Minimum distance estimators for count data based on the probability generating function with applications

Jiménez-Gamero, M. D.; Batsidis, Apostolos

doi:10.1007/s00184-017-0614-3

Cited by 23 publications

(5 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The literature related to the so-called "goodness-of-fit" inferential setting is huge (e.g., [30] or, more recently, [24] and [21]) and suitable test statistics for assessing (1) are often based on the properties of the probability generating function (p.g.f.) (e.g., [31], [32], [25], [17], [4], [29]). Meintainis and Nikitin [26] have proposed families of consistent test statistics for Poissonity based on differential equations concerning the p.g.f.…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Goodness-of-fit test for count distributions with finite second moment

Noia¹,

Barabesi²,

Marcheselli³

et al. 2021

Preprint

View full text Add to dashboard Cite

A consistent omnibus goodness-of-fit test for count distributions is proposed. The test is of wide applicability since any count distribution indexed by a k-variate parameter with finite moment of order 2k can be considered under the null hypothesis. The test statistic is based on the probability generating function and, in addition to have a rather simple form, it is asymptotically normally distributed, allowing a straightforward implementation of the test. The finite-sample properties of the test are investigated by means of an extensive simulation study, where the empirical power is evaluated against some common alternative distributions and against contiguous alternatives. The test shows an empirical significance level always very close to the nominal one already for moderate sample sizes and the empirical power is rather satisfactory, also compared to that of the chi-squared test.

show abstract

Section: Preliminariesmentioning

confidence: 99%

“…against alternatives belonging to a large family. In a more general framework, Jiménez-Gamero and Batsidis [17] presented a test statistic based on a distance between the empirical p.g.f. and the p.g.f.…”

Section: Introductionmentioning

confidence: 99%

Goodness-of-fit test for count distributions with finite second moment

Noia¹,

Barabesi²,

Marcheselli³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The fact that the specific small portion of data is sufficient for testing purposes is due to the fact that this part of the data is associated with a tail characterization that distinguishes exponential and non-exponential distributions. As opposed to classical tests (see e.g., Baratpour and Rad 2012;Huber-Carol et al 2002;Jimenez-Gamero and Batsidis 2017;Novikov et al 2015;Rogozhnikov and Lemeshko 2012;Vonta et al 2012), in this work, the emphasis is placed exclusively on the tail by ignoring the rest of the distribution. It should be noted that although classical tests based on the entire dataset often fail to reject a null hypothesis, the proposed testing procedure checks the fit of the tail and makes a decision exclusively on the available data from the extreme part of the distribution.…”

Section: Introductionmentioning

confidence: 98%

An Exponentiality Test of Fit Based on a Tail Characterization against Heavy and Light-Tailed Alternatives

Karagrigoriou,

Mavrogiannis,

Papasotiriou

et al. 2023

Risks

View full text Add to dashboard Cite

Log-concavity and log-convexity play a key role in various scientific fields, especially in those where the distinction between exponential and non-exponential distributions is necessary for inferential purposes. In the present study, we introduce a testing procedure for the tail part of a distribution which can be used for the distinction between exponential and non-exponential distributions. The conspiracy and catastrophe principles are initially used to establish a characterization of (the tail part of) the exponential distribution, which is one of the main contributions of the present work, leading the way for the construction of the new test of fit. The proposed test and its implementation are thoroughly discussed, and an extended simulation study has been undertaken to clarify issues related to its implementation and explore the extent of its capabilities. A real data case is also investigated.

show abstract

“…We often state that divergences measure the discrepancy between two probability distributions or the information needed in order to distinguish one from the other. There is plethora of estimators and hypothesis tests associated with such measures for several cases [3,4], many tests of fit based on measures of divergence and take into account dissimilarities between the distributions involved [5] or based on maximum entropy principle [6]. Also, model selection criteria [7][8][9] are based on such type of information measures.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Aspects on Measures of Directed Information with Simulations

Gkelsinis

Karagrigoriou

2020

Mathematics

View full text Add to dashboard Cite

Measures of directed information are obtained through classical measures of information by taking into account specific qualitative characteristics of each event. These measures are classified into two main categories, the entropic and the divergence measures. Many times in statistics we wish to emphasize not only on the quantitative characteristics but also on the qualitative ones. For example, in financial risk analysis it is common to take under consideration the existence of fat tails in the distribution of returns of an asset (especially the left tail) and in biostatistics to use robust statistical methods to trim extreme values. Motivated by these needs in this work we present, study and provide simulations for measures of directed information. These measures quantify the information with emphasis on specific parts (or events) of their probability distribution, without losing the whole information of the less significant parts and at the same time by concentrating on the information of the parts we care about the most.

show abstract

Minimum distance estimators for count data based on the probability generating function with applications

Cited by 23 publications

References 35 publications

Goodness-of-fit test for count distributions with finite second moment

Goodness-of-fit test for count distributions with finite second moment

An Exponentiality Test of Fit Based on a Tail Characterization against Heavy and Light-Tailed Alternatives

Theoretical Aspects on Measures of Directed Information with Simulations

Contact Info

Product

Resources

About