scholarly journals Nonparametric independence testing via mutual information

Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 547-566 ◽  
Author(s):  
T B Berrett ◽  
R J Samworth
Keyword(s):  
Mutual Information ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Real Data ◽  
Nearest Neighbour ◽  
Local Power ◽  
Goodness Of Fit Tests ◽  
Numerical Studies ◽  
Independence Testing ◽  
Power Analyses

Summary We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach is based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recently developed efficient entropy estimators derived from nearest neighbour distances. The proposed critical values may be obtained by simulation in the case where an approximation to one marginal is available or by permuting the data otherwise. This facilitates size guarantees, and we provide local power analyses, uniformly over classes of densities whose mutual information satisfies a lower bound. Our ideas may be extended to provide new goodness-of-fit tests for normal linear models based on assessing the independence of our vector of covariates and an appropriately defined notion of an error vector. The theory is supported by numerical studies on both simulated and real data.

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 Local Power Properties of Kernel Based Goodness of Fit Tests

2001 ◽  
Vol 78 (2) ◽  
pp. 161-190 ◽  
Author(s):  
Christian Gouriéroux ◽  
Carlos Tenreiro
Keyword(s):  
Goodness Of Fit ◽  
Local Power ◽  
Goodness Of Fit Tests ◽  
Power Properties

scholarly journals Goodness-of-fit tests in semi-linear models

2011 ◽  
Vol 22 (4) ◽  
pp. 967-979 ◽  
Author(s):  
Simos G. Meintanis ◽  
Jochen Einbeck
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Goodness Of Fit Tests

Stochastic model of contractions at a point in the duodenum

1975 ◽  
Vol 229 (3) ◽  
pp. 613-617 ◽  
Author(s):  
RB Singerman ◽  
EO Macagno ◽  
Glover ◽  
J Christensen
Keyword(s):  
Slow Wave ◽  
Goodness Of Fit ◽  
Human Subjects ◽  
Real Data ◽  
Type Model ◽  
Chi Square ◽  
Frequency Distributions ◽  
The Real ◽  
Goodness Of Fit Tests ◽  
Wave Cycle

Contractions at one point in the human duodenum were studied as a time series. Manometric records were made over long time periods from the duodenum in fed human subjects. A 5-s grid was superimposed on the time axis of the records. Each 5-s interval was treated as a slow-wave cycle within which either a contraction or a no-contraction could occur. The resulting series of alternating runs of contractions and no-contractions was tested for the existence of trends. Trends were found indicating possible temporal dependence. A Markov-type model was used to try to generate data similar to the real data. Success was achieved by a model that assumed a probability of contraction dependent on the three previous slow-wave cycles. The frequency distributions obtained from the real and generated data were compared using Chi-square goodness-of-fit tests and found to be statistically similar. The correlations in time found for the contractions might be due to a time dependency in the controls for contraction over four successive slow-wave periods, 20 s in humans.

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 R2ucare: An R package to perform goodness-of-fit tests for capture-recapture models

2017 ◽  
Author(s):  
Olivier Gimenez ◽  
Jean-Dominique Lebreton ◽  
Remi Choquet ◽  
Roger Pradel
Keyword(s):  
Statistical Model ◽  
Goodness Of Fit ◽  
Real Data ◽  
R Package ◽  
Goodness Of Fit Tests ◽  
State Capture ◽  
Capture Recapture ◽  
Quality Of Fit

Assessing the quality of fit of a statistical model to data is a necessary step for conducting safe inference. We introduce R2ucare, an R package to perform goodness-of-fit tests for open single- and multi-state capture-recapture models. R2ucare also has various functions to manipulate capture-recapture data. We remind the basics and provide guidelines to navigate towards testing the fit of capture-recapture models. We demonstrate the functionality of R2ucare through its application to real data.

NN goodness-of-fit tests for linear models

1996 ◽  
Vol 53 (1) ◽  
pp. 75-92 ◽  
Author(s):  
W. Stute ◽  
W.González Manteiga
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Goodness Of Fit Tests
Sign in / Sign up

Export Citation Format

Share Document