Inference and Prediction in Large Dimensions

Bosq, Denis; Blanke, Delphine

doi:10.1002/9780470724033

Cited by 96 publications

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“…We consider statistical prediction theory as an extension of statistical estimation theory as presented in Bosq and Blanke (2007). To put this extension in perspective we briefly recall the framework of statistical estimation before presenting the framework of statistical prediction.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Cramér–Rao inequality for prediction and efficient predictors

Onzon

2011

Statistics & Probability Letters

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Please cite this article as: Onzon, E., Multivariate Cramér-Rao inequality for prediction and efficient predictors. Statistics and Probability Letters (2010Letters ( ), doi:10.1016Letters ( /j.spl.2010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPTMultivariate Cramér-Rao inequality for prediction and efficient predictorsEmmanuel Onzon -UPMC LSTA AbstractWe derive and discuss a matricial Cramér-Rao type inequality for the quadratic prediction error matrix. A study of the attainment of the bound follows. Then we introduce an unbiased predictor for a bivariate Poisson process and prove that it is efficient, i.e. its quadratic error attains the Cramér-Rao bound.

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Section: Introductionmentioning

confidence: 99%

Multivariate Cramér–Rao inequality for prediction and efficient predictors

Onzon

2011

Statistics & Probability Letters

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“…Mean prediction of functional data has been studied before for the V ⊂ R case; Bosq (2006) provides a comprehensive account of the linear functional autoregressive process of order 1, Bosq and Blanke (2007) provides a general definition of the the functional autoregressive process (see page 243), whilst Kargin and Onatski (2008) develop the predictive factors procedure for one-step prediction under the same assumption. Although the theoretical properties obtained by Kargin and Onatski (2008) can be used to justify their procedure, the recent study of Didericksen (2012) shows that in finite samples, the predictive factors procedure never outperforms the approach of Bosq (2006), and in some cases performs poorly, even when the data are generated artificially as a functional autoregressive process of order 1, which we henceforth refer to as FAR(1).…”

Section: Introductionmentioning

confidence: 99%

Conditional estimation for dependent functional data

Battey

Sancetta

2013

Journal of Multivariate Analysis

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Suppose we observe a Markov chain taking values in a functional space. We are interested in exploiting the time series dependence in these infinite dimensional data in order to make non-trivial predictions about the future. Making use of the Karhunen Loève (KL) representation of functional random variables in terms of the eigenfunctions of the covariance operator, we present a deliberately over-simplified nonparametric model, which allows us to achieve dimensionality reduction by considering one dimensional nearest neighbour (NN) estimators for the transition distribution of the random coefficients of the KL expansion. Under regularity conditions, we show that the NN estimator is consistent even when the coefficients of the KL expansion are estimated from the observations. This also allows us to deduce consistency of conditional regression function estimators for functional data. We show via simulations and two empirical examples that the proposed NN estimator outperforms the state of the art when data are generated both by the functional autoregressive (FAR) model of Bosq (2006) and by more general data generating mechanisms.

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“…An account of the research in this field may be found e.g. in two complementary monographs by Bosq and Blanke [9] and Kutoyants [19], and in Lejeune [23] for the particular case of piecewise linear estimators.…”

Section: Introductionmentioning

confidence: 99%

Piecewise linear density estimation for sampled data

Lejeune

2011

Math. Meth. Stat.

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-Nonparametric density estimation is considered for a discretely observed stationary continuous-time process. For each of three given time sampling procedures either random or deterministic, we establish that histograms and frequency polygons can reach the same optimal L 2 -rates as in the independent and identically distributed case. Moreover, thanks to a suitable "high frequency" sampling design, these rates are derived together with a minimized time of observation depending on the regularity of sample paths.

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Inference and Prediction in Large Dimensions

Cited by 96 publications

References 0 publications

Multivariate Cramér–Rao inequality for prediction and efficient predictors

Multivariate Cramér–Rao inequality for prediction and efficient predictors

Conditional estimation for dependent functional data

Piecewise linear density estimation for sampled data

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