Fitting and Interpreting Correlated Random-coefficient Models Using Stata

In this article, we introduce the community-contributed command randcoef, which fits the correlated random-effects and correlated random-coefficient models discussed in Suri (2011, Econometrica 79: 159–209). While this approach has been around for a decade, its use has been limited by the computationally intensive nature of the estimation procedure that relies on the optimal minimum distance estimator. randcoef can accommodate up to five rounds of panel data and offers several options, including alternative weight matrices for estimation and inclusion of additional endogenous regressors. We also present postestimation analysis using sample data to facilitate understanding and interpretation of results.

Asymptotic Distribution of Cramer-von Mises Statistic When Contamination Exists

In this paper, asymptotic distribution of Cram\'er-von Mises goodness-of-fit test statistic is investigated when contamination exists.<br />We first derive the asymptotic distribution of the Cram\'er-von Mises statistic when the observations are contaminated with noise as a mixture.<br />The result is extended to the case where the parameters are estimated by the minimum distance estimator,<br />which minimizes the Cram\'er-von Mises statistic.<br />In both cases the asymptotic distribution of the Cram\'er-von Mises statistic is given by that of the weighted infinite sum of non-central $\chi^2_1$ variables and the effect of contamination appears only in the non-centrality of the variables.<br />We also demonstrate the robustness of the goodness-of-fit test by Monte Carlo simulations when the parameters are estimated<br />by the minimum distance estimator and the maximum likelihood estimator.<br />Numerical experiments indicate that the use of the minimum distance estimator makes the test insensitive to contamination whereas the power is retained almost the same as that of the maximum likelihood estimator.

Parameter Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion

We study the asymptotic properties of minimum distance estimator of drift parameter for a class of nonlinear scalar stochastic differential equations driven by mixed fractional Brownian motion. The consistency and limit distribution of this estimator are established as the diffusion coefficient tends to zero under some regularity conditions.