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The Cox hazards model ( Cox, 1972 , Journal of the Royal Statistical Society, Series B 34, 187–220) for survival data is routinely used in many applied fields, sometimes, however, with too little emphasis on the fit of the model. A useful alternative to the Cox model is the Aalen additive hazards model ( Aalen, 1980 , in Lecture Notes in Statistics-2, 1–25) that can easily accommodate time changing covariate effects. It is of interest to decide which of the two models that are most appropriate to apply in a given application. This is a nontrivial problem as these two classes of models are nonnested except only for special cases. In this article we explore the Mizon–Richard encompassing test for this particular problem. It turns out that it corresponds to fitting of the Aalen model to the martingale residuals obtained from the Cox regression analysis. We also consider a variant of this method, which relates to the proportional excess model ( Martinussen and Scheike, 2002 , Biometrika 89, 283–298). Large sample properties of the suggested methods under the two rival models are derived. The finite-sample properties of the proposed procedures are assessed through a simulation study. The methods are further applied to the well-known primary biliary cirrhosis data set. [ABSTRACT FROM AUTHOR]

In this article we consider the problem of fitting a five-parameter generalization of the lambda distribution to data given in the form of a grouped frequency table. The estimation of parameters is done by six different procedures: percentiles, moments, probability-weighted moments, minimum Cramér-Von Mises, maximum likelihood, and pseudo least squares. These methods are evaluated and compared using a Monte Carlo study where the parent populations were generalized lambda distribution (GLD) approximations of Normal, Beta, Gamma random variables, and for nine combinations of sample sizes and number of classes. Of the estimators analyzed it is concluded that, although the method of pseudo least squares suffers from a number of limitations, it appears to be the candidate procedure to estimate the parameters of a GLD from grouped data. [ABSTRACT FROM AUTHOR]

A power study suggests that a good test of fit analysis for the Poisson distribution is provided by a data dependent Chernoff-Lehmann X2 test with class expectations greater than unity, and its components. These data dependent statistics involve arithmetically simple parameter estimation, convenient approximate distributions, and provide a comprehensive assessment of how well the data agree with a Poisson distribution. We suggest that a well-performed single test of fit statistic is the Anderson-Darling statistic. Three examples are discussed. [ABSTRACT FROM AUTHOR]

Latent regression models are powerful tools for studying the relation between a latent outcome variable and observed covariates. In this paper goodness of fit tests for latent regression models based on loglinear Rasch models are proposed. The properties of the tests are discussed using a simulation. [ABSTRACT FROM AUTHOR]

Multinomial tests for the fit of iid observations X[sub l], ...., X[sub n] to a specified distribution F are based on the counts N[sub l] of observations falling in k cells E[sub l], . . . , E[sub k], that partition the range of the X[sub j]. The earliest such test is based on the Pearson (1900) chi-squared statistic: chi[sup 2]: SIGMA[sup k, sub l=1] (N[sub 1] - np[sub 1])[sup 2]/np[sub l], where p[sub l] = P[sub F](X[sub j] in E[sub l]) are the cell probabilities under the null hypothesis. A common competing test is the likelihood ratio test based on LR = 2 SIGMA[sup k, sub l = 1] N[sub l]log(N[sub l]/np[sub l]). Cressie and Read (1984) introduced a class of multinomial goodness-of-fit statistics, R[sup lambda], based on measures of the divergence between discrete distributions. This class includes both chi[sup 2] (when lambda = 1) and LR (when lambda = 0). All of the R[sup lambda] have the same chi-squared limiting null distribution. The power of the commonly used members of the class is usually approximated from a noncentral chi-squared distribution that is also the same for all lambda. We propose new approximations to the power that vary with the statistic chosen. Both the computation and results on asymptotic error rates suggest that the new approximations are greatly superior to the traditional power approximation for statistics R' other than the Pearson chi[sup 2]. The derivation of the limiting null distribution for the Cressie-Read statistics, following that for LR, is based on a Taylor series expansion of R', in which chi[sup 2] is the dominant term. The same expansion produces the traditional noncentral chi-squared power approximation by considering sequences of alternative distributions for the X[sub j] that approach the hypothesis F at a suitable rate. Our power approximations are obtained from a Taylor series expansion that is valid for arbitrary sequences of... [ABSTRACT FROM AUTHOR]