In this paper, we propose nonparametric estimators of sharp bounds on the distribution of treatment effects of a binary treatment and establish their asymptotic distributions. We note the possible failure of the standard bootstrap with the same sample size and apply the fewer-than-<italic>n</italic> bootstrap to...

This paper develops a wavelet (spectral) approach to testing the presence of a unit root in a stochastic process. The wavelet approach is appealing, since it is based directly on the different behavior of the spectra of a unit root process and that of a short memory stationary process. By...

Let <italic>F</italic> denote a distribution function defined on the probability space (Ω,null,<italic>P</italic>), which is absolutely continuous with respect to the Lebesgue measure in <italic>R</italic> with probability density function <italic>f</italic>. Let <italic>f</italic>₀(·,β) be a parametric density function that depends on an unknown <italic>p</italic> × 1 vector β. In this...

In this paper we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models. We establish minimax risk lower bounds in mean integrated squared error...

Financial practices often need to estimate an integrated volatility matrix of a large number of assets using noisy high-frequency data. Many existing estimators of a volatility matrix of small dimensions become inconsistent when the size of the matrix is close to or larger than the sample size....