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In this work, we study semiparametric copula models under bivariate censoring. Basing on divergences theory, we propose new estimates for the parameter of the considered model and we establish thei...

In this paper, we use extensive empirical data sets from Shanghai 50ETF (SH50ETF) and SH50ETF options markets in China to study how regime-switching jump-diffusion models improve goodness of fit an...

International audience; Goodness-of-fit testing is addressed in the stratified proportional hazards model for survival data. A test statistic based on within-strata cumulative sums of martingale residuals over covariates is proposed and its asymptotic distribution is derived under the null hypothesis of model adequacy. A Monte Carlo procedure is proposed to approximate the critical value of the test. Simulation studies are conducted to examine finite-sample performance of the proposed statistic.

This work considers goodness-of-fit for the life test data with hybrid censoring. An alternative representation of the Kolmogorov–Smirnov (KS) statistics is provided under Type-I censoring. The alt...

In this paper we introduced a single parameter, absolutely continuous and radially symmetric bivariate extension of the Farlie-Gumbel-Morgenstern (FGM) family of copulas. Specifically, this extensi...

This paper presents some powerful omnibus tests for multivariate normality based on the likelihood ratio and the characterizations of the multivariate normal distribution. The power of the proposed...

Gandy and Jensen (2005) proposed goodness-of-fit tests for Aalen's additive risk model. In this article, we demonstrate that the approach of Gandy and Jensen (2005) can be applied to left-truncated right-censored (LTRC) data and doubly censored data. A simulation study is conducted to investigate the performance of the proposed tests. The proposed tests are illustrated using heart transplant data.

Many analyses in the epidemiological and the prognostic studies and in the studies of event history data require methods that allow for unobserved covariates or “frailties”. We consider the shared frailty model in the framework of parametric proportional hazard model. There are certain assumptions about the distribution of frailty and baseline distribution. The exponential distribution is the commonly used distribution for analyzing lifetime data. In this paper, we consider shared gamma frailty model with bivariate exponential of Marshall and Olkin (1967) distribution as baseline hazard for bivariate survival times. We solve the inferential problem in a Bayesian framework with the help of a comprehensive simulation study and real data example. We fit the model to the real-life bivariate survival data set of diabetic retinopathy data. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the proposed model and then compare the true...

In this article, we introduce two goodness-of-fit tests for testing normality through the concept of the posterior predictive p-value. The discrepancy variables selected are the Kolmogorov-Smirnov (KS) and Berk-Jones (BJ) statistics and the prior chosen is Jeffreys’ prior. The constructed posterior predictive p-values are shown to be distributed independently of the unknown parameters under the null hypothesis, thus they can be taken as the test statistics. It emerges from the simulation that the new tests are more powerful than the corresponding classical tests against most of the alternatives concerned.

The main purpose of this article is to consider the covariate-adjusted regression (CAR) model for time series. The CAR model was initially proposed by Senturk and Muller (2005) for such situations where predictor and response variables are not directly observed, but are distorted by some common observable covariate. Despite CAR being originally designed for independent cross-sectional data, multiple works have extended this method to dependent data setting. In this article, the authors extend CAR to the distorted time series setting. This extension is meaningful in many fields such as econometrics, mathematical finance, and signal processing. The estimates of regression parameters are proposed by establishing connection with functional-coefficient time series model. The consistency and asymptotic normality of the proposed estimates are investigated under the α-mixing conditions. Real data and simulated examples are provided for illustration.

For the analysis of survey-weighted categorical data, one recommended method of analysis is a log-rate model. For each cell in a contingency table, the survey weights are averaged across subjects and incorporated into an offset for a loglinear model. Supposedly, one can then proceed with the analysis of unweighted observed cell counts. We provide theoretical and simulation-based evidence to show that the log-rate analysis is not an effective statistical analysis method and should not be used in general. The root of the problem is in its failure to properly account for variability in the individual weights within cells of a contingency table. This results in goodness-of-fit tests that have higher-than-nominal error rates and confidence intervals for odds ratios that have lower-than-nominal coverage.

The regression model with randomly censored data has been intensively investigated. In this article, we consider a goodness-of-fit test for this model. Empirical likelihood (EL) tests are constructed. The asymptotic distributions of the test statistic under null hypothesis and the local alternative hypothesis are given. Simulations are carried out to illustrate the methodology.

The results (tables of percentage points and statistic distribution models) for the Kolmogorov, Cramer–Von Mises–Smirnov, and Anderson–Darling tests, when unknown parameters are estimated by their MLEs, are presented in this article.

