Статті в журналах: "Spectral Estimators"

1

Konofagou, Elisa E., Tomy Varghese, and Jonathan Ophir. "Spectral estimators in elastography." Ultrasonics 38, no. 1-8 (March 2000): 412–16. http://dx.doi.org/10.1016/s0041-624x(99)00116-x.

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2

Herment, A., and J. F. Giovannelli. "An Adaptive Approach to Computing the Spectrum and Mean Frequency of Doppler Signals." Ultrasonic Imaging 17, no. 1 (January 1995): 1–26. http://dx.doi.org/10.1177/016173469501700101.

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Modern ultrasound Doppler systems are facing the problem of processing increasingly shorter data sets. Spectral analysis of the strongly nonstationary Doppler signal needs to shorten the analysis window while maintaining a low variance and high resolution spectrum. Color flow imaging requires estimation of the Doppler mean frequency from even shorter Doppler data sets to obtain both a high frame rate and high spatial resolution. We reconsider these two estimation problems in light of adaptive methods. A regularized parametric method for spectral analysis as well as an adapted mean frequency estimator are developed. The choice of the adaptive criterion is then addressed and adaptive spectral and mean frequency estimators are developed to minimize the mean square error on estimation in the presence of noise. Two suboptimal spectral and mean-frequency estimators are then derived for real-time applications. Finally, their performance is compared to that of both the FFT based periodogram and the AR parametric spectral analysis for the spectral estimator, and, to both the correlation angle and the Kristoffersen's [8] estimators for the mean frequency estimator using Doppler data recorded in vitro.

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3

Stine, Robert A., and Paul Shaman. "Bias of Autoregressive Spectral Estimators." Journal of the American Statistical Association 85, no. 412 (December 1990): 1091–98. http://dx.doi.org/10.1080/01621459.1990.10474980.

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4

Gerard, David, and Peter Hoff. "Adaptive higher-order spectral estimators." Electronic Journal of Statistics 11, no. 2 (2017): 3703–37. http://dx.doi.org/10.1214/17-ejs1330.

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5

Chang, Christopher, and Dimitris Politis. "Aggregation of spectral density estimators." Statistics & Probability Letters 94 (November 2014): 204–13. http://dx.doi.org/10.1016/j.spl.2014.07.017.

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6

Bakar, M. A. A., D. A. Green, and A. V. Metcalfe. "Comparison of Spectral and Wavelet Estimators of Transfer Function for Linear Systems." East Asian Journal on Applied Mathematics 2, no. 3 (August 2012): 214–37. http://dx.doi.org/10.4208/eajam.170512.270712a.

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AbstractWe compare spectral and wavelet estimators of the response amplitude operator (RAO) of a linear system, with various input signals and added noise scenarios. The comparison is based on a model of a heaving buoy wave energy device (HBWED), which oscillates vertically as a single mode of vibration linear system. HBWEDs and other single degree of freedom wave energy devices such as oscillating wave surge convertors (OWSC) are currently deployed in the ocean, making such devices important systems to both model and analyse in some detail. The results of the comparison relate to any linear system. It was found that the wavelet estimator of the RAO offers no advantage over the spectral estimators if both input and response time series data are noise free and long time series are available. If there is noise on only the response time series, only the wavelet estimator or the spectral estimator that uses the cross-spectrum of the input and response signals in the numerator should be used. For the case of noise on only the input time series, only the spectral estimator that uses the cross-spectrum in the denominator gives a sensible estimate of the RAO. If both the input and response signals are corrupted with noise, a modification to both the input and response spectrum estimates can provide a good estimator of the RAO. A combination of wavelet and spectral methods is introduced as an alternative RAO estimator. The conclusions apply for autoregressive emulators of sea surface elevation, impulse, and pseudorandom binary sequences (PRBS) inputs. However, a wavelet estimator is needed in the special case of a chirp input where the signal has a continuously varying frequency.

