Critical dimension in profile semiparametric estimation

Andresen, Andreas; Spokoiny, Vladimir

doi:10.1214/14-ejs982

Cited by 7 publications

(22 citation statements)

References 27 publications

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“…The random variable ξ ∈ IR p and the matrix D ∈ IR p×p are related to the efficient influence function in semiparametric models and its covariance. These are up to ρ k R 0 the same properties as those proven for the pME in Andresen and Spokoiny (2013) k) with some 0 < τ < 1 and…”

Section: Introductionsupporting

confidence: 74%

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Two convergence results for an alternation maximization procedure

Andresen,

Spokoiny

2015

Preprint

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Andresen and Spokoiny's (2013) "critical dimension in semiparametric estimation" provide a technique for the finite sample analysis of profile M-estimators. This paper uses very similar ideas to derive two convergence results for the alternating procedure to approximate the maximizer of random functionals such as the realized log likelihood in MLE estimation. We manage to show that the sequence attains the same deviation properties as shown for the profile M-estimator in Andresen and Spokoiny (2013), i.e. a finite sample Wilks and Fisher theorem.Further under slightly stronger smoothness constraints on the random functional we can show nearly linear convergence to the global maximizer if the starting point for the procedure is well chosen.

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Section: Introductionsupporting

confidence: 74%

“…We address this difficulty via employing new finite sample techniques of Andresen and Spokoiny (2013) and Spokoiny (2012) which allow to answer the above questions:…”

Section: Introductionmentioning

confidence: 99%

Two convergence results for an alternation maximization procedure

Andresen,

Spokoiny

2015

Preprint

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“…The finite sample deviation and large deviations bound of quasi-MLE under model misspecification is discussed in Spokoiny (2012). Similar results for semiparametric models are presented in Andresen and Spokoiny (2014). An interesting future development is the exact large deviations rate under this setting.…”

Section: Discussionmentioning

confidence: 66%

Chernoff index for Cox test of separate parametric families

Liu

Ying

2018

Ann. Statist.

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The asymptotic efficiency of a generalized likelihood ratio test proposed by Cox is studied under the large deviations framework for error probabilities developed by Chernoff. In particular, two separate parametric families of hypotheses are considered (Cox, 1961, 1962). The significance level is set such that the maximal type I and type II error probabilities for the generalized likelihood ratio test decay exponentially fast with the same rate. We derive the analytic form of such a rate that is also known as the Chernoff index (Chernoff, 1952), a relative efficiency measure when there is no preference between the null and the alternative hypotheses. We further extend the analysis to approximate error probabilities when the two families are not completely separated. Discussions are provided concerning the implications of the present result on model selection.

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“…Our results are consistent with the conclusion of that papers. We refer to Andresen and Spokoiny (2014) for a version of such result in context of semiparametric profile estimation. That paper also provides an example of an i.i.d.…”

Section: Quasi Mle In An Iid Modelmentioning

confidence: 99%

Penalized maximum likelihood estimation and effective dimension

Spokoiny

2017

Ann. Inst. H. Poincaré Probab. Statist.

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This paper extends some prominent statistical results including Fisher Theorem and Wilks phenomenon to the penalized maximum likelihood estimation with a quadratic penalization. It appears that sharp expansions for the penalized MLE θ G and for the penalized maximum likelihood can be obtained without involving any asymptotic arguments, the results only rely on smoothness and regularity properties of the of the considered log-likelihood function. The error of estimation is specified in terms of the effective dimension p G of the parameter set which can be much smaller than the true parameter dimension and even allows an infinite dimensional functional parameter. In the i.i.d. case, the Fisher expansion for the penalized MLE can be established under the constraint " p

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Critical dimension in profile semiparametric estimation

Cited by 7 publications

References 27 publications

Two convergence results for an alternation maximization procedure

Two convergence results for an alternation maximization procedure

Chernoff index for Cox test of separate parametric families

Penalized maximum likelihood estimation and effective dimension

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