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We propose three new classes of goodness-of-fit tests for the Pareto type I distribution based on a characterization. The asymptotic null distribution for the tests are derived and their Bahadur efficiencies are compared to the efficiencies of some of the existing tests. It is found that the new integral type test has superior local efficiencies amongst the new tests, and in general, has higher efficiencies than the competing tests considered. The finite-sample performance of the newly proposed tests is evaluated and compared to that of other existing tests by means of a Monte Carlo study. It is found that the new tests (especially the integral type tests) perform favourably compared to the other tests.

We derive the efficiencies of two new tests for exponentiality which are based on a recent characterization that uses the idea of a random shift. The finite-sample performance of the newly proposed tests is evaluated and compared to other existing tests by means of Monte Carlo simulations. It is found that the new tests perform favourably when compared to the other tests. Overall the best performing tests seem to be our new Kolmogorov-Smirnov type test, the score function based test by Cox and Oakes, and the Kolmogorov-Smirnov type test based on the mean residual life. The tests are also applied to a real-world data set with i.i.d. data as well as to simulated data from a Cox-proportional hazards model, where we test whether the so-called Cox–Snell residuals follow a standard exponential distribution

The exponential distribution plays a key role in the practical application of reliability theory, survival analysis, engineering and queuing theory. These applications often rely on the underlying assumption that the observed data originate from an exponential distribution. In this paper, two new tests for exponentiality are proposed, which are based on a conditional second moment characterisation. The proposed tests are compared to various established tests for exponentiality by means of a simulation study where it is found that the new tests perform favourably relative to the existing tests. The tests are also applied to real-world data sets with independent and identically distributed data as well as to simulated data from a Cox proportional hazards model, to determine whether the residuals obtained from the fitted model follow a standard exponential distribution.

We consider a variety of tests for testing goodness-of-fit in a parametric Cox proportional hazards (PH) model and compare their performance. Aspects of the model under test include the baseline distribution and time-invariance of covariates. We also test for the PH model itself against a certain generalization. This is done through an extensive Monte Carlo study where we simulate the performance of the tests for these three paired hypotheses. The results show that the tests based on the empirical characteristic function and those based on the empirical Laplace transform have the best overall power performance. It is also found that the distributions of the considered test statistics do not depend on the specific functional form of the covariate function

Survival analysis has become a popular technique to more accurately model the probability of default in the credit risk environment with the ultimate goal of finding the optimal price for credit. In this paper we present an overview of some of the basic concepts of survival analysis. The focus is specifically on the Cox Proportional Hazards (CPH) model and the mixture cure model, which is a general alternative to the CPH model. A detailed algorithm that can be used to simulate survival times (default times) from a mixture cure model is provided. A parametric CPH and mixture cure model are fitted to a simulated data set and the benefits of fitting the latter model are illustrated.

Quasi-stationary distributions have many applications in diverse research fields. We develop a bootstrap-based maximum likelihood (BML) method to deal with quasi-stationary distributions in statist...

We consider a semiparametric model whereby the response variable following a transformation can be expressed by means of a regression model. In this model, the form of the transformation is specified analytically (up to an unknown transformation parameter), while the regression function is completely unknown. We develop testing procedures for the null hypothesis that this semiparametric model adequately describes the data at hand. In doing so, the test statistic is formulated on the basis of Fourier-type conditional expectations, an idea first put forward by Bierens (J Econom 20:105–134, 1982). The asymptotic distribution of the test statistic is obtained under the null as well as under alternative hypotheses. Since the limit null distribution is nonstandard, a bootstrap version is utilized in order to actually carry out the test procedure. Monte Carlo results are included that illustrate the finite-sample properties of the new method.

We propose two new tests for symmetry based on well-known characterisations of symmetric distributions. The performance of the new tests is evaluated and compared to that of other existing tests by means of a Monte Carlo study. All tests are carried out in a regression setup where we test whether the error distribution in a linear regression model is symmetric. It is found that the newly proposed tests perform favourably compared to the other tests.

