Testing Lattice Conditional Independence Models

Lattice Models for Conditional Independence in a Multivariate Normal Distribution

Unbiasedness of the Likelihood Ratio Testfor Lattice Conditional Independence Models

The lattice conditional independence (LCI) model N(C)<) is defined to be the set of all normal distributions N(O, E) on IR I such that for every pair L, M E 1<, XL and xM are conditionally independent given xLnM (ct , [AP] (1993a)). Here C)< is a ring of subsets (hence a distributive lattice) of the finite index set I such that 0, IE ".K, while for K E 1<, XK is the coordinate projection of x E...

Normal Linear Models with Lattice Conditional Independence Restrictions

Michael D. Perlman-It is shown that each multivariate normal model determined by lattice conditional independence (LeI) restrictions on the covariances may be extended in a, natural way to a normal linear model with corresponding lattice restrictions on the means. For these extended models it remains true that the likelihood function (LF) and parameter space (PS) can be factored into the produc...

Testing Conditional Independence using Conditional Martingale Transforms

This paper investigates testing conditional independence between Y and Z given λθ(X) for some θ ∈ Θ ⊂ R, for a function λθ(·) known upto a parameter θ ∈ Θ. First, the paper proposes a new method of conditional martingale transforms under which tests are asymptotically pivotal and asymptotically unbiased against √ n-converging Pitman local alternatives. Second, the paper performs an analysis of ...

Nonparametric testing of conditional independence

Conditional independence of Y and Z given X holds if and only if the following two conditions hold: • CI1: The expected conditional covariance between arbitrary functions of Y and Z given X is zero (where the expectation is taken with respect to X). • CI2: The conditional covariance between arbitrary functions of Y and Z given X does not depend on X. Based on this decomposition, we propose a si...