Residual analysis is useful for assessing how well the fitted regression model explains the observed data, including the impact and significance of an observation on the overall results. Such residual analysis works well when a fully parametric model is assumed. However, its usefulness in evaluating goodness of fit for semiparametric models is not well studied. In this article, we propose various definitions of residuals for a semiparametric regression model and apply them to a multi-center two-armed clinical trial for Scleroderma patients. We show we can gain interesting insights on the longitudinal data using our proposed residuals.

To improve the goodness of fit between a regression model and observations, the model can be complicated; however, that can reduce the statistical power when the complication does not lead significantly to an improved model. In the context of two-phase (segmented) logistic regressions, the model evaluation needs to include testing for simple (one-phase) versus two-phase logistic regression models. In this article, we propose and examine a class of likelihood ratio type tests for detecting a change in logistic regression parameters that splits the model into two-phases. We show that the proposed tests, based on Shiryayev–Roberts type statistics, are on average the most powerful. The article argues in favor of a new approach for fixing Type I errors of tests when the parameters of null hypotheses are unknown. Although the suggested approach is partly based on Bayes–Factor-type testing procedures, the classical significance levels of the proposed tests are under control. We demonstrate applications of the av...

A goodness-of-fit test for multivariate normality is proposed which is based on Shapiro–Wilk's statistic for univariate normality and on an empirical standardization of the observations. The critical values can be approximated by using a transformation of the univariate standard normal distribution. A Monte Carlo study reveals that this test has a better power performance than some of the best known tests for multinormality against a wide range of alternatives.

Using the framework proposed by Bickel et al. (2006), we provide a score-based testing method to check the exclusion restriction in quantile regression, i.e., H: να(Y|U, V) = να(Y|U) w.p.1, where να denotes the αth (0

This paper addresses problem of testing whether an individual covariate in the Cox model has a proportional (i.e., time-constant) effect on the hazard. Two existing methods are considered: one is based on the component of the score process, and the other is a Neyman type smooth test. Simulations show that, when the model contains both proportional and nonproportional covariates, these methods are not reliable tools for discrimination. A simple yet effective solution is proposed based on smooth modeling of the effects of the covariates not in focus.

One of the most basic topics in many introductory statistical methods texts is inference for a population mean, μ. The primary tool for confidence intervals and tests is the Student t sampling distribution. Although the derivation requires independent identically distributed normal random variables with constant variance, σ2, most authors reassure the readers about some robustness to the normality and constant variance assumptions. Some point out that if one is concerned about assumptions, one may statistically test these prior to reliance on the Student t. Most software packages provide optional test results for both (a) the Gaussian assumption and (b) homogeneity of variance. Many textbooks advise only informal graphical assessments, such as certain scatterplots for independence, others for constant variance, and normal quantile–quantile plots for the adequacy of the Gaussian model. We concur with this recommendation. As convincing evidence against formal tests of (a), such as the Shapiro–Wilk, we offer...

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.

Testing goodness of fit for a Poisson distribution is routine when the mean is sufficiently large; the scaled deviance G 2 or Pearson's X 2 statistic follow approximate chi-square distributions and perform the task well. When the mean is low, typically less than one, the approximations to chi-square distributions are poor. In this paper we explore the underlying reasons for this behaviour and present a practical resolution of the problem, in both single distribution and regression contexts. An extension to negative binomial models is also given. This research is motivated by a real example drawn from road accident modelling.

A latent variable model is considered for the analysis of twin data with an ordinal response. The underlying latent multivariate normally distributed variable is expressed in terms of genetic and environmental effects, and the variance components associated with these effects are estimated. We illustrate this approach with analysis of the NHLBI Twin Study. Model assessment is ascertained by proposing a goodness-of-fit test for ordered categorical data. Extensions of this approach for the investigation of how genetic effects vary over time are discussed.

Regression diagnostics are an important tool of the professional statistician, and they are neglected at one's peril Deletion and local influence diagnostics (see Cook 1977, 1986 for origins) relevant to Normal linear regression are considered here, as these are in most common use. The presentation extends beyond the traditional parameter estimate influence to indicate the possibilities for model test influence and model goodness of fit influence, both also based on familiar uses of the likelihood. Two real-life data sets are presented and analysed using some of the more traditional diagnostics.

This paper develops an approach to testing the adequacy of both classical and Bayesian models given sample data. An important feature of the approach is that we are able to test the practical scientific hypothesis of whether the true underlying model is close to some hypothesized model. The notion of closeness is based on measurement precision and requires the introduction of a metric for which we consider the Kolmogorov distance. The approach is nonparametric in the sense that the model under the alternative hypothesis is a Dirichlet process.

