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Nonparametric moment-based goodness-of-fit tests are developed for the family of chi-square copulas of arbitrary dimensions. This class of dependence models allows for tail asymmetries and contains the family of multivariate normal copulas as a special case. The proposed tests are based on two rank correlation coefficients whose population versions are equal, up to a monotone transformation, when the underlying dependence structure is a chi-square copula. The test statistics are computed from natural rank-based estimations of these two correlation coefficients and their large-sample distributions under the null hypothesis of a chi-square copula are derived; the validity of a parametric bootstrap procedure for the computation of p-values is formally established as well. Particular attention is given to tests for the families of normal and centered chi-square copulas. The simulations that are reported indicate that the new tests are reliable alternatives to those based on the empirical copula, both in the bivariate and multivariate cases. The usefulness of the introduced methodology is illustrated on the five-dimensional Nutrient dataset.

This research provides a projection-based test to check parametric single-index regression structure in variable-adjusted models. An adaptive-to-model strategy is employed, which makes the proposed test work better on the significance level maintenance and more powerful than existing tests. With mild conditions, the proposed test asymptotically behaves like a test that is for classical regression setup without distortion errors in observations. Numerical studies with simulated and real data are conducted to examine the performance of the test in finite sample scenarios.

Analyzing correlated data by goodness-of-fit type tests is a critical statistical problem in many applications. A unified framework is provided through a general family of goodness-of-fit tests (GGOF) to address this problem. The GGOF family covers many classic and newly developed tests, such as the minimal p-value test, Simes test, the GATES, one-sided Kolmogorov-Smirnov type tests, one-sided phi-divergence tests, the generalized Higher Criticism, the generalized Berk-Jones, etc. It is shown that the omnibus test that automatically adapts among GGOF statistics for given data, i.e., the GGOF-O, is still contained in the GGOF family and is computationally efficient. For analytically controlling the type I error rate of any GGOF tests, exact calculation is deduced under the Gaussian model with positive equal correlations. Based on that, the effective correlation coefficient (ECC) algorithm is proposed to address arbitrary correlations. Simulations are used to explore how signal and correlation patterns jointly influence typical GGOF tests' statistical power. The GGOF-O is shown robustly powerful across various signal and correlation patterns. As demonstrated by a study of bone mineral density, the GGOF framework has good potential for detecting novel disease genes in genetic summary data analysis. Computational tools are available in the R package SetTest on the CRAN.

A projection-averaging-based cumulative divergence to characterize the conditional mean independence is proposed. As a natural extension of Zhou et al. (2020) , the new metric has several appealing features. It ranges from zero to one, and equals zero if and only if the conditional mean independence holds. It has an elegant closed-form expression that involves no tuning parameters, making it easy to implement. The sample estimator of new metric is n-consistent under the conditional mean independence and root-n-consistent otherwise. A goodness-of-fit test for single-index models based on the variant of the proposed metric is further introduced, which generalizes the projected-based test of Escanciano (2006) to a semiparametric regression setting that allows an unspecified link function. The proposed test is consistent against any global alternatives and can detect the local alternatives distinct from the null at the parametric rate of O ( n − 1 / 2 ) . The effectiveness of our proposals is demonstrated through simulation examples and a real application.

The development of nonparametric procedures for testing shape constraint (monotonicity, convexity, unimodality, etc.) has received increasing interest. Nevertheless, testing the k -monotonicity of a discrete density for k larger than 2 has received little attention. To deal with this issue, several testing procedures based on the empirical distribution of the observations have been developed. They are non-parametric, easy to implement and proven to be asymptotically of the desired level and consistent. An estimator of the degree of k -monotonicity of the distribution is presented. An application to the estimation of the total number of classes in a population is proposed. A large simulation study makes it possible to assess the performances of the various procedures.

Regression models are widely used statistical procedures, and the validation of their assumptions plays a crucial role in the data analysis process. Unfortunately, validating assumptions usually depends on the availability of tests tailored to the specific model of interest. A novel Bayesian goodness-of-fit hypothesis testing approach is presented for a broad class of regression models the response variable of which is univariate and continuous. The proposed approach relies on a suitable transformation of the response variable and a Bayesian prior induced by a predictor-dependent mixture model. Hypothesis testing is performed via Bayes factor, the asymptotic properties of which are discussed. The method is implemented by means of a Markov chain Monte Carlo algorithm, and its performance is illustrated using simulated and real data sets.

