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Books on the topic 'Spectral Estimators'

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Published: 10 March 2023

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1

Center, Langley Research, ed. An overdetermined system for improved autocorrelation based spectral moment estimator performance. Hampton, VA: National Aeronautics and Space Administration, Langley Research Center, 1996.

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2

Francis, Nier, ed. Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians. Berlin: Springer, 2005.

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3

Weber, Andreas. Heat kernel estimates and L_1hnp spectral theory of locally symmetric spaces. Karlsruhe: Univ.-Verl. Karlsruhe, 2006.

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4

Helffer, Bernard, and Francis Nier. Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/b104762.

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5

Birman, M., ed. Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations. Providence, Rhode Island: American Mathematical Society, 1991. http://dx.doi.org/10.1090/advsov/007.

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6

Elsner, Guido. Distributions of values of indefinite forms and higher-order spectral estimates for finite Markov chains. Bielefeld: [s.n.], 2007.

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7

Elsner, Guido. Distributions of values of indefinite forms and higher-order spectral estimates for finite Markov chains. Bielefeld: [s.n.], 2007.

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8

Andrew, Michael E. Methods for computing confidence intervals for spectral estimates in monthly reports of the California Coastal Data Information Program. Vicksburg, Miss: Dept. of the Army, Waterways Experiment Station, Corps of Engineers, 1985.

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9

Jonggil, Lee, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., eds. The pulse-pair algorithm as a robust estimator of turbulent weather spectral parameters using airborne pulse Doppler radar. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1991.

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10

Jonggil, Lee, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., eds. The pulse-pair algorithm as a robust estimator of turbulent weather spectral parameters using airborne pulse Doppler radar. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1991.

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11

Baxa, Ernest G. The pulse-pair algorithm as a robust estimator of turbulent weather spectral parameters using airborne pulse Doppler radar. Hampton, Va: Langley Research Center, 1991.

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12

Jonggil, Lee, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., eds. The pulse-pair algorithm as a robust estimator of turbulent weather spectral parameters using airborne pulse Doppler radar. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1991.

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13

Center, Langley Research, ed. On the use of the noncentral chi-square density function for the distribution of helicopter spectral estimates. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

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14

Center, Langley Research, ed. On the use of the noncentral chi-square density function for the distribution of helicopter spectral estimates. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

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15

Eberhard, Wynn. Improvements in profiler wind estimates using smoothed data in the spectrum finder algorithm. Boulder, Colo: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, 1987.

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16

Center, Langley Research, ed. On the appropriateness of applying chi-square distribution based confidence intervals to spectral estimates of helicopter flyover data. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1988.

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17

C, Wilshusen Gregory, and United States. Government Accountability Office, eds. Defense Department cyber efforts: Definitions, focal point, and methodology needed for DOD to develop full-spectrum cyberspace budget estimates. Washington, DC: U.S. Govt. Accountability Office, 2011.

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18

Bouchaud, Jean-Philippe. Random matrix theory and (big) data analysis. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0006.

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This chapter reviews methods from random matrix theory to extract information about a large signal matrix C (for example, a correlation matrix arising in big data problems), from its noisy observation matrix M. The chapter shows that the replica method can be used to obtain both the spectral density and the overlaps between noise-corrupted eigenvectors and the true ones, for both additive and multiplicative noise. This allows one to construct optimal rotationally invariant estimators of C based on the observation of M alone. This chapter also discusses the case of rectangular correlation matrices and the problem of random singular value decomposition.

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19

Sogge, Christopher D. Improved spectral asymptotics and periodic geodesics. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160757.003.0005.

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This chapter proves an improved Weyl formula under the assumption that the set of periodic geodesics for (M,g) has measure zero. It then shows trace estimates associated with shrinking spectral bands, details and proves a lemma, and gives a related generalization of the Weyl formula from Chapter 3 that involves pseudodifferential operators. The chapter then proves its main result by using a version of the Duistermaat-Guillemin theorem, which allows the use of the Hadamard parametrix and the arguments from Chapter 3. To conclude, the chapter shows that one can improve the sup-norm estimates from Chapter 3 if one assumes a condition on the geodesic flow that is similar to a hypothesis laid out in the Duistermaat-Guillemin theorem.

