The one-way Fubini property and conditional independence: An equivalence result

The One - way Fubini Property and Conditional Independence : An Equivalence Result

A general parameter process defined by a continuum of random variables is not jointly measurable with respect to the usual product σ-algebra. For the case of independent random variables, a one-way Fubini extension of the product space was constructed in [11] to satisfy a limited form of joint measurability. For the general case we show that this extension exists if and only if there is a count...

Joint Measurability and the One-way Fubini Property for a Continuum of Independent Random Variables

As is well known, a continuous parameter process with mutually independent random variables is not jointly measurable in the usual sense. This paper proposes an extension of the usual product measure-theoretic framework, using a natural “one-way Fubini” property. When the random variables are independent even in a very weak sense, this property guarantees joint measurability and defines a uniqu...

Independence , Monotonicity , and Latent Index Models : an Equivalence Result

A common problem in economics is to evaluate the effect of a treatment when individuals self-select whether to receive the treatment. This problem arises when trying to evaluate the union/nonunion wage differential, the effect of job training on earnings, and the returns to schooling, where being unionized or making a human capital investment is the treatment. One standard approach to this prob...

The Essential Equivalence of Pairwise and Mutual Conditional Independence∗

For a large collection of random variables, pairwise conditional independence and mutual conditional independence are shown to be essentially equivalent. Unlike in the finite setting, a large collection of random variables remains essentially conditionally independent under further conditioning. The essential equivalence of pairwise and multiple versions of exchangeability also follows as a cor...

The Conditional Independence Property in Filtrations Associated to Stopping Lines