Minimax estimation of the noise level and of the deconvolution density in a semiparametric convolution model

By Cristina Butucea, Catherine Matias. 2005

78 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/44de658b26145464c6ed00299f2fc47ab30884e3

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Citations in the corpus

Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process (2008, unknown): “326–327 in Butucea and Matias (2005). For all unexplained terminology and notation used in the sequel we refer to Chapter 2 of van der Vaart and Wellner (1996).”
DECONVOLUTION WITH UNKNOWN ERROR DISTRIBUTION (2007, unknown): “Butucea and Matias (2005) or Meister (2004, 2006)).”
Density estimation with heteroscedastic error (2008, background): “However, this can only be done by imposing more restrictive conditions on fX since a specific lower bound on f ft X has to be assumed (see Butucea and Matias (2005) or Meister (2006)).”
DENSITY ESTIMATION WITH NORMAL MEASUREMENT ERROR WITH UNKNOWN VARIANCE (2006, methodology): “Since the smoothness classes of Butucea and Matias (2004) are not subsets of our class F , we cannot use those results.”
Penalized contrast estimator for adaptive density deconvolution (2006, methodology): “Devroye (1989), Fan (1991a,b), Liu & Taylor (1989), Masry (1991), Stefanski & Carroll (1990), Zhang (1990), Koo (1999), Cator (2001). Smoother densities g with exponential decrease of their Fourier transform were first consid ered by Pensky & Vidakovic (1999), Butucea (2004) and Butucea & Tsybakov (”
Methodology for non‐parametric deconvolution when the error distribution is unknown (2016, background): “We mention here particularly the work of Carroll and Hall (1988) and Stefanski and Carroll (1990), who constructed a consistent kernel deconvolution estimator of fX, and Stefanski (1990) and Fan (1991, 1993), who derived its general asymptotic properties. Li and Vuong (1998), Lin and Carroll (2006),”
Goodness-of-fit testing and quadratic functional estimation from indirect observations (2006, methodology): “Following results by Butucea and Matias [5], we can consider noise distributions with unknown scaling parameter (some more assumptions are needed in order to insure identifiability in the model).”