scholarly journals Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Šárka Hudecová ◽  
Marie Hušková ◽  
Simos G. Meintanis
Keyword(s):  
Goodness Of Fit ◽  
Probability Generating Function ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Generalized Poisson ◽  
Goodness Of Fit Tests ◽  
Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

scholarly journals GOODNESS-OF-FIT TESTS FOR MULTIVARIATE COPULA-BASED TIME SERIES MODELS

2016 ◽  
Vol 33 (2) ◽  
pp. 292-330 ◽  
Author(s):  
Betina Berghaus ◽  
Axel Bücher
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Mixing Time ◽  
Parametric Bootstrap ◽  
Stationary Time Series ◽  
Time Series Models ◽  
Finite Sample ◽  
Copula Functions ◽  
Cross Sectional ◽  
Goodness Of Fit Tests

In recent years, stationary time series models based on copula functions became increasingly popular in econometrics to model nonlinear temporal and cross-sectional dependencies. Within these models, we consider the problem of testing the goodness-of-fit of the parametric form of the underlying copula. Our approach is based on a dependent multiplier bootstrap and it can be applied to any stationary, strongly mixing time series. The method extends recent i.i.d. results by Kojadinovic et al. (2011) and shares the same computational benefits compared to methods based on a parametric bootstrap. The finite-sample performance of our approach is investigated by Monte Carlo experiments for the case of copula-based Markovian time series models.

GOODNESS-OF-FIT TESTS BASED ON KERNEL DENSITY ESTIMATORS WITH FIXED SMOOTHING PARAMETERS

1998 ◽  
Vol 14 (5) ◽  
pp. 604-621 ◽  
Author(s):  
Yanqin Fan
Keyword(s):  
Density Function ◽  
Goodness Of Fit ◽  
Kernel Estimator ◽  
Parametric Bootstrap ◽  
Smoothing Parameter ◽  
Local Power ◽  
Finite Sample ◽  
Sample Distribution ◽  
Bootstrap Procedure ◽  
Goodness Of Fit Tests

In this paper, we study the bias-corrected test developed in Fan (1994). It is based on the integrated squared difference between a kernel estimator of the unknown density function of a random vector and a kernel smoothed estimator of the parametric density function to be tested under the null hypothesis. We provide an alternative asymptotic approximation of the finite-sample distribution of this test by fixing the smoothing parameter. In contrast to the normal approximation obtained in Fan (1994) in which the smoothing parameter shrinks to zero as the sample size grows to infinity, we obtain a non-normal asymptotic distribution for the bias-corrected test. A parametric bootstrap procedure is proposed to approximate the critical values of this test. We show both analytically and by simulation that the proposed bootstrap procedure works. Consistency and local power properties of the bias-corrected test with a fixed smoothing parameter are also discussed.

scholarly journals Goodness-of-fit tests for the beta Gompertz distribution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 69-81
Author(s):  
Hanaa Abu-Zinadah ◽  
Asmaa Binkhamis
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Likelihood Method ◽  
Test Statistics ◽  
Gompertz Distribution ◽  
Goodness Of Fit Tests ◽  
Lilliefors Test ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This article studied the goodness-of-fit tests for the beta Gompertz distribution with four parameters based on a complete sample. The parameters were estimated by the maximum likelihood method. Critical values were found by Monte Carlo simulation for the modified Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and Lilliefors test statistics. The power of these test statistics founded the optimal alternative distribution. Real data applications were used as examples for the goodness of fit tests.

scholarly journals New Equivalence Tests for Hardy–Weinberg Equilibrium and Multiple Alleles

Stats ◽  
2020 ◽  
Vol 3 (1) ◽  
pp. 34-39
Author(s):  
Vladimir Ostrovski
Keyword(s):  
Bootstrap Method ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Multiple Alleles ◽  
Weinberg Equilibrium ◽  
Equivalence Tests ◽  
Hardy Weinberg Equilibrium ◽  
The Bootstrap Method

We consider testing equivalence to Hardy–Weinberg Equilibrium in case of multiple alleles. Two different test statistics are proposed for this test problem. The asymptotic distribution of the test statistics is derived. The corresponding tests can be carried out using asymptotic approximation. Alternatively, the variance of the test statistics can be estimated by the bootstrap method. The proposed tests are applied to three real data sets. The finite sample performance of the tests is studied by simulations, which are inspired by the real data sets.

scholarly journals CHARACTERIZATIONS OF MULTINORMALITY AND CORRESPONDING TESTS OF FIT, INCLUDING FOR GARCH MODELS

2018 ◽  
Vol 35 (03) ◽  
pp. 510-546 ◽  
Author(s):  
Norbert Henze ◽  
M. Dolores Jiménez–Gamero ◽  
Simos G. Meintanis
Keyword(s):  
Goodness Of Fit ◽  
Moment Generating Function ◽  
Multivariate Garch ◽  
Affine Invariant ◽  
Test Statistics ◽  
Finite Sample ◽  
Goodness Of Fit Tests ◽  
Multivariate Garch Model ◽  
The Moment ◽  
Tests Of Fit

We provide novel characterizations of multivariate normality that incorporate both the characteristic function and the moment generating function, and we employ these results to construct a class of affine invariant, consistent and easy-to-use goodness-of-fit tests for normality. The test statistics are suitably weighted L2-statistics, and we provide their asymptotic behavior both for i.i.d. observations as well as in the context of testing that the innovation distribution of a multivariate GARCH model is Gaussian. We also study the finite-sample behavior of the new tests and compare the new criteria with alternative existing tests.

