Model selection for Poisson processes with covariates

Sart, Mathieu

doi:10.1051/ps/2014022

Cited by 4 publications

(6 citation statements)

References 16 publications

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“…When applied to the discretized models S η used for the construction of T-estimators, Baraud's estimators can be viewed as a particular version of T-estimators, but this alternative construction allows to relax some of the assumptions needed for the use of T-estimators. The procedure has been taken back later by Sart (2014;2015) in a context of dependent data. A modification of Baraud's construction, following an idea of Sart, finally led to the construction of ρ-estimators that we shall present here.…”

Section: 4mentioning

confidence: 99%

A new method for estimation and model selection: $$\rho $$ ρ -estimation

2016

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Abstract. The aim of this paper is to present a new estimation procedure that can be applied in various statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density estimation, they asymptotically coincide with the celebrated maximum likelihood estimators at least when the statistical model is regular enough and contains the true density to estimate. For very general models of densities, including non-compact ones, these estimators are robust with respect to the Hellinger distance and converge at optimal rate (up to a possible logarithmic factor) in all cases we know. In the regression setting, our approach improves upon the classical least squares in many respects. In simple linear regression for example, it provides an estimation of the coefficients that are both robust to outliers and simultaneously rateoptimal (or nearly rate-optimal) for a large class of error distributions including Gaussian, Laplace, Cauchy and uniform among others.

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Section: 4mentioning

confidence: 99%

A new method for estimation and model selection: $$\rho $$ ρ -estimation

2016

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“…Remarks. The definition of T comes from a decomposition of the Hellinger distance initiated by Baraud (2011) and taken back in Baraud (2013); Sart (2014Sart ( , 2015; Baraud et al (2016). We shall show in the proof of Theorem 1 that for all f, f ′ ∈ L(A, µ), ξ > 0, the two following assertions hold true with probability larger than 1 − e −nξ :…”

Section: Selection Rule and Main Theorem Letmentioning

confidence: 99%

Estimating the conditional density by histogram type estimators and model selection

Sart

2017

ESAIM: PS

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Abstract. We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By using a deterministic Hellinger distance as loss, we prove that the selected function satisfies a non-asymptotic oracle type inequality under minimal assumptions on the statistical setting. We derive an adaptive piecewise constant estimator on a random partition that achieves the expected rate of convergence over (possibly inhomogeneous and anisotropic) Besov spaces of small regularity. Moreover, we show that this oracle inequality may lead to a general model selection theorem under very mild assumptions on the statistical setting. This theorem guarantees the existence of estimators possessing nice statistical properties under various assumptions on the conditional density (such as smoothness or structural ones).Mathematics Subject Classification. 62G05, 62G07.

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“…More recently, Birgé [9] significantly extended the scope of these procedures by relating them to the problem of model selection, providing at the same time new perspectives on estimation theory. It gave birth to a series of papers; see Birgé [10][11][12], Baraud and Birgé [4], Baraud [2,3], Sart [26,27], Baraud et al [5]. The main feature of these procedures is that they allow to obtain general theoretical results in various statistical settings (such as general model selection theorems) which are usually unattainable by the traditional procedures (such as those based on the minimization of a penalized contrast).…”

Section: Estimation Via Testingmentioning

confidence: 99%

Robust estimation on a parametric model via testing

Sart¹

2016

Bernoulli

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We are interested in the problem of robust parametric estimation of a density from n i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk bounds with respect to the Hellinger distance under mild assumptions on the parametric model. We show that the estimator is robust even for models for which the maximum likelihood method is bound to fail. A numerical simulation illustrates its robustness properties. When the model is true and regular enough, we prove that the estimator is very close to the maximum likelihood one, at least when the number of observations n is large. In particular, it inherits its efficiency. Simulations show that these two estimators are almost equal with large probability, even for small values of n when the model is regular enough and contains the true density.

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Model selection for Poisson processes with covariates

Cited by 4 publications

References 16 publications

A new method for estimation and model selection: $$\rho $$ ρ -estimation

A new method for estimation and model selection: $$\rho $$ ρ -estimation

Estimating the conditional density by histogram type estimators and model selection

Robust estimation on a parametric model via testing

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