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7

Politis, Dimitris N. "HIGHER-ORDER ACCURATE, POSITIVE SEMIDEFINITE ESTIMATION OF LARGE-SAMPLE COVARIANCE AND SPECTRAL DENSITY MATRICES." Econometric Theory 27, no. 4 (March 3, 2011): 703–44. http://dx.doi.org/10.1017/s0266466610000484.

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A new class of large-sample covariance and spectral density matrix estimators is proposed based on the notion of flat-top kernels. The new estimators are shown to be higher-order accurate when higher-order accuracy is possible. A discussion on kernel choice is presented as well as a supporting finite-sample simulation. The problem of spectral estimation under a potential lack of finite fourth moments is also addressed. The higher-order accuracy of flat-top kernel estimators typically comes at the sacrifice of the positive semidefinite property. Nevertheless, we show how a flat-top estimator can be modified to become positive semidefinite (even strictly positive definite) while maintaining its higher-order accuracy. In addition, an easy (and consistent) procedure for optimal bandwidth choice is given; this procedure estimates the optimal bandwidth associated with each individual element of the target matrix, automatically sensing (and adapting to) the underlying correlation structure.

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8

Candes, Emmanuel J., Carlos A. Sing-Long, and Joshua D. Trzasko. "Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators." IEEE Transactions on Signal Processing 61, no. 19 (October 2013): 4643–57. http://dx.doi.org/10.1109/tsp.2013.2270464.

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9

Wen, Li, Changxue Wang, and Peter Sherman. "Using Variability Related to Families of Spectral Estimators for Mixed Random Processes." Journal of Dynamic Systems, Measurement, and Control 123, no. 4 (February 21, 2001): 572–84. http://dx.doi.org/10.1115/1.1409257.

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Traditionally, characterization of spectral information for wide sense stationary processes has been addressed by identifying a single best spectral estimator from a given family. If one were to observe significant variability in neighboring spectral estimators then the level of confidence in the chosen estimator would naturally be lessened. Such variability naturally occurs in the case of a mixed random process, since the influence of the point spectrum in a spectral density characterization arises in the form of approximations of Dirac delta functions. In this work we investigate the nature of the variability of the point spectrum related to three families of spectral estimators: Fourier transform of the truncated unbiased correlation estimator, the truncated periodogram, and the autoregressive estimator. We show that tones are a significant source of bias and variability. This is done in the context of Dirichlet and Fejer kernels, and with respect to order rates. We offer some expressions for estimating statistical and arithmetic variability. Finally, we include an example concerning helicopter vibration. These results are especially pertinent to mechanical systems settings wherein harmonic content is prevalent.

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10

Teimouri, Mahdi, Saeid Rezakhah, and Adel Mohammadpour. "U-Statistic for Multivariate Stable Distributions." Journal of Probability and Statistics 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/3483827.

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A U-statistic for the tail index of a multivariate stable random vector is given as an extension of the univariate case introduced by Fan (2006). Asymptotic normality and consistency of the proposed U-statistic for the tail index are proved theoretically. The proposed estimator is used to estimate the spectral measure. The performance of both introduced tail index and spectral measure estimators is compared with the known estimators by comprehensive simulations and real datasets.

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11

Alam, S. Kaisar, Frederic L. Lizzi, Tomy Varghese, Ernest J. Feleppa, and Sarayu Ramachandran. "Adaptive Spectral Strain Estimators for Elastography." Ultrasonic Imaging 26, no. 3 (July 2004): 131–49. http://dx.doi.org/10.1177/016173460402600301.

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12

Sandoval-Ibarra, Y., V. H. Diaz-Ramirez, V. I. Kober, and V. N. Karnaukhov. "Speech enhancement with adaptive spectral estimators." Journal of Communications Technology and Electronics 61, no. 6 (June 2016): 672–78. http://dx.doi.org/10.1134/s1064226916060218.

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13

Konofagou, E. E., T. Varghese, J. Ophir, and S. K. Alam. "Power spectral strain estimators in elastography." Ultrasound in Medicine & Biology 25, no. 7 (September 1999): 1115–29. http://dx.doi.org/10.1016/s0301-5629(99)00061-7.

