2,952 research outputs found
Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator
Kim and Pollard (Annals of Statistics, 18 (1990) 191?219) showed that a general class of M-estimators converge at rate n1/3 rather than at the standard rate n1/2. Many times, this situation arises when the objective function is non-smooth. The limiting distribution is the (almost surely unique) random vector that maximizes a certain Gaussian process and is difficult to analyze analytically. In this paper, we propose the use of the subsampling method for inferential purposes. The general method is then applied to Manski?s maximum score estimator and its small sample performance is highlighted via a simulation study.Publicad
Solar hard X-ray imaging by means of Compressed Sensing and Finite Isotropic Wavelet Transform
This paper shows that compressed sensing realized by means of regularized
deconvolution and the Finite Isotropic Wavelet Transform is effective and
reliable in hard X-ray solar imaging.
The method utilizes the Finite Isotropic Wavelet Transform with Meyer
function as the mother wavelet. Further, compressed sensing is realized by
optimizing a sparsity-promoting regularized objective function by means of the
Fast Iterative Shrinkage-Thresholding Algorithm. Eventually, the regularization
parameter is selected by means of the Miller criterion.
The method is applied against both synthetic data mimicking the
Spectrometer/Telescope Imaging X-rays (STIX) measurements and experimental
observations provided by the Reuven Ramaty High Energy Solar Spectroscopic
Imager (RHESSI). The performances of the method are compared with the results
provided by standard visibility-based reconstruction methods.
The results show that the application of the sparsity constraint and the use
of a continuous, isotropic framework for the wavelet transform provide a
notable spatial accuracy and significantly reduce the ringing effects due to
the instrument point spread functions
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