Signal Processing in the Linear Statistical Model

Scharf, Louis L.; Mullis, C.T.

doi:10.1007/978-94-009-2289-1_25

Cited by 5 publications

(3 citation statements)

References 6 publications

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“…If z f(y), where the dimension of z is smaller than that of y and p y (y j z) p(y j z), then we say that z captures all the useful information in y. Furthermore, z is more memory-ecient than y since f(Á) compresses y into a sucient statistic (Scharf, 1991). Sucient statistics are closely related to class separability.…”

Section: Sucient Statistics and Class Separabilitymentioning

confidence: 99%

Classification Cramer-Rao bounds on stock price prediction

Shin

Kil

1998

J. Forecast.

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In parameter estimation, we take advantage of the Cramer–Rao lower bound (CRLB) to evaluate the performance of estimation algorithms since the CRLB provides a theoretical upper bound on estimation accuracy. In pattern recognition, the same concept can be quite useful in terms of knowing the point of diminishing return. In this paper, we develop an innovative approach to quantifying the classification CRLB by combining the concepts of sufficient statistics and data compression with a metric that measures class separability. This approach allows us to assess the degree of performance optimality attained by each classifier. Instead of ranking performance of each classifier based on a confusion matrix, the proposed approach assigns a quantity called the optimality score that indicates the extent to which a classifier approximates the Bayes classifier. We illustrate the power of this approach with two interesting examples—two‐class prediction problems with known and unknown class‐conditional probability density functions. The latter case deals with prediction of S&P 500 price‐movement direction based on raw price data and technical indicators. Copyright © 1998 John Wiley & Sons, Ltd.

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Section: Sucient Statistics and Class Separabilitymentioning

confidence: 99%

Classification Cramer-Rao bounds on stock price prediction

Shin

Kil

1998

J. Forecast.

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“…In order to derive optimal detectors for classical detection problems that can be described by linear model and with unknown parameters, invariance principle [8][9][10][11][12] is extensively studied and four fundamental and interrelated detection problems are discussed. For problems that can be described by the linear model, the generalized-likelihoodratio-test (GLRT) and the uniformly-most-powerfulinvariant (UMPI) tests are equivalent [12].…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

Optimal invariant detection of a monochromatic plane wave with five unknown parameters

Cheng

Zhao

et al. 2013

2013 IEEE China Summit and International Conference on Signal and Information Processing

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This paper analyzes the problem of detecting a monochromatic plane wave with unknown amplitude, phase, temporal frequency and direction of arrival (DOA) in complex white Gaussian noise with unknown variance. The uniformly-most-powerful-invariant (UMPI) test is derived by using statistical invariance principle but doesn't exist unless the signal-to-noise ratio (SNR) is known. However, it provides performance bound to evaluate any invariant test's performance when SNR is unknown. Typically, the generalized-likelihood-ratio-test (GLRT) and locally-mostpowerful-invariant (LMPI) test are derived in this paper as realizable suboptimal invariant tests with their performance comparison in different SNR through theoretical analysis. Simulation examples corroborate our analysis and indicate that the GLRT is close to the UMPI bound especially in the low-probability-of-false-alarm region of the receiver operating characteristic (ROC) curve while the performance of LMPI test is close to that of UMPI test in low SNR region.

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“…Unfortunately, uncertainties in the signal operating environment introduce nuisance parameters that do not enter into the hypothesis testing problem; even worse, they preclude one from finding a UMPT. To derive optimal detectors for classical detection problems that can be described by a statistical linear model with unknown parameters, the invariance principle [8–12] is extensively studied and four fundamental, interrelated detection problems are discussed. A traditional method called matched filtering (MF) is optimal for detecting a known signal in an additive white Gaussian noise (AWGN) with known variance.…”

Section: Introductionmentioning

confidence: 99%