The problem of testing the fit of the Levy distribution with unknown scale parameter is addressed. The corresponding empirical process is analysed, and the Cramer-von Mises W2 and the Anderson-Darling's A2 statistics are used. Well known results regarding the relationship between the Levy distribution and the gamma and inverse Gaussian are exploited. Some remarks are made regarding the use of the Rao-Blackwell estimator of the distribution function in the empirical process.

In this note we show how one may construct goodness-of-fit tests to test hypotheses for the restricted MANOVA and GMANOVA models using the multivariate seemingly unrelated regression (MSUR) model.

In this paper, a new test statistic is presented for testing the null hypothesis of equal multinomial cell probabilities versus various trend alternatives. Exact asymptotic critical values are obtained, The power of the test is compared with several other statistics considered by Choulakian et al (1995), The test is shown to have better power for certain trend alternatives.

In regression analysis we are often interested in using an estimator which is “precise” and which simultaneously provides a model with “good fit”, In this paper we consider the risk properties of several estimators of the regression coefficient vector "trader “balanced” loss, This loss function (Zellner, 1994) reflects both of the described attributes. Under a particular form of balanced loss, we derive the predictive risk of the pre-test estimator which results after a test for exact linear restrictions on the coefficient vector. The corresponding risks of Stein-rule and positive-part Stein-rale estimators are also established. The risks based on loss functions which allow only for estimation precision, or only for goodness of fit, are special cases of our results, and we draw appropriate comparisons, In particular, we show that some of the well-known results under (quadratic) precision-only loss are not robust to our generalization of the loss function

In this paper, relying on the sample breakdown points, we investigate the sample breakdown properties of some nonparametric tests. It is shown that the sample breakdown points of the sign test asymptotically dominate those of the Wilcoxon test for one–sided hypotheses, However, the different conclusion is derived in the case of testing some shrinking neighborhood hypotheses. The breakdown behaviors of the Kolmogorov test and X2–test are also explored. These studies unify or refine some existing breakdown analyses of tests.

Using divergence measures based on entropy functions, a procedure to test statistical hypotheses is proposed. Replacing the parameters by suitable estimators in the expresion of the divergence measure, the test statistics are obtained. Asymptotic distributions for these statistics are given in several cases when maximum likelihood estimators are considered, so they can be used to construct confidence intervals and to test statistical hypotheses based on one or more samples. These results can also be applied to multinomial populations. Tests of goodness of fit and tests of homogeneity can be constructed.

An overview is given of methodology for testing goodness of fit of parametric models using nonparametric function estimation techniques. The ideas are illustrated in two settings: the classical one-sample goodness-of-fit scenario and testing the goodness of fit of a polynomial regression model.

A wide selection of tests for exponentiality is discussed and compared. Power computations, using simulations, were done for each procedure. Certain tests (e.g. Gnedenko (1969), Lin and Mudholkar (1980), Harris (1376), Cox and Oakes (1384), and Deshpande (1983)) performed well for alternative distributions with non-monotonic hazard rates, while others (e.g. Deshpande (1983), Gail and Gastwirth (1978), Kolmogorov-Smirnov (LillViefors (1969)), Hahn and Shapiro (1967), Hollander and Proschan (1972), and Cox and Oakes (1984)) fared well for monotonic hazard rates. Of all the procedures compared, the score test presented in Cox and Oakes (1984) appears to be the best if one does not have a particular alternative in mind.

A test is proposed for testing bivariate exponentiality against the Bivariate Increasing Failure Rate (BIFR) class of alternatives. The test statistic is a function of U-statistics and hence asymptotically normally distributed and consistent

Wilks's A was factorized by Bartlett (1951) for testing the hypothesis of goodness of fit of a hypothetical discriminant function in the case of several groups. This test has applications in various areas such as Econometrics, contingency tables, growth curves, principal components analysis, design of experiments and so on. This paper gives a consolidated account of the research done in these areas on the application of factors of Wilks's A

Measures of influence of multivariate cases on the estimated parameter matrix in MANOVA are developed. The development is based on the confidence region resulting from the likelihood ratio criterion, and is patterned after the development of Cook's univariate DImeasure. Influence measures corresponding to the other 3 common multivariate test criteria are presented. Relationships to the measures of Caroni (1987), and Barrett and Ling (1988) are noted. A numerical example is included.

Exact goodness-of-fit tests for the power law process, a nonhomogeneous Poisson process with intensity function , can be constructed by making one of two transformations of the event times. The Kolmogorov-Smirnov, Cramer-von Mises or Anderson-Darling test can then be applied to these transformed variables. In this article it is shown that these two transformations lead to the same test statistics in one particular case. The results of a simulation study show that these tests have very low power when the alternative hypothesis is a renewal process. A transformation of these transformed variables, suggested by Durbin, increases the power substantially.