Bayesian empirical likelihood (BEL) method with missing data depends heavily on the prior specification and missing data mechanism assumptions. It is well known that the resulting Bayesian estimations and tests may be sensitive to these assumptions and observations. To this end, a Bayesian local influence procedure is proposed to assess the effect of various perturbations to the individual observations, priors, estimating equations (EEs) and missing data mechanism in general EEs with nonignorable missing data. A perturbation model is introduced to simultaneously characterize various perturbations, and a Bayesian perturbation manifold is constructed to characterize the intrinsic structure of these perturbations. The first- and second-order adjusted local influence measures are developed to quantify the effect of various perturbations. The proposed methods are adopted to systematically investigate the tenability of nonignorable missing mechanism assumption, the sensitivity of the choice of the nonresponse instrumental variable and the sensitivity of EEs assumption, and goodness-of-fit statistics are presented to assess the plausibility of the posited EEs. Simulation studies are conducted to investigate the performance of the proposed methodologies. An example is analyzed. Propose a Bayesian local influence to assess the effect of various perturbations.Introduce a perturbation model to simultaneously characterize various perturbations.Construct a Bayesian perturbation manifold to characterize the structure of various perturbations.Develop the adjusted local influence measures to quantify the effect of various perturbations.Present goodness-of-fit statistics to assess the plausibility of the posited EEs.

A unifying approach to the shape and change-point hypotheses is extended generally to a discrete univariate exponential family. The maximal contrast type tests are newly proposed for the convexity and sigmoidicity hypotheses based on the complete class lemma of tests for the restricted alternatives. Those tests are also efficient score tests for the slope change-point and inflection point models, respectively. For each of those tests the successive component statistics are the doubly- and triply-accumulated statistics. They have nice Markov properties for the exact and efficient recursion formulae for calculating the p -value. Further the sum of squares of the component statistics are developed as the cumulative chi-squared statistics for the directional goodness-of-fit tests of the dose-response model. Therefore the interesting applications will be in monitoring of spontaneous reporting of the adverse drug events and the directional goodness-of-fit tests.

Field studies in ecology often make use of data collected in a hierarchical fashion, and may combine studies that vary in sampling design. For example, studies of tree recruitment after disturbance may use counts of individual seedlings from plots that vary in spatial arrangement and sampling density. To account for the multi-level design and the fact that more than a few plots usually yield no individuals, a mixed effects zero inflated Poisson model is often adopted. Although it is a convenient modeling strategy, various aspects of the model could be misspecified. A comprehensive test procedure, based on the cumulative sum of the residuals, is proposed. The test is proven to be consistent, and its convergence properties are established as well. The application of the proposed test is illustrated by a real data example and simulation studies.

New characterizations of the Poisson distribution based on an identity involving the Binomial thinning operator are presented. These characterizations allow the construction of statistics for testing the Poisson distribution against alternatives belonging to a large family called the LC-class, and against general alternatives. The usefulness and the power of the tests are illustrated with several examples of applications in Biodosimetry.

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.

Multiple-testing problems have received much attention. Different strategies have been considered in order to deal with this problem. The false discovery rate (FDR) is, probably, the most studied criterion. On the other hand, the sequential goodness of fit (SGoF), is a recently proposed approach. Most of the developed procedures are based on the independence among the involved tests; however, in spite of being a reasonable proviso in some frameworks, independence is not realistic for a number of practical cases. Therefore, one of the main problems in order to develop appropriate methods is, precisely, the effect of the dependence among the different tests on decisions making. The consequences of the correlation on the z-values distribution in the general multitesting problem are explored. Some different algorithms are provided in order to approximate the distribution of the expected rejection proportions. The performance of the proposed methods is evaluated in a simulation study in which, for comparison purposes, the Benjamini and Hochberg method to control the FDR, the Lehmann and Romano procedure to control the tail probability of the proportion of false positives (TPPFP), and the Beta-Binomial SGoF procedure are considered. Three different dependence structures are considered. As usual, for a better understanding of the problem, several practical cases are also studied.

