We present a systematic examination of real network datasets using maximum likelihood estimation for exponential random graph models as well as new procedures to evaluate how well the models fit the observed graphs. These procedures compare structural statistics of the observed graph with the corresponding statistics on graphs simulated from the fitted model. We apply this approach to the study...

Mixed models, with both random and fixed effects, are most often estimated on the assumption that the random effects are normally distributed. In this paper we propose several formal tests of the hypothesis that the random effects and/or errors are normally distributed. Most of the proposed methods can be extended to generalized linear models where tests for non-normal distributions are of inte...

By Leah Jager∗ and Jon A. Wellner† Grinnell College and University of Washington A unified family of goodness-of-fit tests based on φ−divergences is introduced and studied. The new family of test statistics Sn(s) includes both the supremum version of the Anderson-Darling statistic and the test statistic of Berk and Jones (1979) as special cases (s = 2 and s = 1 respectively). We also introduce ...

Meta-analysis is a very useful tool to combine information from different sources. Fixed effect and random effect models are widely used in meta-analysis. Despite their popularity, they may give us misleading results if the models don't fit the data but are blindly used. Therefore, like any statistical analysis, checking the model fitting is an important step. However, in practice, the goodness...

The definition of an appropriate measure for goodness-of-fit in case of survival data comparable to R in linear regression is difficult due to censored observations. In this paper, a variety of answers based on different residuals and variance of survival curves are presented together with a newly introduced criterion. In univariate simulation studies, the presented criteria are examined with r...

In this article, we develop a test for the null hypothesis that a real-valued function belongs to a given parametric set against the non-parametric alternative that it is monotone, say decreasing. The method is described in a general model that covers the monotone density model, the monotone regression and the right-censoring model with monotone hazard rate. The criterion for testing is an L p-...

An axiomatic approach is used to develop a one-parameter family of measures of divergence between distributions. These measures can be used to perform goodness-of-fit tests with good statistical properties. Asymptotic theory shows that the test statistics have well-defined limiting distributions which are however analytically intractable. A parametric bootstrap procedure is proposed for impleme...

In this talk we shall discuss the problem of fitting a distribution function to the marginal distribution of a long memory process. It is observed that unlike in the i.i.d. set up, classical tests based on empirical process are relatively easy to implement. More importantly, we discuss fitting the marginal distribution of the error process in location, scale and linear regression models. An int...

Conventional econometric tests of optimizing models typically involve embedding the optimizing model in a parametric specification and then examining the parametric restrictions imposed by the optimization hypothesis, The optimization hypothesis is rejected if the estimated parameters are significantly different, in the statistical sense, from the values implied by optimization. I argue that a ...

We survey in some detail the rather small literature on Bayes nonparametric Testing. We mostly concentrate on Bayesian testing of goodness of fit to a parametric null with nonparametric alternatives. We also survey briefly some related unpublished material. We discuss both methodology and posterior consistency.