Introduction. The goodness of t tests of the empirical data to one theoretical distribution, and particularly the χ of Pearson, are very used in practice, also as preliminary step for the use of methods of parametric inference which are consistent with precise models of distribution. Gasser [10] explored the χ test for correlated data by simulations and, subsequently, Moore [14] and Gleser and ...

“Chi-squared tests” refers to a family of statistical test whose large-sample asymptotics are related in one way or another to the χ family of distributions. These are our first examples of “non-parametric procedures.” Let me mention one particularly useful chi-squared test here before we get started properly. Consider a population whose distribution is believed to follow a known density functi...

Scientists often use the Chi-square (χ) test to determine the “goodness of fit” between theoretical and experimental data. In this test, we compare observed values with theoretical or expected values. Observed values are those that the researcher obtains empirically through direct observation. The theoretical or expected values are developed on the basis of an established theory or a working hy...

We consider the problem of fitting a parametric model to an astronomical dataset. This occurs when fitting simple heuristic models (e.g. powerlaw relation in a bivariate scatter diagram) or complex astrophysical models (e.g. thermal plasma model of an X-ray spectrum). After regression procedures have found the ‘best’ fit, the chi-squared (χ2) or Kolmogorov-Smirnov (K-S) statistics are often use...

The paper discusses tests for the correct speci…cation of a model when data is observed in a d-dimensional lattice, extending previous work when the data is collected in the real line. As it happens with the latter type of data, the asymptotic distribution of the tests are functionals of a Gaussian sheet process, say B ( ), 2 [0; ]. Because it is not easy to …nd a time transformation h ( ) such...