Nonparametric Versus Parametric Goodness of Fit

Liero, Hannelore; Läuter, H.; Konakov, Valentin

doi:10.1080/02331889808802632

Cited by 13 publications

(9 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…. , p, are bounded for θ in a neighborhood of θ 0 for all x (for more details, see [5,18,24]), the same cutoff points may be used for testing the specified composite hypothesis using statistic ξ W (x, θ n ). This is due to the fact that the normalizing factor √ n in the Kolmogorov-Smirnov test statistic is of the same order as the square of the rate of consistency of the parameter estimator, while in the density test case this factor is n|W | which tends to infinity slower.…”

Section: Analytical Approximation Of the Null Distribution Of The Stamentioning

confidence: 99%

“…A comprehensive review of the goodness of fit density tests is presented in the recent paper by Gonzalez et al [12]. With some exceptions, see [18], particular attention in the overwhelming majority of mentioned works were devoted to the criteria based on L p , p = 1, 2, distance between the density estimate f (x) = f (x, X n ) and its expected value under the null hypothesis. This is presumably explained by the more competitive performance of integrated distance tests against a wide range of practical alternatives in comparison with sumpremum-type density tests, which are the objective of this paper.…”

Section: Introductionmentioning

confidence: 99%

“…Consideration of the deviations in the uniform metric is justified by the investigation of a specific type of alternative hypothesis, where the null distribution is contaminated with a small tight cluster. Similar "sharp peak" alternatives in univariate case were also considered in [11,18].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multivariate goodness-of-fit tests based on kernel density estimators

Bakshaev

Rudzkis

2015

NAMC

View full text Add to dashboard Cite

The paper is devoted to multivariate goodness-of-fit ests based on kernel density estimators. Both simple and composite null hypotheses are investigated. The test statistic is considered in the form of maximum of the normalized deviation of the estimate from its expected value. The produced comparative Monte Carlo power study shows that the proposed test is a powerful competitor to the existing classical criteria for testing goodness of fit against a specific type of an alternative hypothesis. An analytical way to establish the asymptotic distribution of the test statistic is discussed, using the approximation results for the probabilities of high excursions of differentiable Gaussian random fields.

show abstract

Section: Analytical Approximation Of the Null Distribution Of The Stamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multivariate goodness-of-fit tests based on kernel density estimators

Bakshaev

Rudzkis

2015

NAMC

View full text Add to dashboard Cite

show abstract

“…The number of selected functions in the expansion turns out to be a smoothing parameter, and testing the null hypothesis reduces to test the nullity of the coefficients in the expansion.This can be done thanks to likelihood ratio or score test statistics with a datadriven calibration of the smoothing parameter; see Ledwina (1994) or Fan (1996). Another popular approach for testing a parametric model versus a non-parametric alternative is to reject the null hypothesis if a non-parametric estimator is too far from a parametric estimator computed under the null hypothesis; see among others Hardle & Mammen (1993), Alcalá et al (1999), Stute & González-Manteiga (1996), Hart (1997), Liero et al (1998), Liero & Läuter (2006). In the aforementioned papers, the alternative is not subjected to a monotonicity constraint.…”

Section: Introductionmentioning

confidence: 99%

Goodness-of-Fit Test for Monotone Functions

Durot

Reboul

2010

Scandinavian Journal of Statistics

View full text Add to dashboard Cite

ABSTRACT. In this article, we develop a test for the null hypothesis that a real-valued function belongs to a given parametric set against the non-parametric alternative that it is monotone, say decreasing. The method is described in a general model that covers the monotone density model, the monotone regression and the right-censoring model with monotone hazard rate. The criterion for testing is an L L L L p -distance between a Grenander-type non-parametric estimator and a parametric estimator computed under the null hypothesis. A normalized version of this distance is shown to have an asymptotic normal distribution under the null, whence a test can be developed. Moreover, a bootstrap procedure is shown to be consistent to calibrate the test.

show abstract

“…Down-weighting the tails of the distribution is a desirable feature for many applications. The choice of the supremum norm is motivated by its sensitivity to local violations of monotonicity (see Liero et al 1998) and by the fact that it results in a relevant and interpretable measure of the deviation from the null model. It is shown in Section 4 that the evaluation of this distance T n 4c5 reduces to the computation of a simple expression and that computing the MLE O f c n for various scales c goes hand in hand with the workings of the iterative algorithm employed.…”

Section: The Multiscale Mlementioning

confidence: 99%

Detecting the Presence of Mixing with Multiscale Maximum Likelihood

Walther

2002

Journal of the American Statistical Association

View full text Add to dashboard Cite

A test of homogeneity tries to decide whether observations come from a single distribution or from a mixture of several distributions. A powerful theory has been developed for the case where the component distributions are members of an exponential family. When no parametric assumptions are appropriate, the standard approach is to test for bimodality, which is known not to be very sensitive for detecting heterogeneity. To develop a more sensitive procedure, this article builds on an approach employed in sampling literature and models the component distributions as logarithmically concave densities. It is shown how this leads to a special semiparametric model, in which the homogeneity problem is equivalent to testing whether a parameter c equals zero, versus the alternative that c > 0. This setup leads naturally to a novel multiscale maximum likelihood procedure, where the multiscale character re ects the desirable property of adaptivity to the unknown value of the parameter c under the alternative, to ensure a test with high power. The test can also be extended, in principle, to a multivariate situation. In a univariate setting, the multiscale procedure is well suited to computation with the iterative convex minorant algorithm, a recent innovation in computational nonparametric statistics. The test is applied to simulated data and to the stamp data of Izenman and Sommer.

show abstract

Nonparametric Versus Parametric Goodness of Fit

Cited by 13 publications

References 7 publications

Multivariate goodness-of-fit tests based on kernel density estimators

Multivariate goodness-of-fit tests based on kernel density estimators

Goodness-of-Fit Test for Monotone Functions

Detecting the Presence of Mixing with Multiscale Maximum Likelihood

Contact Info

Product

Resources

About