Limited information statistics have been recommended as the goodness-of-fit measures in sparse 2^k contingency tables, but the p-values of these test statistics are computationally difficult to obtain. A Bayesian model diagnostic tool, Relative Entropy-Posterior Predictive Model Checking (RE-PPMC), is proposed to assess the global fit for latent trait models in this paper. This approach utilizes the relative entropy (RE) to resolve possible problems in the original PPMC procedure based on the posterior predictive p-value (PPP-value). Compared with the typical conservatism of PPP-value, the RE value measures the discrepancy effectively. Simulated and real data sets with different item numbers, degree of sparseness, sample sizes, and factor dimensions are studied to investigate the performance of the proposed method. The estimates of univariate information and difficulty parameters are found to be robust with dual characteristics, which produce practical implications for educational testing. Compared with parametric bootstrapping, RE-PPMC is much more capable of evaluating the model adequacy.

In this paper, using simulations, we compare specification procedures for testing the null hypothesis of a Gaussian distribution for the innovations of GARCH models. More precisely, Cramer-von Mises and Kolmogorov-Smirnov type statistics are computed for empirical processes based on the standardized residuals and their squares. For computing P-values, we use the parametric bootstrap method and the multipliers method. We also use the so-called Khmaladze's transform to obtain an approximated Brownian motion under the null hypothesis, for which we compute also Cramer-von Mises and Kolmogorov-Smirnov type statistics, using both the standardized residuals and their squares.

The dependence structure between WTI and Brent crude oil spot log-returns is analysed using modern copula techniques. In a first step, to account for autocorrelation and volatility clustering in the marginals, several single equation models are applied. Second, to select both copulas and tail copulas characterising the joint dynamics between the time series, newly introduced bootstrap-based goodness-of-fit tests are implemented and evaluated. Based on each approach, a comprehensive backtesting is performed by simulating and comparing the risk measures Value-at-Risk and Expected Shortfall with observed values.

The classical spatial scan test, which derived by maximizing the likelihood ratio statistic over a collection of cluster candidates, is widely used in spatial cluster detection. As the likelihood ratio statistic is only a special case in the family of power divergence (PD) goodness-of-fit statistics, the classical spatial scan test is extended to the family of PD spatial scan tests. Therefore, the family of PD spatial scan tests includes not only the classical case but also many other cases. The test statistics, the asymptotic null distribution, and the methods to incorporate overdispersion in the cluster detection are derived. It is found that in the absence of independent variables, the asymptotic null distribution of the PD spatial scan statistics only depends on the ratio of at risks populations and the collection of cluster candidates. Particularly, the focus is on three special cases in the family. They are the deviance, the Pearson, and the Freeman-Tukey spatial scan tests, where the deviance spatial scan test is equivalent to the classical spatial scan test. In simulation studies, it is found that the three test statistics are almost equally powerful for cluster detection.

We propose a frequency domain generalized likelihood ratio test for testing nonstationarity in time series. The test is constructed in the frequency domain by comparing the goodness of fit in the log-periodogram regression under the varying coefficient fractionally exponential models. Under such a locally stationary specification, the proposed test is capable of detecting dynamic changes of short-range and long-range dependences in a regression framework. The asymptotic distribution of the proposed test statistic is known under the null stationarity hypothesis, and its finite sample distribution can be approximated by bootstrap. Numerical results show that the proposed test has good power against a wide range of locally stationary alternatives.

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.

This paper proposes a new method for choosing regression models which may produce multiple models with sufficient explanatory power and parsimony unlike the traditional model selection procedures that aim at obtaining a single best model. The method ensures interpretability of the resulting models even under strong multicollinearity. The algorithm proceeds in the forward stepwise manner with two requirements for the selected regression models to be fulfilled: goodness of fit and the magnitude of update in loss functions. For the latter criterion, the standardized update is newly introduced, which is closely related with the model selection criteria including the Mallows' C"p, Akaike information criterion and Bayesian information criterion. Simulation studies demonstrate that the proposed algorithm works well with and without strong multicollinearity and even with many explanatory variables. Application to real data is also provided.