The exponential distribution is one of the most popular choices of model, especially in survival analysis and reliability theory. Typically, to test the hypothesis that the underlying distribution of lifetimes are exponentially distributed based on censored data, the standard goodness‐of‐fit tests used in the complete sample case are modified. However, none of the characteristic or Laplace function based tests have been adapted to incorporate censored data. In this paper, we modify three well‐known tests for exponentiality on the basis of either the characteristic function or Laplace transform to accommodate Type II right censored data. We compare the power of the three newly changed tests to some existing modified tests in an independent identically distributed (i.i.d.) and a model‐based setup through a Monte Carlo study, where it was found that the newly adjusted Baringhaus and Henze test outperformed all other tests considered

International audience; We propose and study new goodness-of-fit tests for the Rayleigh distribution based on a characterization involving a conditional expectation. The asymptotic properties of the tests are explored and the performance of the new tests are evaluated and compared to that of existing tests by means of a Monte Carlo study. It is found that the newly proposed tests perform satisfactory compared to the competitor tests.

International audience; We consider tests for serial independence of arbitrary finite order for the innovations in vector autoregressive models. The tests are expressed as L2-type criteria involving the difference of the joint empirical characteristic function and the product of corresponding marginals. Asymptotic as well as Monte-Carlo results are presented.

Fourier methods are proposed for testing the distribution of random effects in classical and robust multivariate mixed effects models. The test statistics involve estimation of the characteristic function of random effects. Theoretical and computational issues are addressed while Monte Carlo results show that the new procedures compare favorably with other methods.

We propose a data-dependent method for choosing the tuning parameter appearing in many recently developed goodness-of-fit test statistics. The new method, based on the bootstrap, is applicable to a class of distributions for which the null distribution of the test statistic is independent of unknown parameters. No data-dependent choice for this parameter exists in the literature; typically, a fixed value for the parameter is chosen which can perform well for some alternatives, but poorly for others. The performance of the new method is investigated by means of a Monte Carlo study, employing three tests for exponentiality. It is found that the Monte Carlo power of these tests, using the data-dependent choice, compares favourably to the maximum achievable power for the tests calculated over a grid of values of the tuning parameter.

We introduce the notion of the probability weighted characteristic function (PWCF) as a generalization of the characteristic function. Some of the properties of the PWCF and of its empirical counterpart are studied and the potential use of these quantities in goodness-of-fit testing is examined in detail. The corresponding limiting null distributions and consistency results for location-scale models are derived and finite-sample comparisons are presented. Also, the notion of the PWCF is extended to arbitrary dimension Research Grant 11699 of the Special Account for Research Grants of the National and Kapodistrian University of Athens. National Research Foundation of South Africa

We derive the joint distribution of the ranks associated with a given bivariate random sample. Using these results, exact non-asymptotic expressions and asymptotic expansions for the mean and variance of the classical empirical copula estimator are obtained. An explicit expression of the coefficient appearing in the O ( 1 / n ) -term for the mean can, for example, be found; a result that apparently does not appear in the existing literature. Furthermore, it is shown that similar explicit non-asymptotic expressions as well as asymptotic expansions can be derived for the rank-based Bernstein copula estimator.

The traditional non-parametric bootstrap (referred to as the n-out-of-n bootstrap) is a widely applicable and powerful tool for statistical inference, but in important situations it can fail. It is well known that by using a bootstrap sample of size m, different from n, the resulting m-out-of-n bootstrap provides a method for rectifying the traditional bootstrap inconsistency. Moreover, recent studies have shown that interesting cases exist where it is better to use the m-out-of-n bootstrap in spite of the fact that the n-out-of-n bootstrap works. In this paper, we discuss another case by considering its application to hypothesis testing. Two new data-based choices of m are proposed in this set-up. The results of simulation studies are presented to provide empirical comparisons between the performance of the traditional bootstrap and the m-out-of-n bootstrap, based on the two data-dependent choices of m, as well as on an existing method in the literature for choosing m. These results show that the m-out-o...

