123,594 research outputs found
Spectral goodness of fit for network models
We introduce a new statistic, 'spectral goodness of fit' (SGOF) to measure
how well a network model explains the structure of an observed network. SGOF
provides an absolute measure of fit, analogous to the standard R-squared in
linear regression. Additionally, as it takes advantage of the properties of the
spectrum of the graph Laplacian, it is suitable for comparing network models of
diverse functional forms, including both fitted statistical models and
algorithmic generative models of networks. After introducing, defining, and
providing guidance for interpreting SGOF, we illustrate the properties of the
statistic with a number of examples and comparisons to existing techniques. We
show that such a spectral approach to assessing model fit fills gaps left by
earlier methods and can be widely applied
Data-driven smooth tests when the hypothesis Is composite
In recent years several authors have recommended smooth tests for testing goodness of fit. However, the number of components in the smooth test statistic should be chosen well; otherwise, considerable loss of power may occur. Schwarz's selection rule provides one such good choice. Earlier results on simple null hypotheses are extended here to composite hypotheses, which tend to be of more practical interest. For general composite hypotheses, consistency of the data-driven smooth tests holds at essentially any alternative. Monte Carlo experiments on testing exponentiality and normality show that the data-driven version of Neyman's test compares well to other, even specialized, tests over a wide range of alternatives
An overview of the goodness-of-fit test problem for copulas
We review the main "omnibus procedures" for goodness-of-fit testing for
copulas: tests based on the empirical copula process, on probability integral
transformations, on Kendall's dependence function, etc, and some corresponding
reductions of dimension techniques. The problems of finding asymptotic
distribution-free test statistics and the calculation of reliable p-values are
discussed. Some particular cases, like convenient tests for time-dependent
copulas, for Archimedean or extreme-value copulas, etc, are dealt with.
Finally, the practical performances of the proposed approaches are briefly
summarized
Goodness-of-fit testing based on a weighted bootstrap: A fast large-sample alternative to the parametric bootstrap
The process comparing the empirical cumulative distribution function of the
sample with a parametric estimate of the cumulative distribution function is
known as the empirical process with estimated parameters and has been
extensively employed in the literature for goodness-of-fit testing. The
simplest way to carry out such goodness-of-fit tests, especially in a
multivariate setting, is to use a parametric bootstrap. Although very easy to
implement, the parametric bootstrap can become very computationally expensive
as the sample size, the number of parameters, or the dimension of the data
increase. An alternative resampling technique based on a fast weighted
bootstrap is proposed in this paper, and is studied both theoretically and
empirically. The outcome of this work is a generic and computationally
efficient multiplier goodness-of-fit procedure that can be used as a
large-sample alternative to the parametric bootstrap. In order to approximately
determine how large the sample size needs to be for the parametric and weighted
bootstraps to have roughly equivalent powers, extensive Monte Carlo experiments
are carried out in dimension one, two and three, and for models containing up
to nine parameters. The computational gains resulting from the use of the
proposed multiplier goodness-of-fit procedure are illustrated on trivariate
financial data. A by-product of this work is a fast large-sample
goodness-of-fit procedure for the bivariate and trivariate t distribution whose
degrees of freedom are fixed.Comment: 26 pages, 5 tables, 1 figur
Karhunen-loève basis in goodness-of-fit tests decomposition: an evaluation
In a previous paper (Grané and Fortiana 2006) we studied a flexible class of goodness-of-fit tests associated with an orthogonal sequence, the Karhunen-Loève decomposition of a stochastic process derived from the null hypothesis. Generally speaking, these tests outperform Kolmogorov-Smirnov and Cramér-von Mises, but we registered several exceptions. In this work we investigate the cause of these anomalies and, more precisely, whether and when such poor behaviour may be attributed to the orthogonal sequence itself, by replacing it with the Legendre polynomials, a commonly used basis for smooth tests. We find an easily computable formula for the Bahadur asymptotic relative efficiency, a helpful quantity in choosing an adequate basis
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