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20

Birman, M. Sh. Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations (Advances in Soviet Mathematics, Vol 7). American Mathematical Society, 1991.

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21

National Aeronautics and Space Administration (NASA) Staff. Overdetermined System for Improved Autocorrelation Based Spectral Moment Estimator Performance. Independently Published, 2018.

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22

Fatigue life estimates for helicopter loading spectra. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1989.

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23

An overdetermined system for improved autocorrelation based spectral moment estimator performance. Clemson, SC: Electrical and Computer Engineering Dept., Clemson University, 1996.

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24

National Aeronautics and Space Administration (NASA) Staff. Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information. Independently Published, 2018.

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25

Zinn-Justin, Paul, and Jean-Bernard Zuber. Multivariate statistics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.28.

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This article considers some classical and more modern results obtained in random matrix theory (RMT) for applications in statistics. In the classic paradigm of parametric statistics, data are generated randomly according to a probability distribution indexed by parameters. From this data, which is by nature random, the properties of the deterministic (and unknown) parameters may be inferred. The ability to infer properties of the unknown Σ (the population covariance matrix) will depend on the quality of the estimator. The article first provides an overview of two spectral statistical techniques, principal components analysis (PCA) and canonical correlation analysis (CCA), before discussing the Wishart distribution and normal theory. It then describes extreme eigenvalues and Tracy–Widom laws, taking into account the results obtained in the asymptotic setting of ‘large p, large n’. It also analyses the results for the limiting spectra of sample covariance matrices..

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26

Mayer, Steven G. Size estimates of molecular clusters using elastic light scattering and CARS spectroscopy. 1997.

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27

The pulse-pair algorithm as a robust estimator of turbulent weather spectral parameters using airborne pulse Doppler radar. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1991.

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28

Popova, Svetlana, Shannon Lange, Larry Burd, and Jürgen Rehm. Burden and Social Cost of Fetal Alcohol Spectrum Disorders. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780199935291.013.78.

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Damage to the central nervous system is a unifying concept for nearly all of the diagnoses that fall under the Fetal Alcohol Spectrum Disorders (FASD) umbrella. Thus, FASD are an important public health and social problem worldwide that consumes a large amount of resources, both economic and societal by imparting a large burden on society through such sectors as the healthcare system, mental health and substance abuse treatment services, foster care, the criminal justice system, and the long-term care of individuals with intellectual and physical disabilities. Existing estimates of the economic impact of FASD demonstrate significant cost implications on the individual, the family and society. Many of the costs associated with FASD can be reduced with the implementation of effective social policies and intervention programs.

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29

Nier, Francis, and Bernard Helffer. Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians (Lecture Notes in Mathematics Book 1862). Springer, 2005.

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30

Voigt, Jens-Uwe. Quantification of left ventricular function and synchrony using tissue Doppler, strain imaging, and speckle tracking. Oxford University Press, 2011. http://dx.doi.org/10.1093/med/9780199599639.003.0006.

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Modern echocardiographic systems allow the quantitative and qualitative assessment of regional myocardial function by measuring velocity, motion, deformation, and other parameters of myocardial function.Both colour Doppler (CD) and spectral Doppler modes provide one-dimensional estimates of velocity. From CD data only, further parameters can be derived. Tracking techniques have recently been introduced which provide all parameters two-dimensionally, but at the cost of lower temporal resolution.Several clinical applications have been proposed, including regional and global systolic function assessment, evaluation of diastolic cardiac properties, and assessment of ventricular dyssynchrony.This chapter provides an introduction to the method of Doppler- and tracking-based function assessment and provides a basis for understanding its different clinical applications.

