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Due to its conceptual simplicity and its proven effectiveness in real-time detection and removal of radio frequency interference (RFI) from radio astronomy data, the Spectral Kurtosis (SK) estimator is likely to become a standard tool of a new generation of radio telescopes. However, the SK estimator in its original form must be developed from instantaneous power spectral density (PSD) estimates, and hence cannot be employed as an RFI excision tool downstream of the data pipeline in existing instruments where any time averaging is performed. In this letter, we develop a generalized estimator with wider applicability for both instantaneous and averaged spectral data, which extends its practical use to a much larger pool of radio instruments.
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We obtain analytical approximations for the expectation and variance of the Spectral Kurtosis estimator in the case of Gaussian and coherent transient time domain signals mixed with a quasi-stationary Gaussian background, which are suitable for practical estimations of their signal-to-noise ratio and duty-cycle relative to the instrumental integration time. We validate these analytical approximations by means of numerical simulations and demonstrate that such estimates are affected by statistical uncertainties that, for a suitable choice of the integration time, may not exceed a few percent. Based on these analytical results, we suggest a multiscale Spectral Kurtosis spectrometer design optimized for real-time detection of transient signals, automatic discrimination based on their statistical signature, and measurement of their properties.
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We propose a generalized version of the Dantzig selector. We show that it satisfies sparsity oracle inequalities in prediction and estimation. We consider then the particular case of high-dimensional linear regression model selection with the Huber loss function. In this case we derive the sup-norm convergence rate and the sign concentration property of the Dantzig estimators under a mutual coherence assumption on the dictionary.
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