change and then provides an elementary prooffor their stochastic equiconti-
nuity. An application is considered for testing structural change in a linear regression
and in a single equation of a simultaneous equations system.
Key words and phrases: Stochastic equicontinuity, weak convergence, sequential em-
pirical process, two-parameter Brownian bridge, structural change.
Stochastic Equicontinuity and Weak
Convergence of Unbounded Sequential
Empirical Processes
Jushan Bai
Massachusetts Institute of Technology
[phone]
email: [email protected]
Revised: January 1994
APRS
1994