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31

Sogge, Christopher D. The sharp Weyl formula. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160757.003.0003.

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This chapter considers the sharp Weyl formula using the tools provided in the previous chapter. It attempts to prove the sharp Weyl formula which says that there is a constant c, depending on (M,g) in a natural way, so that N(λ‎) = cλ‎ⁿ + O(λ‎superscript n minus 1). The chapter then details the sup-norm estimates for eigenfunctions and spectral clusters. Next, this chapter proves the sharp Weyl formula and in doing so, outlines a number of theorems, the first of which the chapter focuses on in establishing its sharpness and in obtaining improved bounds for its Weyl formula's error term. Finally, the chapter shows that improved bounds are also available for the remainder term in the Weyl formula when (M,g) has nonpositive sectional curvature.

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32

Sogge, Christopher D. Geodesics and the Hadamard parametrix. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160757.003.0002.

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This chapter studies the spectrum of Laplace–Beltrami operators on compact manifolds. It begins by defining a metric on an open subset Ω‎ ⊂ Rn, in order to lift their results to corresponding ones on compact manifolds. The chapter then details some elliptic regularity estimates, before embarking on a brief review of geodesics and normal coordinates. The purpose of this review is to show that, with given a particular Laplace–Beltrami operator and any point y0 in Ω‎, one can choose a natural local coordinate system y = κ‎(x) vanishing at y0 so that the quadratic form associated with the metric takes a special form. To conclude, the chapter turns to the Hadamard parametrix.

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33

Clark, Terrell A. Assessment and Development of Deaf Children with Multiple Challenges. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190880545.003.0002.

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The proportion of children who are deaf or hard of hearing and also have other medical, neurodevelopmental, behavioral, or psychosocial conditions is increasing. Prevalence estimates run as high as 50% to 70%. The shifting complexity challenges not only the learners but also the teachers, administrators, and policymakers responsible for the education of deaf students. Documentation of diagnostic profiles contributes to understanding the learning profile of deaf students with concomitant conditions. This may also inform policy decisions, programmatic design, calibration of parental expectations, and implementation of effective teaching strategies. Through illustrative case examples, this chapter explores the principles of differential diagnosis and the implications of various conditions. Topics covered include genetic syndromes, vestibular dysfunction, intrauterine viral infection with associated congenital hearing loss, autism spectrum disorder, reactive attachment disorder, complex medical histories resulting in severe neurologic compromise, intellectual disabilities, cerebral palsy, and nonsyndromic genetic conditions.

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34

Calamari, John E., Heather M. Chik, Noelle K. Pontarelli, and Brandon L. DeJong. Phenomenology and Epidemiology of Obsessive Compulsive Disorder. Edited by Gail Steketee. Oxford University Press, 2012. http://dx.doi.org/10.1093/oxfordhb/9780195376210.013.0016.

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Obsessive compulsive disorder (OCD) is a complex, often debilitating syndrome that significantly diminishes quality of life. Although the exact prevalence of OCD is unclear, estimates suggest that it is a common form of psychopathology in the West and throughout the world. A challenge to researchers and clinicians is the significant heterogeneity of OCD. Initial heterogeneity research points to important subtypes of the disorder. Elucidation of disorder heterogeneity might advance etiologic theory and treatment research, and suggest where OCD or OCD-like conditions should be placed in a comprehensive psychiatric disorder nosology. OCD more often occurs with other psychiatric disorders, and evaluation of OCD comorbidity will help clarify this condition’s relation to anxiety disorders, mood disorders, and conditions posited to be part of a broad OCD spectrum. Despite significant advancements, much work remains before we can fully understand obsessional disorders and the relation of OCD to commonly experienced negative intrusive thoughts.

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35

Nine Mathematical Challenges : An Elucidation: Linde Hall Inaugural Math Symposium, February 22-24, 2019, California Institute of Technology, Pasadena, California. American Mathematical Society, 2021.

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