A method used to compilsate for nonresponse is to impute missing vaiues; that is, to complete the data set by using the respondent data to replace all nonresponses. Due to the re-use of the respondent data, the distribution theory of statistics computed from a completed data set is more complex than that of the sane statistics when there are no missing data. The asymptotic distribution of the goodness-of-fit chi-square statistic computed from a completed data set is derived. The effect of the characteristics of the imputation procedure on this distrihtion is examined for several imputation procedures

Characterizing a set of data as a random sample from a specified distribution is often a precursor to statistical inference or hypothesis testing involving the extremes of the distribution -precisely the regions of greatest uncertainty. It seems reasonable then to exploit as best we can our limited knowledge of this region. Toward this end we investigate here the areas in the tails of the distribution as determined by the extreme order statistics as a criterion for testing goodness-of-fit.

A gamma regression model with an exponential link function for the means Is considered. Moment properties of the deviance statistics based on maximum likelihood and weighted least squares fits are used to define modified deviance statistics which provide alternative global goodness of fit tests. The null distribution properties of the deviances and modified deviances are compared with those of the approximating chi-square distribution and It is shown that the use of the modified deviances gives much better control over the significance levels of the tests.

Application of the conditional probablity integral transformations for multivariate normal distribtions derived in Rincon-Gallardo,Quesenberry and O'Reality (1979) are considered assuming multiple samples. a component-wise analysis with pooling over smples is introduced and illustrated with three examples

Analysis of two-phase regression has traditionally been carried out using a variety of likelihood approaches. In this paper we present an alternative procedure based on a goodness of fit criterion. Exact hypothesis tests for a known switch point are developed. Approximate (conservative) tests for an unknown switch point are also obtained

A goodness of fit test statistic for the univariate logistic response model proposed by Prentice (1976) for quantal response bioassays is described and extended to the multiple regressor. variable situation. The size and power characteristics of the test statistic was found to be adequately described by a chi square variate for sample sizes as small as SO and its power was found to be dependent upon both the sample size and the true underlying response model.

This paper considers the building of stochastic models and the related analysis of discrete data in two biological problems, The first arises from the reproduction of yeast cells, while the secondis concerned with the aggregation of nucleoli. Galton-Watson and aggregation models are constructed for the respective processes and their goodness of fit to the data tested

Goodness-of-fit tests based on the order statistics of a random sample are given which are particularly effective in detecting long tailedness or outliers.

The theory of chi-square tests with data-dependent cells is applied to provide tests of fit to the family of p-variate normal distributions. The cells are bounded by hyperellipses (x-[Xbar])'S-1 (x-[Xbar]) = ci centered at the sample mean [Xbar] and having shape deter-mined by the sample covariance matrix S. The Pearson statistic with these cells is affine-invariant, has a null distribution not depending on the true mean and covariance, and has asymptotic critical points between those of x2 (M-1) and x2 (M-2) when M cells are employed. The test is insensitive to lack of symmetry, but peakedness, broad shoulders and heavy tails are easily discerned in the cell counts. Multivariate normality of logarithms of relative prices of common stocks, a common assumption in finan-cial markets theory, is studied using the statistic described here and a large data base.

A goodness of fit test for multivariate normality is developed. The test procedure reduces the composite null hypothesis to a simple null hypothesis that requires one to test uniformity of a set of observations between 0 and 1.

Various aspects of assessing multivariate normality are discussed. Practical recommendations are given, and areas of further research interest are noted.

Many goodness of fit tests for bivariate normality are not rigorous procedures because the distributions of the proposed statistics are unknown or too difficult to manipulate. Two familiar examples are the ring test and the line test. In both tests the statistic utilized generally is approximated by a chi-square distribution rather than compared to its known beta distribution. These two procedures are re-examined and re-evaluated in this paper. It is shown that the chi-square approximation can be too conservative and can lead to unnecessary rejection of normality.

A test for lack of fit in regression is presented. Unlike other methods, this one doesn't require replicates or a prior estimate of variance. It can be used for linear or multiple regression, and would be easy to add to existing computer packages. It is based on comparing a fit over low leverage points with a fit over the entire set of data. Distribution theory results are pre¬sented, with examples of power. A discussion of its use for de¬tecting violations of other regression assumptions is also given.

A test based on empirical distribution function has been devised for testing second order stochastic dominance of distribution functions. The test is useful for comparison of random ehonomic prospects for risk averters.