We prove asymptotic normality of a suitably standardized integrated square difference between a kernel type error density estimator based on residuals and the expected value of the error density estimator based on innovations in GARCH models. This result is similar to that of Bickel-Rosenblatt under i.i.d. set up. Consequently the goodness-of-fit test for the innovation density of the GARCH pro...

We introduce a formal testing procedure to assess the goodness-of-fit of a fitted inhomogeneous spatial Poisson process model. Our method is based on a discrepancy measure function Dc(t; θ̂) that is constructed by using residuals obtained from the fitted model. We derive the asymptotic distributional properties of Dc(t; θ̂) and then develop a test statistic based on these properties. Our test sta...

For the heteroscedastic nonparametric regression model Yni = m(xni)+σ(xni)2ni, i = 1, ..., n, a novel method is proposed for testing that the regression function m is constant. The test statistic is motivated by recent developments in the asymptotic theory for analysis of variance when the number of factor levels is large. Its asymptotic normality is derived under the null hypothesis and suitab...

We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the false negative rate. These features are constructed via Stein’s method, meaning that it is not necessary to compute the normalising constant of the model. We a...

Objective: The purpose of this study is to propound the structural model of executive functions and extramarital relationship with the mediating role of marital commitment. Methods: The samples were selected by convenience sampling method. In experimental situation, for assessing the executive function of the participants did computerized exams, including Stroop test, Wisconsin test, Go-No-Go ...

The Inverse Gaussian (IG) distribution is commonly introduced to model and examine right skewed data having positive support. When applying the IG model, it is critical to develop efficient goodness-of-fit tests. In this article, we propose a new test statistic for examining the IG goodness-of-fit based on approximating parametric likelihood ratios. The parametric likelihood ratio methodology i...

This paper develops an approach to testing the adequacy of both classical and Bayesian models given sample data. An important feature of the approach is that we are able to test the practical scientiic hypothesis of whether the true underlying model is close to some hypothesized model. The notion of closeness is based on measurement precision and requires the introduction of a metric for which ...