The problem of validity of a model on the informativeness of the right-censoring random variable on the inter-event time with recurrent events is considered. The generalized Koziol-Green model for recurrent events has been used in the literature to account for informativeness in the estimation of the gap time distribution or the cumulative hazard rate function. No formal procedure for validating such assumption has been developed for a recurrent failure time data. In this manuscript, we propose procedures for assessing the validity of the assumed model with recurrent events. Our tests are based on the scaled difference of two competing estimators of the cumulative hazard rate possessing nice asymptotic properties. Large sample properties of the proposed procedures are presented. The asymptotic results are applied for the construction of @g^2 and Kolmogorov-Smirnov type tests. Results of a simulation study on Type-I error probabilities and powers are presented. The procedures are also applied to real recurrent event data.

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.

With numerous statistical packages being easily available to conduct the logistic regression analysis, assessment for the goodness-of-fit in the logistic case-control studies becomes more important in practice. While various methods for model checking in conventional case-control studies have been proposed in the literature, methods for checking model adequacy with matched case-control data get relatively less attention. In this study, we propose an omnibus goodness-of-fit test to assess adequacy of the conditional logistic model for matched case-control data. The proposed test can be either constructed based on the discrepancy between two moment estimations or derived to be a score-type test under a general random-effects model. Computation of the proposed test is quite simple in which it does not need to partition the covariate space or to estimate p -value of the test via simulations. The asymptotic null distribution and power calculation of the test are derived under a sequence of alternatives. Empirical type I error rates and powers of the test are performed by simulation studies. An example has been used to illustrate the proposed method as well.

Goodness-of-fit and symmetry tests are proposed for the innovation distribution in generalized autoregressive conditionally heteroscedastic models. The tests utilize an integrated distance involving the empirical characteristic function (or the empirical Laplace transform) computed from properly standardized observations. A bootstrap version of the tests serves the purpose of studying the small sample behaviour of the proclaimed procedures in comparison with more classical approaches. Finally, all tests are applied to some financial data sets.

Plotting points of order statistics are often used in the determination of goodness-of-fit of observed data to theoretical percentiles. Plotting points are usually determined by using nonparametric methods which produce, for example, the mean- and median-ranks. Here, we use a distribution-based approach which selects plotting points (quantiles) based on the simultaneous-closeness of order statistics to population quantiles. We show that the plotting points so determined are robust over a multitude of symmetric distributions and then demonstrate their usefulness by examining the power properties of a correlation goodness-of-fit test for normality.

Suppose that one can observe bivariate random variables (L,X) only when L@?X holds. Such data are called left-truncated data and found in many fields, such as experimental education and epidemiology. Recently, a method of fitting a parametric model on (L,X) has been considered, which can easily incorporate the dependent structure between the two variables. A primary concern for the parametric analysis is the goodness-of-fit for the imposed parametric forms. Due to the complexity of dependent truncation models, the traditional goodness-of-fit procedures, such as Kolmogorov-Smirnov type tests based on the Bootstrap approximation to null distribution, may not be computationally feasible. In this paper, we develop a computationally attractive and reliable algorithm for the goodness-of-fit test based on the asymptotic linear expression. By applying the multiplier central limit theorem to the asymptotic linear expression, we obtain an asymptotically valid goodness-of-fit test. Monte Carlo simulations show that the proposed test has correct type I error rates and desirable empirical power. It is also shown that the method significantly reduces the computational time compared with the commonly used parametric Bootstrap method. Analysis on law school data is provided for illustration. R codes for implementing the proposed procedure are available in the supplementary material.