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14

Yu, Tian-You, Xiao Xiao, and Yadong Wang. "Statistical Quality of Spectral Polarimetric Variables for Weather Radar." Journal of Atmospheric and Oceanic Technology 29, no. 9 (September 1, 2012): 1221–35. http://dx.doi.org/10.1175/jtech-d-11-00090.1.

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Abstract Spectral polarimetry for weather radar capitalizes on both Doppler and polarimetric measurements to reveal polarimetric variables as a function of radial velocity through spectral analysis. For example, spectral differential reflectivity at a velocity represents the differential reflectivity from all the scatterers that have the same radial velocity of interest within the radar resolution volume. Spectral polarimetry has been applied to suppress both ground and biological clutter, retrieve individual drop size distributions from a mixture of different types of hydrometeors, and estimate turbulence intensity, for example. Although spectral polarimetry has gained increasing attention, statistical quality of the estimation of spectral polarimetric variables has not been investigated. In this work, the bias and standard deviation (SD) of spectral differential reflectivity and spectral copolar correlation coefficient estimated from averaged spectra were derived using perturbation method. The results show that the bias and SD of the two estimators depend on the spectral signal-to-noise ratio, spectral copolar correlation coefficient, the number of spectrum average, and spectral differential reflectivity. A simulation to generate time series signals for spectral polarimetry was developed and used to verify the theoretical bias and SD of the two estimators.

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15

van Leeuwen, G. H., A. P. G. Hoeks, and R. S. Reneman. "Simulation of Real-Time Frequency Estimators for Pulsed Doppler Systems." Ultrasonic Imaging 8, no. 4 (October 1986): 252–71. http://dx.doi.org/10.1177/016173468600800403.

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Four time-domain oriented, real-time frequency estimators, based on the detection of phase, zero-crossings, instantaneous frequency or autocorrelation, were simulated on a digital computer and subjected to computer generated Doppler signals, enabling the investigation of the influence of spectral shape, filtering, frequency shift, noise and quantization. Three estimators, the autocorrelator as well as the instantaneous frequency detector and the autocorrelator, both with extended frequency range, appeared to be very accurate. They exhibit a bias in the estimator output of less than 2 percent over a wide frequency range, the former up to nearly the Nyquist frequency, the latter two beyond, even for skew spectra and under poor signal conditions regarding bandwidth and noise.

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16

Mohd Shariff, Khairul Khaizi, Suraya Zainuddin, Noor Hafizah Abdul Aziz, Nur Emileen Abd Rashid, and Nor Ayu Zalina Zakaria. "Spectral estimator effects on accuracy of speed-over-ground radar." International Journal of Electrical and Computer Engineering (IJECE) 12, no. 4 (August 1, 2022): 3900. http://dx.doi.org/10.11591/ijece.v12i4.pp3900-3910.

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<p>Spectral estimation is a critical signal processing step in speed-over-ground (SoG) radar. It is argued that, for accurate speed estimation, spectral estimation should use low bias and variance estimator. However, there is no evaluation on spectral estimation techniques in terms of estimating mean Doppler frequency to date. In this paper, we evaluate two common spectral estimation techniques, namely periodogram based on Fourier transformation and the autoregressive (AR) based on burg algorithm. These spectral estimators are evaluated in terms of their bias and variance in estimating a mean frequency. For this purpose, the spectral estimators are evaluated with different Doppler signals that varied in mean frequency and signal-to-noise ratio (SNR). Results in this study indicates that the periodogram method performs well in most of the tests while the AR method did not perform as well as these but offered a slight improvement over the periodogram in terms of variance.</p>

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17

Kirlin, R. Lynn. "The relationship between semblance and eigenstructure velocity estimators." GEOPHYSICS 57, no. 8 (August 1992): 1027–33. http://dx.doi.org/10.1190/1.1443314.

