The Probability of Information (PIN)-based trading introduced by Easley <italic>et al</italic>. (1996, 2002) has been adopted to address a variety of issues in empirical finance. To obtain PIN using numerical Maximum Likelihood Estimation (MLE) from transaction data, one may suffer from the numerical overflow or...

We consider approximating a multivariate regression function by an affine combination of one-dimensional conditional component regression functions. The weight parameters involved in the approximation are estimated by least squares on the first-stage nonparametric kernel estimates. We establish...

The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in L1 are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for...

For the pth-order linear ARCH model, , where [alpha]0 0, [alpha]i [greater-or-equal, slanted] 0, I = 1, 2, ..., p, {[var epsilon]t} is an i.i.d. normal white noise with E[var epsilon]t = 0, E[var epsilon]t2 = 1, and [var epsilon]t is independent of {Xs, s t}, Engle (1982) obtained the...

For spatio-temporal regression models with observations taken regularly in time but irregularly over space, we investigate the effect of spatial smoothing on the reduction of variance in estimating both parametric and nonparametric regression functions. The processes concerned are stationary in...

In this note, the condition to ensure the L1 geometric ergodicity of a multivariate nonlinear AR model mixed with an ARCH term (also called conditional heteroscedastic autoregressive nonlinear model) is investigated. Under some mild conditions on the white noise process with first absolute...

This paper establishes a general moment inequality for spatial processes satisfying the [alpha]-mixing condition [cf., Tran, 1990. Kernel density estimation on random fields. J. Multivariate Analy. 34, 37-53]. Such a general moment inequality is a nontrivial extension of the corresponding result...