Family-based case-control studies are popularly used to study the effect of genes and gene-environment interactions in the etiology of rare complex diseases. We consider methods for the analysis of such studies under the assumption that genetic susceptibility (G) and environmental exposures (E) are independently distributed of each other within families in the source population. Conditional log...

We propose a parsimonious extension of the classical latent class model to cluster categorical data by relaxing the conditional independence assumption. Under this new mixture model, named Conditional Modes Model (CMM), variables are grouped into conditionally independent blocks. Each block follows a parsimonious multinomial distribution where the few free parameters model the probabilities of ...

In chance-constrained optimization problems, a solution is assumed to be feasible only with certain, sufficiently high probability. For computational and theoretical purposes, the convexity property of the resulting constraint set is treated. It is known, for example, that a suitable combination of a concavity property of the probability distribution and concavity of constraint mappings are suf...

Our proof of [1, Theorem 1.1] is partially incorrect. The reason that, contrary to what we claimed, the construction space $${\mathscr {H}}^s$$ depends on orthonormal basis $$(\rho _k)$$ . We give in present note a new that needs little bit stronger assumption.

The conditional independence assumption is commonly used in multivariate mixture models in behavioral research. This assumption postulates the independence of the repeated measurements within an observation, given the status of the observation’s component membership. In this paper, the component distributions in a multivariate mixture model are fitted using an exponential tilt model, in which t...

In the standard stochastic frontier model, the two-sided error term V and the one-sided technical inefficiency error term W are assumed to be independent. In this paper, we relax this assumption by modeling the dependence between V and W using copulas. Nine copula families are considered and their parameters are estimated using maximum simulated likelihood. The best model is then selected using...

Identification and Estimation of Causal Effects of Multiple Treatments Under the Conditional Independence Assumption The assumption that the assignment to treatments is ignorable conditional on attributes plays an important role in the applied statistic and econometric evaluation literature. Another term for it is conditional independence assumption. This paper discusses identification when the...