scholarly journals Goodness-of-fit tests for the beta Gompertz distribution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 69-81
Author(s):  
Hanaa Abu-Zinadah ◽  
Asmaa Binkhamis
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Likelihood Method ◽  
Test Statistics ◽  
Gompertz Distribution ◽  
Goodness Of Fit Tests ◽  
Lilliefors Test ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This article studied the goodness-of-fit tests for the beta Gompertz distribution with four parameters based on a complete sample. The parameters were estimated by the maximum likelihood method. Critical values were found by Monte Carlo simulation for the modified Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and Lilliefors test statistics. The power of these test statistics founded the optimal alternative distribution. Real data applications were used as examples for the goodness of fit tests.

A New Method for Characterizing Replacement Rate Variation in Molecular Sequences: Application of the Fourier and Wavelet Models to Drosophila and Mammalian Proteins

Genetics ◽  
2000 ◽  
Vol 154 (1) ◽  
pp. 381-395
Author(s):  
Pavel Morozov ◽  
Tatyana Sitnikova ◽  
Gary Churchill ◽  
Francisco José Ayala ◽  
Andrey Rzhetsky
Keyword(s):  
Wavelet Transforms ◽  
Parametric Bootstrap ◽  
Real Data ◽  
New Method ◽  
Rate Variation ◽  
Discrete Wavelet ◽  
Data Sets ◽  
Ratio Test ◽  
Replacement Rate ◽  
New Models

Abstract We propose models for describing replacement rate variation in genes and proteins, in which the profile of relative replacement rates along the length of a given sequence is defined as a function of the site number. We consider here two types of functions, one derived from the cosine Fourier series, and the other from discrete wavelet transforms. The number of parameters used for characterizing the substitution rates along the sequences can be flexibly changed and in their most parameter-rich versions, both Fourier and wavelet models become equivalent to the unrestricted-rates model, in which each site of a sequence alignment evolves at a unique rate. When applied to a few real data sets, the new models appeared to fit data better than the discrete gamma model when compared with the Akaike information criterion and the likelihood-ratio test, although the parametric bootstrap version of the Cox test performed for one of the data sets indicated that the difference in likelihoods between the two models is not significant. The new models are applicable to testing biological hypotheses such as the statistical identity of rate variation profiles among homologous protein families. These models are also useful for determining regions in genes and proteins that evolve significantly faster or slower than the sequence average. We illustrate the application of the new method by analyzing human immunoglobulin and Drosophilid alcohol dehydrogenase sequences.

A test for fuzzy exponentiality based on Kullback-Leibler information

2021 ◽  
pp. 1-8
Author(s):  
Lingtao Kong
Keyword(s):  
Biological Sciences ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Experimental Studies ◽  
Real Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Higher Power ◽  
Leibler Information

The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

Estimation of Expected Fisher Information for IRT Models

2019 ◽  
Vol 44 (4) ◽  
pp. 431-447 ◽  
Author(s):  
Scott Monroe
Keyword(s):  
Fisher Information ◽  
Information Matrix ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Irt Models ◽  
Expected Information ◽  
Complex Models ◽  
Multidimensional Irt Models ◽  
Two Parameter

In item response theory (IRT) modeling, the Fisher information matrix is used for numerous inferential procedures such as estimating parameter standard errors, constructing test statistics, and facilitating test scoring. In principal, these procedures may be carried out using either the expected information or the observed information. However, in practice, the expected information is not typically used, as it often requires a large amount of computation. In the present research, two methods to approximate the expected information by Monte Carlo are proposed. The first method is suitable for less complex IRT models such as unidimensional models. The second method is generally applicable but is designed for use with more complex models such as high-dimensional IRT models. The proposed methods are compared to existing methods using real data sets and a simulation study. The comparisons are based on simple structure multidimensional IRT models with two-parameter logistic item models.

The Topp Leone Kumaraswamy-G Family of Distributions with Applications to Cancer Disease Data

2020 ◽  
Author(s):  
Ibrahim Sule ◽  
Sani Ibrahim Doguwa ◽  
Audu Isah ◽  
Haruna Muhammad Jibril
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Logistic Distribution ◽  
Data Sets ◽  
Medical Sciences ◽  
Cancer Disease ◽  
Underlying Distribution ◽  
New Family ◽  
The Family ◽  
Family Of Distributions

Background: In the last few years, statisticians have introduced new generated families of univariate distributions. These new generators are obtained by adding one or more extra shape parameters to the underlying distribution to get more flexibility in fitting data in different areas such as medical sciences, economics, finance and environmental sciences. The addition of parameter(s) has been proven useful in exploring tail properties and also for improving the goodness-of-fit of the family of distributions under study. Methods: A new three-parameter family of distributions was introduced by using the idea of T-X methodology. Some statistical properties of the new family were derived and studied. Results: A new Topp Leone Kumaraswamy-G family of distributions was introduced. Two special sub-models, that is, the Topp Leone Kumaraswamy exponential distribution and Topp Leone Kumaraswamy log-logistic distribution were investigated. Two real data sets were used to assess the flexibility of the sub-models. Conclusion: The results suggest that the two sub-models performed better than their competitors.

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