arXiv subjects

Paul Rochet

Publications and source records attributed to Paul Rochet.

22 records · Page 2Linked to original sources

arXiv2011

A Threshold Regularization Method for Inverse Problems

A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations, e.g. the Tikhonov regularization or the spectral cut-off. In this paper, we point out that in several cases, non-monotonic sequences of filters are more efficient. We study a regularization method that naturally extends the spectral cut-off procedure to non-monotonic sequences and provide several oracle inequalities, showing the method to be nearly optimal under mild assumptions. Then, we extend the method to inverse problems with noisy operator and provide efficiency results in a newly introduced conditional framework.

math.ST↗

arXiv2010

Semiparametric Efficiency of GMM under Approximate Constraints

Generalized empirical likelihood and generalized method of moments are well spread methods of resolution of inverse problems in econometrics. Each method defines a specific semiparametric model for which it is possible to calculate efficiency bounds. By this approach, we provide a new proof of Chamberlain's result on optimal GMM. We also discuss conditions under which GMM estimators remain efficient with approximate moment constraints.

math.ST↗

arXiv2009

Maximum Entropy Estimation for Survey sampling

Calibration methods have been widely studied in survey sampling over the last decades. Viewing calibration as an inverse problem, we extend the calibration technique by using a maximum entropy method. Finding the optimal weights is achieved by considering random weights and looking for a discrete distribution which maximizes an entropy under the calibration constraint. This method points a new frame for the computation of such estimates and the investigation of its statistical properties.

stat.ME↗

arXiv2009

Regularization with Approximated $L^2$ Maximum Entropy Method

We tackle the inverse problem of reconstructing an unknown finite measure $μ$ from a noisy observation of a generalized moment of $μ$ defined as the integral of a continuous and bounded operator $Φ$ with respect to $μ$. When only a quadratic approximation $Φ_m$ of the operator is known, we introduce the $L^2$ approximate maximum entropy solution as a minimizer of a convex functional subject to a sequence of convex constraints. Under several assumptions on the convex functional, the convergence of the approximate solution is established and rates of convergence are provided.

math.ST↗