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This short presentation gives for the first time a formulation of the semblance coefficient in terms of data covariance matrix eigenstructure. Because the high‐resolution wavefront or spectral eigenstructure methods have received so much interest over the past decade, it is necessary to analytically tie the conventionally used semblance produce to eigenstructure, thereby allowing the seismic signal analyst an opportunity to relate the various displays of velocity spectra using more than visual appearance. The eigenstructure form of semblance is compared to a number of the now well‐known eigenstructure‐based spectral estimators that separate signal and noise (vector) subspaces. Because of the inclusion of noise‐space energy in the coherence measure, conventional semblance does not have the resolving power of the newer methods. We suggest an enhanced semblance, based on the signal and noise subspace separation concept. A brief simulation verifies the visual improvement in the velocity spectrum obtained from the enhanced version.

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18

RUANO, M. GRAÇA. "NUMERICAL TECHNIQUES FOR MODELING DOPPLER ULTRASOUND SPECTRA SYSTEMS." Journal of Computational Acoustics 09, no. 03 (September 2001): 805–14. http://dx.doi.org/10.1142/s0218396x0100125x.

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Evaluation of blood-flow Doppler ultrasound spectral content is currently performed on clinical diagnosis. Since mean frequency and bandwidth spectral parameters are determinants on the quantification of stenotic degree, more precise estimators than the conventional Fourier transform should be seek. This paper summarizes studies led by the author in this field, as well as the strategies used to implement the methods in real-time. Regarding stationary and nonstationary characteristics of the blood-flow signal, different models were assessed. When autoregressive and autoregressive moving average models were compared with the traditional Fourier based methods in terms of their statistical performance while estimating both spectral parameters, the Modified Covariance model was identified by the cost/benefit criterion as the estimator presenting better performance. The performance of three time-frequency distributions and the Short Time Fourier Transform was also compared. The Choi–Williams distribution proved to be more accurate than the other methods. The identified spectral estimators were developed and optimized using high performance techniques. Homogeneous and heterogeneous architectures supporting multiple instruction multiple data parallel processing were essayed. Results obtained proved that real-time implementation of the blood-flow estimators is feasible, enhancing the usage of more complex spectral models on other ultrasonic systems.

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19

Barrett, John W., Paul Druce, and Lisa Glaser. "Spectral estimators for finite non-commutative geometries." Journal of Physics A: Mathematical and Theoretical 52, no. 27 (June 7, 2019): 275203. http://dx.doi.org/10.1088/1751-8121/ab22f8.

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20

Beex, A., and M. D. Rahman. "On averaging burg spectral estimators for segments." IEEE Transactions on Acoustics, Speech, and Signal Processing 34, no. 6 (December 1986): 1473–84. http://dx.doi.org/10.1109/tassp.1986.1164987.

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21

Hidalgo, J. "Spectral Analysis for Bivariate Time Series with Long Memory." Econometric Theory 12, no. 5 (December 1996): 773–92. http://dx.doi.org/10.1017/s0266466600007155.

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This paper provides limit theorems for spectral density matrix estimators and functionals of it for a bivariate covariance stationary process whose spectral density matrix has singularities not only at the origin but possibly at some other frequencies and, thus, applies to time series exhibiting long memory. In particular, we show that the consistency and asymptotic normality of the spectral density matrix estimator at a frequency, say λ, which hold for weakly dependent time series, continue to hold for long memory processes when λ lies outside any arbitrary neighborhood of the singularities. Specifically, we show that for the standard properties of spectral density matrix estimators to hold, only local smoothness of the spectral density matrix is required in a neighborhood of the frequency in which we are interested. Therefore, we are able to relax, among other conditions, the absolute summability of the autocovariance function and of the fourth-order cumulants or summability conditions on mixing coefficients, assumed in much of the literature, which imply that the spectral density matrix is globally smooth and bounded.

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22

Soon-Sen Lau, P. J. Sherman, and L. B. White. "Asymptotic statistical properties of AR spectral estimators for processes with mixed spectra." IEEE Transactions on Information Theory 48, no. 4 (April 2002): 909–17. http://dx.doi.org/10.1109/18.992779.

