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An integral inequality on \(C([0,1])\) and dispersion of OLS under near-integration. (English) Zbl 0982.60007

Summary: We obtain an inequality for the sample variance of a vector Brownian motion on \([0,1]\) and an associated Ornstein-Uhlenbeck process. The result is applied to a regression involving near-integrated regressors, and establishes that in the limit the dispersion of the least squares estimator is greater in the near-integrated than in the integrated case. Our proof uses a quite general integral inequality, which appears to be new.

MSC:

60E15 Inequalities; stochastic orderings
60J65 Brownian motion
26D15 Inequalities for sums, series and integrals
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