A non-parametric estimator for the doubly periodic Poisson intensity function

Helmers, Roelof; Mangku, I Wayan; Zitikis, Ričardas

doi:10.1016/j.stamet.2007.02.002

Cited by 12 publications

(11 citation statements)

References 15 publications

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“…In this case the equation H [B w ] = H [F w ] + b holds for b = p, but it may not hold for other b. The use of periodic weight functions can be motivated by problems related to yearly circles or other periodic events (see, e.g., Lu and Garrido (2005), Helmers et al (2007)). Additivity-type properties of H [v, F w ].…”

Section: Invariance and Additivity-type Properties Of H[v F W ]mentioning

confidence: 99%

Weighted premium calculation principles

Furman

Zitikis

2008

Insurance: Mathematics and Economics

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117

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Section: Invariance and Additivity-type Properties Of H[v F W ]mentioning

confidence: 99%

Weighted premium calculation principles

Furman

Zitikis

2008

Insurance: Mathematics and Economics

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117

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“…In an inhomogeneous context with deterministic intensity function, Lu and Garrido [14] have fitted double-periodic Poisson intensity rates to hurricane data, for particular parametric forms (like double-beta and sine-beta intensities) to hurricane data. Helmers et al [8] have provided an in-depth theoretical statistical analysis of such doubly periodic intensities. We aim at carrying out a theoretical statistical analysis in a stochastic intensity framework with seasonality.…”

Section: Introductionmentioning

confidence: 99%

Estimating the parameters of a seasonal Markov-modulated Poisson process

Guillou

Loisel

Stupfler

2015

Statistical Methodology

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ADInternational audienceMotivated by seasonality and regime-switching features of some insurance claim counting processes, we study the statistical analysis of a Markov-modulated Poisson process featuring seasonality. We prove the strong consistency and the asymptotic normality of a maximum split-time likelihood estimator of the parameters of this model, and present an algorithm to compute it in practice. The method is illustrated on a small simulation study and a real data analysis

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“…Helmers et al ( , 2005 constructed and investigated a consistent kernel-type nonparametric estimator of the intensity function, where they used the periodogram-based estimator in Vere-Jones (1982) or the non-parametric estimator in as the frequency or period estimator. Helmers et al (2007) studied the doubly periodic Poisson model non-parametrically under the same assumptions as in Lu and Garrido (2005) that the longterm period is the integer multiple of the short-term period and both periods are known. The non-parametric prediction upper bound for a future observation of a cyclic Poisson process has been studied in Helmers and Mangku (2009).…”

Section: Introductionmentioning

confidence: 99%

Modelling Non-Homogeneous Poisson Processes with Almost Periodic Intensity Functions

Shao

Lii

2010

Journal of the Royal Statistical Society Series B: Statistical Methodology

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We propose a model for the analysis of non-stationary point processes with almost periodic rate of occurrence. The model deals with the arrivals of events which are unequally spaced and show a pattern of periodicity or almost periodicity, such as stock transactions and earthquakes. We model the rate of occurrence of a non-homogeneous Poisson process as the sum of sinusoidal functions plus a baseline. Consistent estimates of frequencies, phases and amplitudes which form the sinusoidal functions are constructed mainly by the Bartlett periodogram. The estimates are shown to be asymptotically normally distributed. Computational issues are discussed and it is shown that the frequency estimates must be resolved with order o.T 1 / to guarantee the asymptotic unbiasedness and consistency of the estimates of phases and amplitudes, where T is the length of the observation period. The prediction of the next occurrence is carried out and the mean-squared prediction error is calculated by Monte Carlo integration. Simulation and real data examples are used to illustrate the theoretical results and the utility of the model.

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A non-parametric estimator for the doubly periodic Poisson intensity function

Cited by 12 publications

References 15 publications

Weighted premium calculation principles

Weighted premium calculation principles

Estimating the parameters of a seasonal Markov-modulated Poisson process

Modelling Non-Homogeneous Poisson Processes with Almost Periodic Intensity Functions

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