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23

Anchieta, David C., and John R. Buck. "Improving the robustness of spectral estimation to loud transients with a truncated order statistics filter." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A143. http://dx.doi.org/10.1121/10.0015832.

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Underwater acoustic recordings often include loud transients from human or natural sources. The transients cause a positive bias for Welch's average periodogram spectral estimator when estimating the power spectral density of the background environment. Estimators based on single order statistics (e.g., the sample median) avoid the bias caused by outliers at the cost of a higher variance than the sample mean. Schwock and Abadi (2021) showed that, for exponential random variables, the estimator based on the 80th sample percentile has the lowest variance among any unbiased estimator based on a single order statistics. This work tests a hybrid approach between Welch's and order statistics estimators by performing a weighted sum of the quietest subset of ordered samples of the periodograms. By discarding the loudest samples of the periodogram, the truncated linear order statistics filter (TLOSF) reduces the bias caused by loud transients. By combining multiple order statistics into the estimate, the TLOSF achieves a lower variance than the 80th percentile estimator. The TLOSF reduced the MSE by 1dB compared to Schwock & Abadi's 80th percentile estimator for a mixture combining an exponential distribution with 1% outliers 23 dB above the background. On periodograms of shallow water hydrophone recordings, the TLOSF yielded a lower output power in the frequency bins where both the Welch's and 80th percentile estimators had a positive bias due to loud transients. [Work supported by ONR Code 321US.]

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24

Bharath, A. A., and R. I. Kitney. "Advanced Spectral Estimators for Detailed Blood Flow Studies." Journal of Biomechanical Engineering 114, no. 1 (February 1, 1992): 34–39. http://dx.doi.org/10.1115/1.2895446.

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Recent publications have emphasized the relationship between the spectrum of the backscattered acoustic signal, beam geometry, and flow patterns in the measurement of blood flow by Doppler ultrasound. On this basis, we believe that in the future more importance will be placed on analyzing various characteristics of the spectral shape rather than absolute parameters of measurement, such as the mean frequency. The potential of this approach for extracting more information from the raw Doppler signal is introduced by considering the Spectral Broadening Index (SBI). We explain the use of the SBI parameter for measuring flow angle under restricted flow conditions. This is done by using an analytic/computational model for prediction of the spectral broadening effect. By simulation study, the performance of various spectral estimators for determining the SBI from finite Doppler signal segments is evaluated.

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25

Zhou, Jianwei. "The a Posteriori Error Estimates for Chebyshev-Galerkin Spectral Methods in One Dimension." Advances in Applied Mathematics and Mechanics 7, no. 2 (March 23, 2015): 145–57. http://dx.doi.org/10.4208/aamm.2013.m193.

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AbstractIn this paper, the Chebyshev-Galerkin spectral approximations are employed to investigate Poisson equations and the fourth order equations in one dimension. Meanwhile, p-version finite element methods with Chebyshev polynomials are utilized to solve Poisson equations. The efficient and reliable a posteriori error estimators are given for different models. Furthermore, the a priori error estimators are derived independently. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error indicators and a priori error estimations.

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26

Perron, Pierre, and Serena Ng. "AN AUTOREGRESSIVE SPECTRAL DENSITY ESTIMATOR AT FREQUENCY ZERO FOR NONSTATIONARITY TESTS." Econometric Theory 14, no. 5 (October 1998): 560–603. http://dx.doi.org/10.1017/s0266466698145024.

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Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero of some process. Commonly used are kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR(1) regression. However, it is known that with substantially correlated errors, the OLS estimate of the AR(1) parameter is severely biased. In this paper, we first show that this least-squares bias induces a significant increase in the bias and mean-squared error (MSE) of kernel-based estimators. We then consider a variant of the autoregressive spectral density estimator that does not share these shortcomings because it bypasses the use of the estimate from the AR(1) regression. Simulations and local asymptotic analyses show its bias and MSE to be much smaller than those of a kernel-based estimator when there is strong negative serial correlation. We also include a discussion about the appropriate choice of the truncation lag.

