AN INTEGRAL INEQUALITY ON C ([0,1]) AND DISPERSION OF OLS UNDER NEAR-INTEGRATION
C([0,1]) 上的积分不等式与近单整下 OLS 的离散程度
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.