Metabolomics data are typically complex and high dimensional. Multivariate dimension-reducing techniques have thus been developed for analysing metabolomics data to disclose underlying relationships, with principal component analysis (PCA) as the technique mostly applied. Despite its widespread use in metabolomics, PCA has shortcomings that limit its applicability. Several approaches have been made to overcome these limitations and we describe an advanced disjoint PCA (DPCA) model, termed concurrent class analysis and abbreviated as CONCA. CONCA is a new model, and is unique in linking DPCA models to a traditional PCA model. This is accomplished by restructuring the input data matrix, applying DPCA group models to the restructured data, and combining the DPCA models in order to replicate a traditional PCA. We applied the CONCA model to a metabolomics data set on isovaleric acidaemia (IVA), a rare inherited metabolic disorder. The outcome showed that three of the variables with high discrimination value identified through the CONCA analysis are prominent organic acid biomarkers for IVA. Moreover, three further minor metabolites associated with the disease, and two as a consequence of treatment, were likewise identified as important discriminatory variables. The benefit of the CONCA model thus is its ability to disclose information concerning each individual group and to identify the variables important in discrimination (VIDs) which are also responsible for group separation. http://dx.doi.org/10.1007/s11306-011-0327-y From the issue entitled "Special Issue: Data Analysis Methods for Metabolomics"

We investigate the finite-sample properties of certain procedures which employ the novel notion of the probability weighted empirical characteristic function. The procedures considered are: (1) Testing for symmetry in regression, (2) Testing for multivariate normality with independent observations, and (3) Testing for multivariate normality of random effects in mixed models. Along with the new tests alternative methods based on the ordinary empirical characteristic function as well as other more well known procedures are implemented for the purpose of comparison.

Background: Artificial neural network modeling of stress single photon emission computed tomography (SPECT) imaging has been shown to be useful in the detection of extensive coronary artery disease (CAD). We tested the hypothesis that ANN modeling can be used to detect extensive CAD in patients with and without diabetes. Methods: 109 patients (38 diabetic patients) with both stress SPECT and coronary angiography were studied. One model was trained for each vessel. The stress images were reduced to 25 points by pixel averaging of the polar map. The model output was 1 for vessel stenosis greater than 60% and 0 otherwise. Results: For patients with diabetes, model sensitivities were 96% (24/25) for Left Anterior Descending (LAD) vs. 68% for visual interpretation (p=0.01); 63% (10/16) for Left Circumflex (LCX) vs. 50% for visual interpretation (p=0.50); 100% (16/16) for the Right Coronary Artery (RCA) vs. 88% for visual interpretation (p=0.24). For patients without diabetes, model sensitivities were 89% (31/35) for LAD vs. 57% for visual interpretation (p=0.004); 77% (10/13) for LCX vs. 62% for visual interpretation (p=0.43); 91% (29/32) for the RCA vs. 72% for visual interpretation (p=0.06). In patients with and without diabetes, two- and three-vessel CAD was correctly predicted in 30/46 patients (65%) by modeling vs. 16/46 patients (35%) by visual interpretation (p=0.004). Comparing the patients with diabetes to the patients without diabetes, no significant difference existed in the detection of single-vessel and multi-vessel disease for both the model results and for visual interpretation. Conclusions: Artificial neural network modeling of stress SPECT imaging can be used to detect extensive CAD in diabetic as well as non-diabetic patients. These models, given their high sensitivity and specificity in detecting extensive CAD, have great promise as an aid in correctly identifying high-risk CAD patients.

This note analyses the problem of stability of hybrid simulation of dynamic systems. Time delays and sample-and-hold operations do cause serious stability problems, and if frequently happens that considerable time and effort are wasted because instability is not known in advance of programming the simulation on the hybrid computer. However, if the system under investigation can be approximated in its response by an equivalent linear system, then it is possible to define a procedure which will predict in advance whether any proposed computing scheme is stable. The text describes one such procedure, together with its implementation as a software package which can be used to predict the stability of simulations of practical size. In addition, the text contains a number of examples which illustrate the application of the software package.