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3-dimensional multivertex reconstruction from 2-dimensional tracks observations using likelihood inference

Nikolai I. Chernov, Genadij A. Ososkov, Luc Pronzato (1992)

Applications of Mathematics

Let v 1 , v 2 , . . . , v k be vertices in the X Y Z -space, each vertex producing several tracks (straight lines) emanating from it within a narrow cone with a small angle about a fixed direction ( Z -axis). Each track is detected (by drift chambers or other detectors) by its projections on X Y and Y Z views independently with small errors. An automated method is suggested for the reconstruction of vertices from noisy observations of the tracks projections. The procedure is based on the likelihood inference for mixtures. An illustrative...

A comparative study of small area estimators.

Laureano Santamaría, Domingo Morales, Isabel Molina (2004)

SORT

It is known that direct-survey estimators of small area parameters, calculated with the data from the given small area, often present large mean squared errors because of small sample sizes in the small areas. Model-based estimators borrow strength from other related areas to avoid this problem. How small should domain sample sizes be to recommend the use of model-based estimators? How robust are small area estimators with respect to the rate sample size/number of domains?To give answers or recommendations...

A comparison of linearization and quadratization domains

Anna Jenčová (1997)

Applications of Mathematics

In a nonlinear model, the linearization and quadratization domains are considered. In the case of a locally quadratic model, explicit expressions for these domains are given and the domains are compared.

A note on the rate of convergence of local polynomial estimators in regression models

Friedrich Liese, Ingo Steinke (2001)

Kybernetika

Local polynomials are used to construct estimators for the value m ( x 0 ) of the regression function m and the values of the derivatives D γ m ( x 0 ) in a general class of nonparametric regression models. The covariables are allowed to be random or non-random. Only asymptotic conditions on the average distribution of the covariables are used as smoothness of the experimental design. This smoothness condition is discussed in detail. The optimal stochastic rate of convergence of the estimators is established. The results...

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2005)

ESAIM: Probability and Statistics

We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate ∫ ℝ f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U -statistics of order 2 due to Houdré and Reynaud.

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2010)

ESAIM: Probability and Statistics

We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate ∫ ℝ f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U-statistics of order 2 due to Houdré and Reynaud.

Adaptive hard-thresholding for linear inverse problems

Paul Rochet (2013)

ESAIM: Probability and Statistics

A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. These filter methods are generally restricted to monotonic transformations, e.g. the Tikhonov regularization or the spectral cut-off. However, in several cases, non-monotonic sequences of filters may appear more appropriate. In this paper, we study a hard-thresholding regularization method that extends the spectral cut-off procedure to non-monotonic sequences....

An eigenvector pattern arising in non linear regression.

Carles Maria Cuadras (1990)

Qüestiió

Let A = (aij) be an n x n matrix defined by aij = aji = i, i = 1,...,n. This paper gives some elementary properties of A and other related matrices. The eigenstructure of A is conjectured: given an eigenvector v of A the remaining eigenvectors are obtained by permuting up to sign the components of v. This problem arises in a distance based method applied to non linear regression.

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