Displaying similar documents to “Adaptive tests of homogeneity for a Poisson process”

Test for exponentiality against Weibull and gamma decreasing hazard rate alternatives

Simos G. Meintanis (2007)

Kybernetika

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A sub-exponential Weibull random variable may be expressed as a quotient of a unit exponential to an independent strictly positive stable random variable. Based on this property, we propose a test for exponentiality which is consistent against Weibull and Gamma distributions with shape parameter less than unity. A comparison with other procedures is also included.

Testing randomness of spatial point patterns with the Ripley statistic

Gabriel Lang, Eric Marcon (2013)

ESAIM: Probability and Statistics

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Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness corresponding to a homogeneous Poisson point process. We first compute the exact first and second moment of the Ripley -statistic under the homogeneous Poisson point process model. Then we prove the asymptotic normality of a vector of such statistics...

Contiguity and LAN-property of sequences of Poisson processes

Friedrich Liese, Udo Lorz (1999)

Kybernetika

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Using the concept of Hellinger integrals, necessary and sufficient conditions are established for the contiguity of two sequences of distributions of Poisson point processes with an arbitrary state space. The distribution of logarithm of the likelihood ratio is shown to be infinitely divisible. The canonical measure is expressed in terms of the intensity measures. Necessary and sufficient conditions for the LAN-property are formulated in terms of the corresponding intensity measures. ...

Checking proportional rates in the two-sample transformation model

David Kraus (2009)

Kybernetika

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Transformation models for two samples of censored data are considered. Main examples are the proportional hazards and proportional odds model. The key assumption of these models is that the ratio of transformation rates (e. g., hazard rates or odds rates) is constant in time. A~method of verification of this proportionality assumption is developed. The proposed procedure is based on the idea of Neyman's smooth test and its data-driven version. The method is suitable for detecting monotonic...

On the role played by the fixed bandwidth in the Bickel-Rosenblatt goodness-of-fit test.

Carlos Tenreiro (2005)

SORT

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For the Bickel-Rosenblatt goodness-of-fit test with fixed bandwidth studied by Fan (1998) we derive its Bahadur exact slopes in a neighbourhood of a simple hypothesis f = f and we use them to get a better understanding on the role played by the smoothing parameter in the detection of departures from the null hypothesis. When f is an univariate normal distribution and we take for kernel the standard normal density function, we compute these slopes for a set of Edgeworth alternatives which...