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In this paper, we study the entropy test for the goodness of fit test in (nonlinear) autoregressive conditional duration (ACD) models. To implement a test, we first explore the null limiting distribution of the residual empirical process from ACD models and verify that it has an asymptotic expansion form that consists of the true empirical process and extra terms yielded by parameter estimation. Then, we show that under regularity conditions, the proposed entropy test approximately follows a distribution that is free from the parameter estimation. For illustration, a simulation study and real data analysis are conducted. In the implementation of the test, a parametric bootstrap method is employed.

Markovian binary trees form a class of continuous-time branching processes where the lifetime and reproduction epochs of individuals are controlled by an underlying Markov process. An Expectation-Maximization (EM) algorithm is developed to estimate the parameters of the Markov process from the continuous observation of some populations, first with information about which individuals reproduce or die (the distinguishable case), and second without this information (the indistinguishable case). The performance of the EM algorithm is illustrated with some numerical examples. Fits resulting from the distinguishable case are shown not to be significantly better than fits resulting from the indistinguishable case using some goodness of fit measures.

The Generalised Normal Variance-Mean (GNVM) model in which the mixing random variable is Gamma distributed is considered. This model generalises the popular Variance-Gamma (VG) distribution. This GNVM model can be interpreted as the addition of noise to a (skew) VG base. The discussion is based on goodness of fit criteria and on parameter estimation. The conclusion is that the shape of the VG distribution can be adjusted in a favourable way by adding noise.

In this paper, we propose a goodness of fit test based on maximum entropy. As an extension of the result on the simple versus simple hypothesis case handled by Lee et al. (2011) , a composite hypothesis case is taken into consideration. To eliminate the parameter estimation effect, we apply the Khmaladze transformation for the empirical process and obtain the asymptotic distribution of the proposed test. The performance of the test is investigated through Monte Carlo simulations.

A new approach for fitting the exploratory factor analysis (EFA) model is considered. The EFA model is fitted directly to the data matrix by minimizing a weighted least squares (WLS) goodness-of-fit measure. The WLS fitting problem is solved by iteratively performing unweighted least squares fitting of the same model. A convergent reweighted least squares algorithm based on iterative majorization is developed. The influence of large residuals in the loss function is curbed using Huber's criterion. This procedure leads to robust EFA that can resist the effect of outliers in the data. Applications to real and simulated data illustrate the performance of the proposed approach.

This paper proposes a bootstrap goodness of fit test for the Generalized Pareto distribution (GPd) with shape parameter @c. The proposed test is an intersection-union test which tests separately the cases of @c>=0 and @c

This paper presents a two-step procedure using the method of moment or percentile to find initial values and then maximize the numerical log likelihood to fit the appropriate generalized lambda distribution to data. This paper demonstrates the use of this procedure to fit well-known statistical distributions as well as some empirical data. Overall, the use of numerical maximum log likelihood estimation is a valuable alternative among existing methods of fitting. It provides not only convincing results in terms of quantile plots and goodness of fit tests but also has the advantage of a lower variability in its parameter estimation compared to the existing starship (King and MacGillivray, 1999) and method of moment (Karian and Dudewicz, 2000) fitting schemes.

Some of the most powerful techniques currently available to test the goodness of fit of a hypothesized continuous cumulative distribution function (CDF) use statistics based on the empirical distribution function (EDF), such as those of Kolmogorov, Cramer-von Mises and Anderson-Darling, among others. The use of EDF statistics was analyzed for estimation purposes. In this approach, maximum goodness-of-fit estimators (also called minimum distance estimators) of the parameters of the CDF can be obtained by minimizing any of the EDF statistics with respect to the unknown parameters. The results showed that there is no unique EDF statistic that can be considered most efficient for all situations. Consequently, the possibility of defining new EDF statistics is entertained; in particular, an Anderson-Darling statistic of degree two and one-sided Anderson-Darling statistics of degree one and two appear to be notable in some situations. The procedure is shown to be able to deal successfully with the estimation of the parameters of homogeneous and heterogeneous generalized Pareto distributions, even when maximum likelihood and other estimation methods fail.

A mixture model for preferences data, which adequately represents the composite nature of the elicitation mechanism in ranking processes, is proposed. Both probabilistic features of the mixture distribution and inferential and computational issues arising from the maximum likelihood parameters estimation are addressed. Moreover, empirical evidence from different data sets confirming the goodness of fit of the proposed model to many real preferences data is shown. © 2004 Elsevier B.V. All rights reserved.

The present paper deals with main-effects models for the analysis of two-way two-mode frequency data that are obtained by summing replicated binary associations over replications. Main-effects generalized linear models (GLM) which explain the transformed expected frequencies as an additive function of row- and column parameters, include many models that only differ in the particular transformation—called link function—that is applied. In this paper, besides the standard logit link, we also consider a log-, a complementary log-, and an identity link as models with these link functions are equivalent to one-feature probability matrix decomposition models (PMD). Reparameterizing main-effects GLMs into one-feature PMD models yields two advantages: First, it offers a process interpretation for the way the observed data are generated; in particular, in PMD models it is assumed that covert events with binary outcomes take place on both the row- and the column side and that these outcomes are subsequently mapped into an observed data point according to a prespecified mapping rule which may reflect a communality or a dominance relation. Second, it may facilitate parameter estimation of these models as for the original parameterization maximum likelihood estimates in the interior of the parameter space may not exist. Methods to evaluate the goodness of fit of the models under study are discussed and the models are applied to data on psychiatric diagnosis and on educational measurement.

A specific scale must be used to collect data in an experiment, but this scale may or may not be the appropriate scale to analyze the data thus collected. In this paper, we study a family of three-parameter distributions which includes the log-normal distribution as a special case, and one of the parameters plays the role of choosing a suitable scale for subsequent analysis. Some basic properties and maximum likelihood estimation of the unknown parameters are discussed, and an easy-to-use goodness-of-fit test is developed. A real data set, to which the usual Weibull, log-normal and gamma distributions cannot be fitted, is used to demonstrate the potential applicability of this family of distributions.