Generalized estimating equations (GEE) were proposed for the analysis of correlated data. They are popular because regression parameters can be consistently estimated even if only the mean structure is correctly specified. GEE have been extended in several ways, including regression diagnostics for outlier detection. However, GEE have rarely been used for analyzing controlled clinical trials. The SB-LOT trial, a double-blind placebo-controlled randomized multicenter trial in which the oedema-protective effect of a vasoactive drug was investigated in patients suffering from chronic insufficiency was re-analyzed using the GEE approach. It is demonstrated that the autoregressive working correlation structure is the most plausible working correlation structure in this study. The effect of the vasoactive drug is a difference in lower leg volume of 2.64 ml per week (p=0.0288, 95% confidence interval 0.27-4.99 ml per week), making a difference of 30 ml at the end of the study. Deletion diagnostics are used for identification of outliers and influential probands. After exclusion of the most influential patients from the analysis, the overall conclusion of the study is not altered. At the same time, the goodness of fit as assessed by half-normal plots increases substantially. In summary, the use of GEE in a longitudinal clinical trial is an alternative to the standard analysis which usually involves only the last follow-up. Both the GEE and the regression diagnostic techniques should accompany the GEE analysis to serve as sensitivity analysis.

A new test for the goodness of fit of parametric forms of the drift and volatility functions of interest rate models is proposed. The test is based on a marked empirical process of the residuals. More specifically, a marked empirical process is constructed using estimators of the integrated regression function and the integrated conditional variance function for the drift function and the volatility function, respectively. Distributions of these processes are approximated using bootstrap techniques. This test is then applied to simulated classical financial models and is illustrated in an empirical application to a EURIBOR data set.

The consequences of model misspecification for multinomial data when using minimum ϕ -divergence or minimum disparity estimators to estimate the model parameters are considered. These estimators are shown to converge to a well-defined limit. Two applications of the results obtained are considered. First, it is proved that the bootstrap consistently estimates the null distribution of certain class of test statistics for model misspecification detection. Second, an application to the model selection test problem is studied. Both applications are illustrated with numerical examples.

In this paper, a data-driven test is proposed to compare two independent or dependent stationary time series, in terms of the second order dynamics. We show that the problem of time series comparison is equivalent to a goodness-of-fit test checking if a constant model is adequate. Using the same framework, the proposed test is easily extended to compare multiple time series and time series of different lengths. Different to previous methods, it is based on generalized score statistics in an estimating equation setting, with some weak and flexible conditions. An extensive simulation study illustrates the validity of the asymptotic result and finite sample properties, using the tapered periodogram. The proposed test is found to perform well for many different situations, including time series with heavy-tailed or skewed innovations. An application to damage detection using vibration data is discussed.

Growth curve models are routinely used in various fields such as biology, ecology, demography, population dynamics, finance, econometrics, etc. to study the growth pattern of different populations and the variables linked with them. Many different kinds of growth patterns have been used in the literature to model the different types of realistic growth mechanisms. It is generally a matter of substantial benefit to the data analyst to have a reasonable idea of the nature of the growth pattern under study. As a result, goodness-of-fit tests for standard growth models are often of considerable practical value. In this paper we develop some natural goodness-of-fit tests based on finite differences of the size variables under consideration. The method is general in that it is not limited to specific parametric forms underlying the hypothesized model so long as an appropriate finite difference of some function of the size variables can be made to vanish. In addition it allows the testing process to be carried out under a set up which manages to relax most of the assumptions made by Bhattacharya et al. (2009); these assumptions are generally reasonable but not guaranteed to hold universally. Thus our proposed method has a very wide scope of application. The performance of the theory developed is illustrated numerically through several sets of real data and through simulations.

A goodness-of-fit testing procedure for Archimedean copula (AC) models is developed based on right-censored data. The proposed approach extends an existing method, which is suitable for the Clayton model, to general AC models. Asymptotic properties of the proposed test statistics under the true model assumption are derived. Simulation analysis shows that the proposed test has reasonable performance. Finally, two real data examples are analyzed for illustrative purposes.

The use of trimming procedures constitutes a natural approach to robustifying statistical methods. This is the case of goodness-of-fit tests based on a distance, which can be modified by choosing trimmed versions of the distributions minimizing that distance. The L"2-Wasserstein distance is used to introduce the trimming methodology for assessing when a data sample can be considered mostly normal. The method can be extended to other location and scale models, introducing a robust approach to model validation, and allows an additional descriptive analysis by determining the subset of the data with the best improved fit to the model. This is a consequence of the use of data-driven trimming methods instead of the more classical symmetric trimming procedures.

