Vladimir G. Spokoiny

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Let a function f be observed with a noise. We wish to test the null hypothesis that the function is identically zero, against a composite nonparametric alternative: functions from the alternative set are sepaŽ . rated away from zero in an integral e.g., L norm and also possess some 2 smoothness properties. The minimax rate of testing for this problem was(More)
Suppose that one observes a process Y on the unit interval, where dY t = n1/2f t dt+dW t with an unknown function parameter f, given scale parameter n ≥ 1 (“sample size”) and standard Brownian motion W. We propose two classes of tests of qualitative nonparametric hypotheses about f such as monotonicity or concavity. These tests are asymptotically optimal(More)
We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastest possible rate. This rate is slower than n. Some existing(More)
In this paper, we prove the complexity bounds for methods of Convex Optimization based only on computation of the function value. The search directions of our schemes are normally distributed random Gaussian vectors. It appears that such methods usually need at most n times more iterations than the standard gradient methods, where n is the dimension of the(More)
Finding non-Gaussian components of high-dimensional data is an important preprocessing step for efficient information processing. This article proposes a new linear method to identify the “nonGaussian subspace” within a very general semi-parametric framework. Our proposed method, called NGCA (non-Gaussian component analysis), is based on a linear operator(More)
We propose a new method of effective dimension reduction for a multiindex model which is based on iterative improvement of the family of average derivative estimates. The procedure is computationally straightforward and does not require any prior information about the structure of the underlying model. We show that in the case when the effective dimension m(More)
We propose a method of adaptive estimation of a regression function and which is near optimal in the classical sense of the mean integrated error. At the same time, the estimator is shown to be very sensitive to discontinuities or change-points of the underlying function f or its derivatives. For instance, in the case of a jump of a regression function,(More)
Diffusion Tensor Imaging (DTI) data is characterized by a high noise level. Thus, estimation errors of quantities like anisotropy indices or the main diffusion direction used for fiber tracking are relatively large and may significantly confound the accuracy of DTI in clinical or neuroscience applications. Besides pulse sequence optimization, noise(More)
Data from functional magnetic resonance imaging (fMRI) consist of time series of brain images that are characterized by a low signal-to-noise ratio. In order to reduce noise and to improve signal detection, the fMRI data are spatially smoothed. However, the common application of a Gaussian filter does this at the cost of loss of information on spatial(More)