Estimating the conditional density by histogram type estimators and model selection

Sart, Mathieu

doi:10.1051/ps/2016026

Cited by 7 publications

(10 citation statements)

References 26 publications

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“…From this point of view, our approach contrasts very much with that based on the classical least squares. An alternative point of view on the particular problem of estimating a conditional density can be found in Sart (2015).…”

mentioning

confidence: 99%

Rho-estimators revisited: General theory and applications

Baraud¹,

Birgé²

2018

Ann. Statist.

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Following Baraud et al. (2017), we pursue our attempt to design a robust universal estimator of the joint ditribution of n independent (but not necessarily i.i.d.) observations for an Hellinger-type loss. Given such observations with an unknown joint distribution P and a dominated model for P, we build an estimator P based on (a ρ-estimator) and measure its risk by an Hellinger-type distance. When P does belong to the model, this risk is bounded by some quantity which relies on the local complexity of the model in a vicinity of P. In most situations this bound corresponds to the minimax risk over the model (up to a possible logarithmic factor). When P does not belong to the model, its risk involves an additional bias term proportional to the distance between P and , whatever the true distribution P. From this point of view, this new version of ρ-estimators improves upon the previous one described in Baraud et al. (2017) which required that P be absolutely continuous with respect to some known reference measure. Further additional improvements have been brought as compared to the former construction. In particular, it provides a very general treatment of the regression framework with random design as well as a computationally tractable procedure for aggregating estimators. We also give some conditions for the Maximum Likelihood Estimator to be a ρ-estimator. Finally, we consider the situation where the Statistician has at his or her disposal many different models and we build a penalized version of the ρ-estimator for model selection and adaptation purposes. In the regression setting, this penalized estimator not only allows one to estimate the regression function but also the distribution of the errors.

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confidence: 99%

Rho-estimators revisited: General theory and applications

Baraud¹,

Birgé²

2018

Ann. Statist.

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“…Several nonparametric methods have been proposed to estimate conditional densities: kernel density estimators [Rosenblatt 1969 ;Hyndman et al 1996 ;Bertin et al 2016] and various methodologies for the selection of the associated bandwidth [Bashtannyk and Hyndman 2001 ;Fan and Yim 2004 ;Hall et al 2004]; local polynomial estimators [Fan et al 1996 ;Hyndman and Yao 2002]; projection series estimators [Efromovich 1999;2007]; piecewise constant estimator [Györfi and Kohler 2007 ;Sart 2017]; copula [Faugeras 2009]. But while most of the aforementioned works are only defined for bivariate data or at least when either X or Y is univariate, they are also computationally intractable as soon as d > 3.…”

Section: Existing Methodologiesmentioning

confidence: 99%

“…However the computation cost is prohibitive when both n and d are large. More recently, Izbicki and Lee have proposed two methodologies using orthogonal series estimators [Izbicki and Lee 2016;2017]. The first method is particularly fast and can handle very large X (with more than 1000 covariates).…”

Section: Existing Methodologiesmentioning

confidence: 99%

Nonparametric method for space conditional density estimation in moderately large dimensions

Nguyen

2018

Preprint

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In this paper, we consider the problem of estimating a conditional density in moderately large dimensions. Much more informative than regression functions, conditional densities are of main interest in recent methods, particularly in the Bayesian framework (studying the posterior distribution, finding its modes...). Considering a recently studied family of kernel estimators, we select a pointwise multivariate bandwidth by revisiting the greedy algorithm Rodeo (Regularisation Of Derivative Expectation Operator). The method addresses several issues: being greedy and computationally efficient by an iterative procedure, avoiding the curse of high dimensionality under some suitably defined sparsity conditions by early variable selection during the procedure, converging at a quasi-optimal minimax rate.

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“…The measurement PDF ( X Ψ ) may be obtained from the histogram of the samples of the random variable. Histograms can accurately compute PDFs [17,18] provided…”

Section: Estimator Realizationmentioning

confidence: 99%

A Nonlinear Subspace Approach for Parametric Estimation of PDFs From Short Data Records With Application to Rayleigh Fading

Masoud

2022

IEEE Access

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This paper tackles the issue of real-time parametric estimation of a wide class of probability density functions from limited datasets. This type of estimation addresses recent applications that require joint sensing and actuation. The suggested estimator operates in the nonlinear subspace that the parameter space of the distribution creates in the measurement sample space. This enables the estimator to embed a priori available information about the distribution in the computations to produce parameter estimates that are induced by signal components belonging only to the correct class of density functions being considered. It also enables it to nullify the effect of those components that do not belong to this class on the estimation process. The estimator can, with high accuracy, compute quickly the parameters of a wide class of probability density functions from short data records. The approach is developed and basic proofs of correctness are carried-out for the Rayleigh distribution, which is used to characterize wireless communication channels experiencing fast fading in heavily cluttered environments. Simulation results demonstrate the capabilities of the suggested procedure and the clear advantages it has over conventional norm-based estimation techniques. The results also show the ability of the suggested approach to estimate other density functions including the two-parameter lognormal distribution used to characterize shadowing in wireless communication.

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Estimating the conditional density by histogram type estimators and model selection

Cited by 7 publications

References 26 publications

Rho-estimators revisited: General theory and applications

Rho-estimators revisited: General theory and applications

Nonparametric method for space conditional density estimation in moderately large dimensions

A Nonlinear Subspace Approach for Parametric Estimation of PDFs From Short Data Records With Application to Rayleigh Fading

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