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27

Farhang-Boroujeny, B. "Prolate Filters for Nonadaptive Multitaper Spectral Estimators With High Spectral Dynamic Range." IEEE Signal Processing Letters 15 (2008): 457–60. http://dx.doi.org/10.1109/lsp.2008.924025.

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28

Lei, Lei, Guifu Zhang, Richard J. Doviak, Robert Palmer, Boon Leng Cheong, Ming Xue, Qing Cao, and Yinguang Li. "Multilag Correlation Estimators for Polarimetric Radar Measurements in the Presence of Noise." Journal of Atmospheric and Oceanic Technology 29, no. 6 (June 1, 2012): 772–95. http://dx.doi.org/10.1175/jtech-d-11-00010.1.

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Abstract The quality of polarimetric radar data degrades as the signal-to-noise ratio (SNR) decreases. This substantially limits the usage of collected polarimetric radar data to high SNR regions. To improve data quality at low SNRs, multilag correlation estimators are introduced. The performance of the multilag estimators for spectral moments and polarimetric parameters is examined through a theoretical analysis and by the use of simulated data. The biases and standard deviations of the estimates are calculated and compared with those estimates obtained using the conventional method.

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29

Ricci, Stefano. "Adaptive spectral estimators for fast flow-profile detection." IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 60, no. 2 (February 2013): 421–27. http://dx.doi.org/10.1109/tuffc.2013.2579.

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30

Ferreira, Eva, and Juan Manuel Rodriguez‐Poo. "Variable Bandwidth Kernel Estimators of the Spectral Density." Journal of Time Series Analysis 20, no. 3 (May 1999): 271–87. http://dx.doi.org/10.1111/1467-9892.00137.

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31

Stoica, Petre, Andreas Jakobsson, and Jian Li. "Matched-filter bank interpretation of some spectral estimators." Signal Processing 66, no. 1 (April 1998): 45–59. http://dx.doi.org/10.1016/s0165-1684(97)00239-9.

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32

Karasalo, I., and L. Götherström. "A regression formulation of Pisarenko's nonlinear spectral estimators." Signal Processing 12, no. 3 (April 1987): 309–11. http://dx.doi.org/10.1016/0165-1684(87)90099-5.

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33

Bromm, B., and E. Scharein. "Parametric spectral estimators: Application to event related potentials." Electroencephalography and Clinical Neurophysiology 61, no. 3 (September 1985): S226. http://dx.doi.org/10.1016/0013-4694(85)90855-7.

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34

Zhou, Wang. "New estimators of spectral distributions of Wigner matrices." Journal of Mathematical Physics 54, no. 3 (March 2013): 033503. http://dx.doi.org/10.1063/1.4794075.

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35

Plourde, Eric, and BenoÎt Champagne. "Auditory-Based Spectral Amplitude Estimators for Speech Enhancement." IEEE Transactions on Audio, Speech, and Language Processing 16, no. 8 (November 2008): 1614–23. http://dx.doi.org/10.1109/tasl.2008.2004304.

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36

Bentkus, R. "Optimal statistical estimators of spectral density in L2." Lithuanian Mathematical Journal 24, no. 3 (1985): 225–38. http://dx.doi.org/10.1007/bf00968040.

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37

Barchan, G. E., A. V. Grigorov, and A. G. Nakonechnyi. "Minimax estimators of spectral intensities of acoustic sources." Journal of Soviet Mathematics 58, no. 5 (February 1992): 483–85. http://dx.doi.org/10.1007/bf01100079.

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38

Crujeiras, Rosa M., Rubén Fernández-Casal, and Wenceslao González-Manteiga. "Comparing spatial dependence structures using spectral density estimators." Environmetrics 18, no. 7 (2007): 793–808. http://dx.doi.org/10.1002/env.879.

