For any generalized linear model, the Pearson goodness of fit statistic is the score test statistic for testing the current model against the saturated model. The relationship between the Pearson statistic and the residual deviance is therefore the relationship between the score test and the likelihood ratio test statistics, and this clarifies the role of the Pearson statistic in generalized li...

Let X be the unique solution started from x0 of the stochastic differential equation dXt = θ(t, Xt)dBt + b(t, Xt)dt with B a standard Brownian motion. We consider an approximation of the volatility θ(t, Xt), the drift being considered as a nuisance parameter. The approximation is based on a discrete time observation of X and we study its rate of convergence as a process. A goodness-of-fit test ...

The most frequency used goodness of fit tests are based on measuring the distance between the theoretical distribution function and the empirical distribution function (EDF), but presence of outliers influences these tests strongly. In this study, we propose a simple robust method for goodness of fit test by using the “Forward Search” (FS) method. The FS method is a powerful general method for ...

We consider spherical data Xi noised by a random rotation εi ∈ SO(3) so that only the sample Zi = εiXi, i = 1, . . . , N is observed. We define a nonparametric test procedure to distinguish H0 : ”the density f of Xi is the uniform density f0 on the sphere” and H1 : ”‖f − f0‖2 ≥ CψN and f is in a Sobolev space with smoothness s”. For a noise density fε with smoothness index ν, we show that an ad...

A modified version of the Kolmogorov-Smirnov (KS) test is presented as a tool to assess whether a specified, although arbitrary, probability model is unsuitable to describe the underlying distribution of a set of observations. The KS test computes distances between points of the sample cumulative distribution function and the hypothetical one as absolute differences between them, and then consi...

Coarse structural nested mean models are tools to estimate treatment effects from longitudinal observational data with time-dependent confounding. There is, however, no guidance on how to specify the treatment effect model, and model misspecification can lead to bias. We derive a goodness-of-fit test based on modified overidentification restrictions tests for evaluating a treatment effect model...

Existing goodness-of-fit tests for survival data are either exclusively graphical in nature or only test specific model assumptions, such as the proportional hazards assumption. We describe a flexible, parameter-free goodnessof-fit test that provides a simple numerical assessment of a model’s suitability regardless of the structure of the underlying model. Intuitively, the goodnessof-fit test u...

Testing the difference between two data samples is of a particular interest in statistics. being unknown continuous cumulative distribution functions, we wish to test the null hypothesis : :. In this talk, we propose an effective and convenient Bayesian nonparametric approach to assess the equality of two unknown distributions. The method is based on the Kolmogorov distance and approximate samp...

We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on discrete observation of the processes, and the diffusion coefficient is a nuisance function which is estimated in our testing procedure. We prove that the limit distribution of our test is the supremum of the standard Brownian motion, and thus our test is ...