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 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 Estimation of flood frequency using statistical method: Mahanadi River basin, India

2020 ◽  
Vol 3 (1) ◽  
pp. 189-207
Author(s):  
Sandeep Samantaray ◽  
Abinash Sahoo
Keyword(s):  
Stream Flow ◽  
Goodness Of Fit ◽  
Central India ◽  
Extreme Value ◽  
Flood Frequency ◽  
Goodness Of Fit Test ◽  
Mahanadi River ◽  
Goodness Of Fit Tests ◽  
Study Results ◽  
Anderson Darling

Abstract Estimating stream flow has a substantial financial influence, because this can be of assistance in water resources management and provides safety from scarcity of water and conceivable flood destruction. Four common statistical methods, namely, Normal, Gumbel max, Log-Pearson III (LP III), and Gen. extreme value method are employed for 10, 20, 30, 35, 40, 50, 60, 70, 75, 100, 150 years to forecast stream flow. Monthly flow data from four stations on Mahanadi River, in Eastern Central India, namely, Rampur, Sundargarh, Jondhra, and Basantpur, are used in the study. Results show that Gumbel max gives better flow discharge value than the Normal, LP III, and Gen. extreme value methods for all four gauge stations. Estimated flood values for Rampur, Sundargarh, Jondhra, and Basantpur stations are 372.361 m3/sec, 530.415 m3/sec, 2,133.888 m3/sec, and 3,836.22 m3/sec, respectively, considering Gumbel max. Goodness-of-fit tests for four statistical distribution techniques applied in the present study are also evaluated using Kolmogorov–Smirov, Anderson–Darling, Chi-squared tests at critical value 0.05 for the four proposed gauge stations. Goodness-of-fit test results show that Gen. extreme value gives best results at Rampur, Sundergarh, and Jondhra gauge stations followed by LP III, whereas LP III is the best fit for Basantpur, followed by Gen. extreme value.

scholarly journals Goodness of Fit Tests for Marshal-Olkin Extended Rayleigh Distribution

2019 ◽  
pp. 587-598
Author(s):  
Naz Saud ◽  
Sohail Chand
Keyword(s):  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Rayleigh Distribution ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Estimated Parameters ◽  
Percentage Points ◽  
Anderson Darling ◽  
Von Mises

A class of goodness of fit tests for Marshal-Olkin Extended Rayleigh distribution with estimated parameters is proposed. The tests are based on the empirical distribution function. For determination of asymptotic percentage points, Kolomogorov-Sminrov, Cramer-von-Mises, Anderson-Darling,Watson, and Liao-Shimokawa test statistic are used. This article uses Monte Carlo simulations to obtain asymptotic percentage points for Marshal-Olkin extended Rayleigh distribution. Moreover, power of the goodness of fit test statistics is investigated for this lifetime model against several alternatives.

scholarly journals A general goodness-of-fit test for survival analysis

2017 ◽  
Author(s):  
Michael Holton Price ◽  
James Holland Jones
Keyword(s):  
Survival Data ◽  
Goodness Of Fit ◽  
Proportional Hazards ◽  
Specific Model ◽  
Early Event ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Martingale Residual ◽  
Late Event ◽  
Event Occurrence

AbstractExisting goodness-of-fit tests for survival data are either exclusively graphical in nature or only test specific model assumptions, such as the proportional hazards assumption. We describe a flexible, parameter-free goodness-of-fit test that provides a simple numerical assessment of a model’s suitability regardless of the structure of the underlying model. Intuitively, the goodness-of-fit test utilizes the fact that for a good model early event occurrence is predicted to be just as likely as late event occurrence, whereas a bad model has a bias towards early or late events. Formally, the goodness-of-fit test is based on a novel generalized Martingale residual which we call the martingale survival residual. The martingale survival residual has a uniform probability density function defined on the interval −0.5 to +0.5 if censoring is either absent or accounted for as one outcome in a competing hazards framework. For a good model, the set of calculated residuals is statistically indistinguishable from the uniform distribution, which is tested using the Kolmogorov-Smirnov statistic.

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.

CHARACTERISTIC FUNCTION–BASED TESTING FOR MULTIFACTOR CONTINUOUS-TIME MARKOV MODELS VIA NONPARAMETRIC REGRESSION

2009 ◽  
Vol 26 (4) ◽  
pp. 1115-1179 ◽  
Author(s):  
Bin Chen ◽  
Yongmiao Hong
Keyword(s):  
Characteristic Function ◽  
Nonparametric Regression ◽  
Continuous Time ◽  
Goodness Of Fit ◽  
Markov Models ◽  
Computational Cost ◽  
Model Specification ◽  
Finite Sample ◽  
Asymptotic Results ◽  
Goodness Of Fit Test

We develop a nonparametric regression-based goodness-of-fit test for multifactor continuous-time Markov models using the conditional characteristic function, which often has a convenient closed form or can be approximated accurately for many popular continuous-time Markov models in economics and finance. An omnibus test fully utilizes the information in the joint conditional distribution of the underlying processes and hence has power against a vast class of continuous-time alternatives in the multifactor framework. A class of easy-to-interpret diagnostic procedures is also proposed to gauge possible sources of model misspecification. All the proposed test statistics have a convenient asymptotic N(0, 1) distribution under correct model specification, and all asymptotic results allow for some data-dependent bandwidth. Simulations show that in finite samples, our tests have reasonable size, thanks to the dimension reduction in nonparametric regression, and good power against a variety of alternatives, including misspecifications in the joint dynamics, but the dynamics of each individual component is correctly specified. This feature is not attainable by some existing tests. A parametric bootstrap improves the finite-sample performance of proposed tests but with a higher computational cost.

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.

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.

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