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39

Melnikov, Valery M., and Dusan S. Zrnić. "Autocorrelation and Cross-Correlation Estimators of Polarimetric Variables." Journal of Atmospheric and Oceanic Technology 24, no. 8 (August 1, 2007): 1337–50. http://dx.doi.org/10.1175/jtech2054.1.

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Abstract Herein are proposed novel estimators of differential reflectivity ZDR and correlation coefficient ρhv between horizontally and vertically polarized echoes. The estimators use autocorrelations and cross correlations of the returned signals to avoid bias by omnipresent but varying white noise. These estimators are considered for implementation on the future polarimetric Weather Surveillance Radar-1988 Doppler (WSR-88D) network. On the current network the reflectivity factor is measured at signal-to-noise ratios (SNRs) as low as 2 dB and the same threshold is expected to hold for the polarimetric variables. At such low SNR and all the way up to SNR = 15 dB, the conventional estimators of differential reflectivity and the copolar correlation coefficient are prone to errors due to uncertainties in noise levels caused by instability of radar devices, thermal radiations of precipitation and the ground, and wideband radiation of electrically active clouds. Noise variations at SNR less than 15 dB can bias the estimates beyond apparatus accuracy. For brevity the authors refer to the estimators of ZDR and ρhv free from noise bias as the “1-lag estimators” because these are derived from 1-lag correlations. The estimators are quite robust and the only weak assumption for validity is that spectral widths of signals from vertically and horizontally polarized returns are equal. This assumption is verified on radar data. Radar observations demonstrate the validity of these estimator and lower sensitivity to interference signals than the conventional algorithms.

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40

El-Morshedy, Mahmoud, Mohammed H. El-Menshawy, Mohammed M. A. Almazah, Rashad M. El-Sagheer, and Mohamed S. Eliwa. "Effect of Fuzzy Time Series on Smoothing Estimation of the INAR(1) Process." Axioms 11, no. 9 (August 24, 2022): 423. http://dx.doi.org/10.3390/axioms11090423.

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In this paper, the effect of fuzzy time series on estimates of the spectral, bispectral and normalized bispectral density functions are studied. This study is conducted for one of the integer autoregressive of order one (INAR(1)) models. The model of interest here is the dependent counting geometric INAR(1) which is symbolized by (DCGINAR(1)). A realization is generated for this model of size n = 500 for estimation. Based on fuzzy time series, the forecasted observations of this model are obtained. The estimators of spectral, bispectral and normalized bispectral density functions are smoothed by different one- and two-dimensional lag windows. Finally, after the smoothing, all estimators are studied in the case of generated and forecasted observations of the DCGINAR(1) model. We investigate the contribution of the fuzzy time series to the smoothing of these estimates through the results.

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41

Anandan, V. K., V. N. Sureshbabu, Toshitaka Tsuda, Jun-ichi Furumoto, and S. Vijayabhaskara Rao. "Estimation and Comparison of Horizontal Winds Using Various Spectral Estimation Methods on Profiler Radars." Journal of Atmospheric and Oceanic Technology 31, no. 3 (March 1, 2014): 620–29. http://dx.doi.org/10.1175/jtech-d-13-00101.1.

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Abstract The lower atmospheric wind profiles are obtained by the postset beam steering (PBS) technique on middle and upper (MU) atmosphere radar data. The Capon beamformer is used to improve the beam synthesizing in the desired directions within the radar transmit beamwidth. From a synthesized beam, the power spectrum is obtained by various spectral estimators, such as Fourier, multiple signal classification (MUSIC), and eigenvector (EV). The wind vector components are derived from radial velocities estimated from the power spectra of synthesized beams. As the reliability of the PBS wind estimate depends on the choice of spectral estimators, a detailed analysis is carried out to compare the performance of estimators in deriving wind profiles on the radar data. The results suggest that EV shows a better performance in deriving possible spectrum parameters and is useful for reliable wind profiling up to the lower stratosphere. The wind profiles derived by PBS with EV are more consistent with near-time observations using GPS sonde and Doppler beam swinging (DBS) methods. The study also suggests that MUSIC cannot be used to reliably estimate atmospheric spectrum parameters.

