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13
Sample eigenvalue based detection of highdimensional signals in white noise using relatively few samples
, 2007
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On the underfitting and overfitting sets of models chosen by order selection criteria
 J. Multivariate Anal
, 1999
"... For a general class of order selection criteria, we establish analytic and nonasymptotic evaluations of both the underfitting and overfitting sets of selected models. These evaluations are further specified in various situations including regressions and autoregressions with finite or infinite varia ..."
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Cited by 12 (0 self)
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For a general class of order selection criteria, we establish analytic and nonasymptotic evaluations of both the underfitting and overfitting sets of selected models. These evaluations are further specified in various situations including regressions and autoregressions with finite or infinite variances. We also show how upper bounds for the misfitting probabilities and hence conditions ensuring the weak consistency can be derived from the given evaluations. Moreover, it is demonstrated how these evaluations, combined with a law of the iterated logarithm for some relevant statistic, can provide conditions ensuring the strong consistency of the model selection criterion used. 1999 Academic Press AMS 1991 subject classifications: 62F12, 62M10, 62M40. Key words and phrases: model selection; AIC; BIC; underfitting and overfitting; weak consistency; strong consistency; regressions and autoregressions; Markov fields; stable law. 1.
Model selection in electromagnetic source analysis with an application to VEF’s
 IEEE Transactions on Biomedical Engineering
, 2002
"... Abstract — In electromagnetic source analysis it is necessary to determine how many sources are required to describe the EEG or MEG adequately. Model selection procedures (MSP’s, or goodness of fit procedures) give an estimate of the required number of sources. Existing and new MSP’s are evaluated i ..."
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Cited by 7 (4 self)
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Abstract — In electromagnetic source analysis it is necessary to determine how many sources are required to describe the EEG or MEG adequately. Model selection procedures (MSP’s, or goodness of fit procedures) give an estimate of the required number of sources. Existing and new MSP’s are evaluated in different source and noise settings: two sources which are close or distant, and noise which is uncorrelated or correlated. The commonly used MSP residual variance is seen to be ineffective, that is it often selects too many sources. Alternatives like the adjusted Hotelling’s test, Bayes information criterion, and the Wald test on source amplitudes are seen to be effective. The adjusted Hotelling’s test is recommended if a conservative approach is taken, and MSP’s such as Bayes information criterion or the Wald test on source amplitudes are recommended if a more liberal approach is desirable. The MSP’s are applied to empirical data (visual evoked fields). I.
Strongly Consistent Model Order Selection for Estimating 2D Sinusoids in Colored Noise
, 801
"... We consider the problem of jointly estimating the number as well as the parameters of twodimensional sinusoidal signals, observed in the presence of an additive colored noise field. We begin by elaborating on the least squares estimation of 2D sinusoidal signals, when the assumed number of sinusoi ..."
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We consider the problem of jointly estimating the number as well as the parameters of twodimensional sinusoidal signals, observed in the presence of an additive colored noise field. We begin by elaborating on the least squares estimation of 2D sinusoidal signals, when the assumed number of sinusoids is incorrect. In the case where the number of sinusoidal signals is underestimated we show the almost sure convergence of the least squares estimates to the parameters of the dominant sinusoids. In the case where this number is overestimated, the estimated parameter vector obtained by the least squares estimator contains a subvector that converges almost surely to the correct parameters of the sinusoids. Based on these results, we prove the strong consistency of a new model order selection rule. Keywords: Twodimensional random fields; model order selection; least squares estimation; strong consistency.
DETECTION PERFORMANCEOF ROY’S LARGESTROOT TESTWHEN THE NOISE COVARIANCEMATRIXISARBITRARY
"... Detecting the presence of a signal embedded in noise from a multisensor system is a fundamental problem in signal and array processing. In this paper we consider the case where the noise covariance matrix is arbitrary and unknown but we are given both signal bearing and noiseonly samples. Using am ..."
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Detecting the presence of a signal embedded in noise from a multisensor system is a fundamental problem in signal and array processing. In this paper we consider the case where the noise covariance matrix is arbitrary and unknown but we are given both signal bearing and noiseonly samples. Using amatrixperturbationapproach,combinedwithknownresults on the eigenvalues of inverse Wishart matrices, we study the behavior of the largest eigenvalue of the relevant covariance matrix, and derive an approximate expression for the detection probability of Roy’s largest root test. The accuracy of our expressions isconfirmed by simulations. Index Terms — signal detection, Roy’s largest root test, matrixperturbation, inverse Wishartdistribution.
An Alternative Algorithm for Maximum Likelihood DOA Estimation and Detection
, 1994
"... The majority of algorithms developed for the narrowband direction of arrival (DOA) estimation problem rely on an eigenvalue decomposition (EVD) to determine both the number of signals and their respective DOAs. In this paper, an alternative algorithm is presented that solves both the DOA detection a ..."
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The majority of algorithms developed for the narrowband direction of arrival (DOA) estimation problem rely on an eigenvalue decomposition (EVD) to determine both the number of signals and their respective DOAs. In this paper, an alternative algorithm is presented that solves both the DOA detection and estimation problems without resorting to an EVD. The algorithm is shown to have asymptotically equivalent performance to that of the (unconditional) maximum likelihood method, and hence it yields asymptotically minimum variance DOA estimates. The computational complexity required to update the DOA estimates in response to additional data from the array is investigated, and the algorithm is shown to be somewhat simpler than other methods with comparable performance. In addition, the asymptotic distribution of the algorithm's cost function is derived, and is shown to be composed of the sum of two differently scaled chisquared random variables. A hypothesis test for determining the number o...