A general procedure to combine estimators

Lavancier, Frédéric; Rochet, Paul

doi:10.1016/j.csda.2015.08.001

Cited by 47 publications

(49 citation statements)

References 28 publications

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“…Moreover, the minimum contrast estimates obtained from the pair correlation and the K ‐function can be combined to provide a better estimate. We refer to Lavancier & Rochet () for details and consider just the example of two estimators

{\overset{q}{true}}_{g}

and

{\overset{q}{true}}_{K}

for q . Then the idea is to seek the weights

(λ_{1}, λ_{2}) \in {double-struckR}^{2}

with λ 1 + λ 2 =1 such that the linear combination

λ_{1} {\overset{q}{true}}_{g} + λ_{2} {\overset{q}{true}}_{K}

has a minimal mean squared error.…”

Section: Simulation and Inferencementioning

confidence: 99%

Modelling Aggregation on the Large Scale and Regularity on the Small Scale in Spatial Point Pattern Datasets

Lavancier

Møller

2015

Scandinavian J Statistics

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We consider a dependent thinning of a regular point process with the aim of obtaining aggregation on the large scale and regularity on the small scale in the resulting target point process of retained points. Various parametric models for the underlying processes are suggested and the properties of the target point process are studied. Simulation and inference procedures are discussed when a realization of the target point process is observed, depending on whether the thinned points are observed or not. The paper extends previous work by Dietrich Stoyan on interrupted point processes.

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{\overset{q}{true}}_{g}

and

{\overset{q}{true}}_{K}

for q . Then the idea is to seek the weights

(λ_{1}, λ_{2}) \in {double-struckR}^{2}

with λ 1 + λ 2 =1 such that the linear combination

λ_{1} {\overset{q}{true}}_{g} + λ_{2} {\overset{q}{true}}_{K}

has a minimal mean squared error.…”

Section: Simulation and Inferencementioning

confidence: 99%

Modelling Aggregation on the Large Scale and Regularity on the Small Scale in Spatial Point Pattern Datasets

Lavancier

Møller

2015

Scandinavian J Statistics

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“…as n → ∞. If V = 0, then, from Chebyshev inequality, L φ(n) converges to a Dirac mass at zero and so (29) does not hold, yielding a contradiction.…”

Section: A2 Proofs Of the Main Resultsmentioning

confidence: 97%

Asymptotic properties of the maximum likelihood and cross validation estimators for transformed Gaussian processes

Bachoc¹,

Betancourt²,

Furrer

et al. 2020

Electron. J. Statist.

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The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of non-Gaussian processes obtained by regular nonlinear transformations of Gaussian processes. We provide the increasingdomain asymptotic properties of the (Gaussian) maximum likelihood and cross validation estimators of the covariance parameters of a non-Gaussian process of this class. We show that these estimators are consistent and asymptotically normal, although they are defined as if the process was Gaussian. They do not need to model or estimate the non-linear transformation. Our results can thus be interpreted as a robustness of (Gaussian) maximum likelihood and cross validation towards non-Gaussianity. Our proofs rely on two technical results that are of independent interest for the increasing-domain asymptotic literature of spatial processes. First, we show that, under mild assumptions, coefficients of inverses of large covariance matrices decay at an inverse polynomial rate as a function of the corresponding observation location distances. Second, we provide a general central limit theorem for quadratic forms obtained from transformed Gaussian processes. Finally, our asymptotic results are illustrated by numerical simulations.

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“…and setf = (f h1 , ...,f h k ) . Following [LR16], we consider an estimator of f expressed as a linear combination of thef hi 's,…”

Section: The Average Estimatormentioning

confidence: 99%

Averaging of density kernel estimators

Chernova

Lavancier

Rochet

2020

Statistics & Probability Letters

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A general procedure to combine estimators

Cited by 47 publications

References 28 publications

Modelling Aggregation on the Large Scale and Regularity on the Small Scale in Spatial Point Pattern Datasets

Modelling Aggregation on the Large Scale and Regularity on the Small Scale in Spatial Point Pattern Datasets

Asymptotic properties of the maximum likelihood and cross validation estimators for transformed Gaussian processes

Averaging of density kernel estimators

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