Basic causality is that a cause is present or absent and that the effect follows with a success or not. This happy state of affairs becomes opaque when there is a third variable that can be present or absent and that might be a seeming cause. The 2 x 2 x 2 layout deserves the standard name of...

We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous. The central limit theorem is shown to have a feasible version. In the process, we show that the...

Traditional literature on impact evaluation often deals with binary programs. In reality, a program can provide different amounts of treatment for people, and it is regarded as a continuous variable. This paper discusses impact evaluation of a continuous program using matching methods and...

We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother...

Conditional dependence is expressed as a projection map in the trivariate copula space. The projected copula, its sample counterpart and the related process are defined. The weak convergence of the projected copula process to a tight centered Gaussian Process is obtained under weak assumptions...

We propose a nonparametric test of conditional independence based on the empirical distribution function. The asymptotic null distribution is a mixture of chi-squares. A bootstrap procedure is proposed for calculating the critical values. Our test has power against alternatives at distance...

In the classical Condorcet jury model, different jurors' votes are independent random variables, where each juror has the same probability p1/2 of voting for the correct alternative. The probability that the correct alternative will win under majority voting converges to 1 as the number of...