The generalized normal-Laplace distribution is a useful law for modelling asymmetric data exhibiting excess kurtosis. Goodness-of-fit tests for this distribution are constructed which utilize the corresponding moment generating function, and its empirical counterpart. The consistency and other properties of the test are investigated under general assumptions, and the proposed procedure is applied, following a non-trivial estimation step, to test the fit of some financial data.

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.

Longitudinal studies involving categorical responses are extensively applied in many fields of research and are often fitted by the generalized estimating equations (GEE) approach and generalized linear mixed models (GLMMs). The assessment of model fit is an important issue for model inference. The purpose of this article is to extend Pan's (2002a) goodness-of-fit tests for GEE models with longitudinal binary data to the tests for logistic proportional odds models with longitudinal ordinal data. Two proposed methods based on Pearson chi-squared test and unweighted sum of residual squares are developed, and the approximate expectations and variances of the test statistics are easily computed. Four major variants of working correlation structures, independent, AR(1), exchangeable and unspecified, are considered to estimate the variances of the proposed test statistics. Simulation studies in terms of type I error rate and the power performance of the proposed tests are presented for various sample sizes. Furthermore, the approaches are demonstrated by two real data sets.

Over the last decade there has been a marked interest in a Laplace distribution and its properties and generalizations, especially in the framework of financial applications. Such an interest has led to a revision and discussion of available goodness-of-fit procedures for a Laplace distribution. Indeed, since most of the studies which employ the Laplace distribution are concerned with modelling heavy tailed patterns, the modern class of possible alternatives is way broader than just testing the Laplace vs. normal distribution. In this paper we propose a new test of fit for a Laplace distribution against deviations with heavier tails than that of the reference Laplace distribution. The proposed goodness-of-fit procedure is based on sample skewness and kurtosis and a robust L"1 estimator of scale about a sample median. The developed test statistic is shown to asymptotically follow a @g^2-distribution with two degrees of freedom. Performance of the new goodness-of-fit test is illustrated by simulations and a case study.

A goodness of fit test for the Pareto distribution, when the observations are subjected to Type II right censoring is proposed. The test statistic involves transformations of the original data and is based on the nonparametric Nelson-Aalen estimator of the cumulative hazard function. By Monte Carlo simulation, the empirical distribution of the test statistic is obtained and the power of the test is investigated for some alternative distributions. The power is compared with adaptations for Type II censored data of the Cramer-von Mises and Anderson-Darling tests, and a test based on Kullback-Leibler information. For some alternative distributions with monotone decreasing hazard function, the proposed test has higher power. The methodology is illustrated by reanalyzing two published data sets.

The likelihood approach based on the empirical distribution functions is a well-accepted statistical tool for testing. However, the proof schemes of the Neyman-Pearson type lemmas induce consideration of density-based likelihood ratios to obtain powerful test statistics. In this article, we introduce the distribution-free density-based likelihood technique, applied to test for goodness-of-fit. We focus on tests for normality and uniformity, which are common tasks in applied studies. The well-known goodness-of-fit tests based on sample entropy are shown to be a product of the proposed empirical likelihood (EL) methodology. Although the efficiency of test statistics based on classes of entropy estimators has been widely addressed in the statistical literature, estimation of the sample entropy has been not invariantly defined, and hence this estimation produces tests that are difficult to be applied to real data studies. The proposed EL approach defines clear forms of the entropy-based tests. Monte Carlo simulation results confirm the preference of the proposed method from a power perspective. Real data examples study the proposed approach in practice.

Goodness-of-fit tests are constructed for the two-parameter Birnbaum-Saunders distribution in the case where the parameters are unknown and are therefore estimated from the data. With each test the procedure starts by computing efficient estimators of the parameters. Then the data are transformed to normality and normality tests are applied on the transformed data, thereby avoiding reliance on parametric asymptotic critical values or the need for bootstrap computations. Two classes of tests are considered, the first class being the classical tests based on the empirical distribution function, while the other class utilizes the empirical characteristic function. All methods are extended to cover the case of generalized three-parameter Birnbaum-Saunders distributions.