This paper considers an extension of the linear non-Gaussian acyclic model (LiNGAM) that determines causal order among variables from a dataset when are expressed by set equations, including noise. In particular, we assume binary. The existing LiNGAM assumes no confounding is present, which restrictive in practice. Based on concept independent component analysis (ICA), this proposes extended fr...

A random variable Y is called an independent symmetrizer of a given random variable X if (a) it is independent of X and (b) the distribution of X + Y is symmetric about 0. In cases where the distribution of X is symmetric about its mean, it is easy to see that the constant random variable Y = EX is a minimum-variance independent symmetrizer. Taking Y to have the same distribution as X clearly p...

Finite-sample properties of non-parametric regression for binary dependent variables are analyzed. Non parametric regression is generally considered as highly variable in small samples when the number of regressors is large. In binary choice models, however, it may be more reliable since its variance is bounded. The precision in estimating conditional means as well as marginal effects is invest...