Browsing by Author "Sapatinas, Theofanis"
Now showing items 21-40 of 58
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Minimax convergence rates under the Lp-risk in the functional deconvolution model
Petsa, A.; Sapatinas, Theofanis (2009)We derive minimax results in the functional deconvolution model under the Lp-risk, 1 ≤ p < ∞. Lower bounds are given when the unknown response function is assumed to belong to a Besov ball and under appropriate smoothness ...
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Minimax goodness-of-fit testing in multivariate nonparametric regression
Ingster, Y. I.; Sapatinas, Theofanis (2009)We consider an unknown response function f defined on Δ = [0, 1] d, 1 ≤ d ≤ ∞, taken at n random uniform design points and observed with Gaussian noise of known variance. Given a positive sequence r n → 0 as n → ∞ and a ...
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Minimax nonparametric testing in a problem related to the radon transform
Ingster, Y. I.; Sapatinas, Theofanis; Suslina, I. A. (2011)We consider the detection problem of a two-dimensional function from noisy observations of its integrals over lines. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, ...
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Minimax rates of convergence and optimality of bayes factor wavelet regression estimators under pointwise risks
Bochkina, N.; Sapatinas, Theofanis (2009)We consider function estimation in nonparametric regression over Besov spaces and under pointwise lu-risks (1 ≤ u < ∞). First we derive both non-adaptive and adaptive minimax pointwise rates of convergence in the standard ...
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Minimax signal detection in ill-posed inverse problems
Ingster, Y. I.; Sapatinas, Theofanis; Suslina, I. A. (2012)Saint Petersburg Electrotechnical University, University of Cyprus and Saint Petersburg University of Information Technologies, Mechanics and Optics Ill-posed inverse problems arise in various scientific fields. We consider ...
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Moment properties of multivariate infinitely divisible laws and criteria for multivariate self-decomposability
Sapatinas, Theofanis; Shanbhag, D. N. (2010)Ramachandran (1969) [9, Theorem 8] has shown that for any univariate infinitely divisible distribution and any positive real number α, an absolute moment of order α relative to the distribution exists (as a finite number) ...
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Moving block and tapered block bootstrap for functional time series with an application to the $K$-sample mean problem
Pilavakis, Dimitrios; Paparoditis, Efstathios; Sapatinas, Theofanis (2019)We consider infinite-dimensional Hilbert space-valued random variables that are assumed to be temporal dependent in a broad sense. We prove a central limit theorem for the moving block bootstrap and for the tapered block ...
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Article
Multichannel boxcar deconvolution with growing number of channels
Pensky, M.; Sapatinas, Theofanis (2011)We consider the problem of estimating the unknown response function in the multichannel deconvolution model with a boxcar-like ker-nel which is of particular interest in signal processing. It is known that, when the number ...
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Multichannel deconvolution with long range dependence: Upper bounds on the Lp-risk (1 ≤ p < ∞)
Kulik, R.; Sapatinas, Theofanis; Wishart, J. R. (2015)We consider multichannel deconvolution in a periodic setting with long-memory errors under three different scenarios for the convolution operators, i.e., super-smooth, regular-smooth and box-car convolutions. We investigate ...
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Multichannel deconvolution with long-range dependence: A minimax study
Benhaddou, R.; Kulik, R.; Pensky, M.; Sapatinas, Theofanis (2014)We consider the problem of estimating the unknown response function in the multichannel deconvolution model with long-range dependent Gaussian or sub-Gaussian errors. We do not limit our consideration to a specific type ...
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Nonparametric regression estimation based on spatially inhomogeneous data: minimax global convergence rates and adaptivity
Antoniadis, Anestis; Pensky, Marianna; Sapatinas, Theofanis (2013)
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Nonparametric regression estimation based on spatially inhomogeneous data: Minimax global convergence rates and adaptivity
Antoniadis, Anestis; Pensky, M.; Sapatinas, Theofanis (2014)We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known density g with a finite number of ...
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Normalized least-squares estimation in time-varying arch models
Fryzlewicz, P.; Sapatinas, Theofanis; Subba Rao, S. (2008)We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants ...
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Article
On Bayesian testimation and its application to wavelet thresholding
Abramovich, F.; Grinshtein, V.; Petsa, A.; Sapatinas, Theofanis (2010)We consider the problem of estimating the unknown response function in the Gaussian white noise model. We first utilize the recently developed Bayesian maximum a posteriori testimation procedure of Abramovich et al. (2007) ...
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On convergence rates equivalency and sampling strategies in functional deconvolution models
Pensky, M.; Sapatinas, Theofanis (2010)Using the asymptotical minimax framework, we examine convergence rates equivalency between a continuous functional deconvolution model and its real-life discrete counterpart over a wide range of Besov balls and for the ...
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On pointwise optimality of Bayes factor wavelet regression estimators
Bochkina, N.; Sapatinas, Theofanis (2006)We investigate the theoretical performance of Bayes factor estimators at a single point in wavelet regression models with independent and identically distributed errors that are not necessarily normally distributed. We ...
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On the estimation of the function and its derivatives in nonparametric regression: A bayesian testimation approach
Petsa, A.; Sapatinas, Theofanis (2011)We consider the problem of estimating the unknown response function and its deriva- tives in the standard nonparametric regression model. Recently, Abramovich et al. (2010) applied a Bayesian testimation procedure in a ...
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On the generalized Rao-rubin condition and some variants
Sapatinas, Theofanis (1996)This paper gives a characterization of some members of the compound Poisson family of distributions based on the generalized Rao-Rubin condition. By considering some variants of this condition and using power series ...
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On the posterior median estimators of possibly sparse sequences
Bochkina, N.; Sapatinas, Theofanis (2005)We adopt the Bayesian paradigm and discuss certain properties of posterior median estimators of possibly sparse sequences. The prior distribution considered is a mixture of an atom of probability at zero and a symmetric ...
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Optimal testing for additivity in multiple nonparametric regression
Abramovich, F.; De Feis, I.; Sapatinas, Theofanis (2009)We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) non- adaptive and adaptive hypothesis testing procedures for additivity ...