Comparison of the Goodness-of-Fit Tests for Truncated Distributions

2019 ◽  
Vol 65 (3) ◽  
pp. 296-313
Author(s):  
Agnieszka Lach ◽  
Łukasz Smaga
Keyword(s):  
Goodness Of Fit ◽  
Asset Returns ◽  
Finite Sample ◽  
Simulation Experiments ◽  
Testing Procedures ◽  
The Past ◽  
Truncated Distributions ◽  
Finite Samples ◽  
Goodness Of Fit Tests ◽  
Power Simulation

The aim of this paper is to investigate the finite sample behavior of seven goodness-of-fit tests for left truncated distributions of Chernobai et al. (2015) in terms of size and power. Simulation experiments are based on artificial data generated from the distributions that were used in the past or are used nowadays to describe the tails of asset returns. The study was conducted for different tail thickness and for changing truncation point. Simulation results indicate that the testing procedures do not work equally well under finite samples, and some of them require quite large number of observations to perform satisfactorily.

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.

A guided nonparametric goodness-of-fit test with application to income distributions

2019 ◽  
Vol 22 (3) ◽  
pp. 207-222
Author(s):  
Kuangyu Wen ◽  
Ximing Wu
Keyword(s):  
Goodness Of Fit ◽  
Bias Reduction ◽  
Density Estimator ◽  
Consistent Estimate ◽  
Finite Sample ◽  
Goodness Of Fit Test ◽  
Normal Mixtures ◽  
Parametric Density ◽  
Income Distributions ◽  
Goodness Of Fit Tests

Summary We have developed a customizable goodness-of-fit test of a parametric density based on its distance to a consistently estimated density. This consistent estimate is obtained via a nonparametric density estimator with a parametric start, wherein the start is set to be the hypothesized parametric density. To cope with the influence of nonparametric estimation bias, nonparametric goodness-of-fit tests have resorted to remedies such as undersmoothing or convolution of the hypothesized density. Our test requires no such devices and possesses enhanced powers against alternative densities because the guided density estimator is free of the typical nonparametric bias under the null hypothesis and attains bias reduction when the underlying density is in a broad nonparametric neighborhood of the hypothesized density. Here, we establish the statistical properties of our test and use Monte Carlo simulations to demonstrate its finite sample performance. We use this test to examine the goodness-of-fit of normal mixtures to the distributions of log income of U.S. states. Although normality is rejected decisively, our results suggest that normal mixtures with two or three components suffice for all but one state.

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 Testing for goodness rather than lack of fit of continuous probability distributions

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0256499
Author(s):  
Stefan Wellek
Keyword(s):  
Goodness Of Fit ◽  
Alternative Hypothesis ◽  
Probability Distributions ◽  
Testing Procedure ◽  
Discrete Distributions ◽  
Testing Procedures ◽  
Continuous Type ◽  
Goodness Of Fit Tests ◽  
True Distribution

The vast majority of testing procedures presented in the literature as goodness-of-fit tests fail to accomplish what the term is promising. Actually, a significant result of such a test indicates that the true distribution underlying the data differs substantially from the assumed model, whereas the true objective is usually to establish that the model fits the data sufficiently well. Meeting that objective requires to carry out a testing procedure for a problem in which the statement that the deviations between model and true distribution are small, plays the role of the alternative hypothesis. Testing procedures of this kind, for which the term tests for equivalence has been coined in statistical usage, are available for establishing goodness-of-fit of discrete distributions. We show how this methodology can be extended to settings where interest is in establishing goodness-of-fit of distributions of the continuous type.

scholarly journals Goodness-of-fit test for $$\alpha$$-stable distribution based on the quantile conditional variance statistics

2021 ◽  
Author(s):  
Marcin Pitera ◽  
Aleksei Chechkin ◽  
Agnieszka Wyłomańska
Keyword(s):  
Goodness Of Fit ◽  
Stable Distribution ◽  
Heavy Tails ◽  
Stable Distributions ◽  
Symmetric Case ◽  
Goodness Of Fit Test ◽  
Testing Procedures ◽  
Alpha Stable Distribution ◽  
Goodness Of Fit Tests ◽  
Distributional Properties

AbstractThe class of $$\alpha$$ α -stable distributions is ubiquitous in many areas including signal processing, finance, biology, physics, and condition monitoring. In particular, it allows efficient noise modeling and incorporates distributional properties such as asymmetry and heavy-tails. Despite the popularity of this modeling choice, most statistical goodness-of-fit tests designed for $$\alpha$$ α -stable distributions are based on a generic distance measurement methods. To be efficient, those methods require large sample sizes and often do not efficiently discriminate distributions when the corresponding $$\alpha$$ α -stable parameters are close to each other. In this paper, we propose a novel goodness-of-fit method based on quantile (trimmed) conditional variances that is designed to overcome these deficiencies and outperforms many benchmark testing procedures. The effectiveness of the proposed approach is illustrated using extensive simulation study with focus set on the symmetric case. For completeness, an empirical example linked to plasma physics is provided.

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.

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