A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context

On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints.

“…We have also discussed two methods of Monte Carlo simulation, namely, the simulation of parameter values (Dardanoni & Forcina, 1998) and the actual simulation of data. The former is simple to implement, but it is based on the assumption of multivariate normality of the parameter estimates.…”

“…Dardanoni andForcina (1998, p. 1117) proposed a procedure to obtain fairly accurate estimates by means of Monte Carlo simulation. Their procedure involves drawing a great number of parameter vectors from a multivariate normal distribution with mean equal to the hypothesized parameter values and covariance matrix equal to the information matrix under the null hypothesis.…”

“…In principle, however, Monte Carlo simulation of parameters as proposed by Dardanoni and Forcina (1998) could also be used. To obtain the weights using this procedure, the quasi-simplex model was fitted to the data, and the correlation matrix of parameters (i.e., the information matrix) was used to ϭ .05…”

Measuring Advances in Equality of Opportunity: The Changing Gender Gap in Educational Attainment in Canada in the Last Half Century

“…Firstly, table 2 examines whether through the 5 decades, children of each parental educational group were made unambiguously worse off or otherwise by employing stochastic dominance tests as prescribed by Linton et al (2005) and Dardanoni and Forcina (1998). With the exception of a few 70s versus 50s comparisons amongst parents with some college and technical education where no dominance relationship was registered, each parental educational group for each cohort stochastically dominated its preceding cohort unanimously, so improvements in educational outcomes were more or less ubiquitous as expected.…”

Bayesian nonparametric inference of stochastically ordered distributions, with Pólya trees and Bernstein polynomials

“…Such methods either involve maximizing the empirical likelihood subject to the stochastic order constraint (Brunk, Franck, Hanson, & Hogg, 1966;Robertson & Wright, 1974;Dykstra, 1982;Dykstra & Feltz, 1985;Lee, 1987;Dykstra and Feltz, 1989;El Barmi & Dykstra, 1994;Dykstra, Lee, & Yan, 1996;Dardanoni & Forcina, 1998;Ho¤, 2000), swapping values between pairs of empirical c.d.f.s that violate the stochastic order (Lo, 1987), or minimizing the squared distance to the K empirical cd.f.s subject to the stochastic order constraint (Gagnon and King, 2002). Most of the recent research has dealt with the estimation of the posterior distribution of F 1 ; :::; F K under the constraints of a stochastic order (Arjas & Gasbarra, 1994Evans, Gilula, Guttman, & Swartz, 1997;Ho¤, et al, 2001;Ho¤, 2003;Gelfand & Kottas, 2001), through the use of Dirichlet Process priors.…”