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42

Farné, Matteo, and Angela Montanari. "Different estimators of the spectral matrix: an empirical comparison testing a new shrinkage estimator." Communications in Statistics - Theory and Methods 45, no. 2 (January 13, 2016): 354–64. http://dx.doi.org/10.1080/03610926.2013.809117.

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43

Carrasco, Marine, and Jean-Pierre Florens. "A SPECTRAL METHOD FOR DECONVOLVING A DENSITY." Econometric Theory 27, no. 3 (October 11, 2010): 546–81. http://dx.doi.org/10.1017/s026646661000040x.

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We propose a new estimator for the density of a random variable observed with an additive measurement error. This estimator is based on the spectral decomposition of the convolution operator, which is compact for an appropriate choice of reference spaces. The density is approximated by a sequence of orthonormal eigenfunctions of the convolution operator. The resulting estimator is shown to be consistent and asymptotically normal. While most estimation methods assume that the characteristic function (CF) of the error does not vanish, we relax this assumption and allow for isolated zeros. For instance, the CF of the uniform and symmetrically truncated normal distributions have isolated zeros. We show that, in the presence of zeros, the density is identified even though the convolution operator is not one-to-one. We propose two consistent estimators of the density. We apply our method to the estimation of the measurement error density of hourly income collected from survey data.

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44

Ponce-Davalos, J. L., and Y. V. Shkvarko. "Spectral Caracterization via Fusing Modified Prony Method with High Resolution Nonparametric Spectral Estimators." IEEE Latin America Transactions 3, no. 3 (July 2005): 255–67. http://dx.doi.org/10.1109/tla.2005.1642416.

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45

Roch, Sebastien, and Karl Rohe. "Generalized least squares can overcome the critical threshold in respondent-driven sampling." Proceedings of the National Academy of Sciences 115, no. 41 (September 25, 2018): 10299–304. http://dx.doi.org/10.1073/pnas.1706699115.

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To sample marginalized and/or hard-to-reach populations, respondent-driven sampling (RDS) and similar techniques reach their participants via peer referral. Under a Markov model for RDS, previous research has shown that if the typical participant refers too many contacts, then the variance of common estimators does not decay like O(n−1), where n is the sample size. This implies that confidence intervals will be far wider than under a typical sampling design. Here we show that generalized least squares (GLS) can effectively reduce the variance of RDS estimates. In particular, a theoretical analysis indicates that the variance of the GLS estimator is O(n−1). We then derive two classes of feasible GLS estimators. The first class is based upon a Degree Corrected Stochastic Blockmodel for the underlying social network. The second class is based upon a rank-two model. It might be of independent interest that in both model classes, the theoretical results show that it is possible to estimate the spectral properties of the population network from a random walk sample of the nodes. These theoretical results point the way to entirely different classes of estimators that account for the network structure beyond node degree. Diagnostic plots help to identify situations where feasible GLS estimators are more appropriate. The computational experiments show the potential benefits and also indicate that there is room to further develop these estimators in practical settings.

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46

Hassler, Uwe. "REGRESSION OF SPECTRAL ESTIMATORS WITH FRACTIONALLY INTEGRATED TIME SERIES." Journal of Time Series Analysis 14, no. 4 (July 1993): 369–80. http://dx.doi.org/10.1111/j.1467-9892.1993.tb00151.x.

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47

Li, H., J. Li, and P. Stoica. "Performance analysis of forward-backward matched-filterbank spectral estimators." IEEE Transactions on Signal Processing 46, no. 7 (July 1998): 1954–66. http://dx.doi.org/10.1109/78.700967.

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48

Zorzi, Mattia. "A New Family of High-Resolution Multivariate Spectral Estimators." IEEE Transactions on Automatic Control 59, no. 4 (April 2014): 892–904. http://dx.doi.org/10.1109/tac.2013.2293218.

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49

Ciaccio, Edward J., Angelo B. Biviano, and Hasan Garan. "Comparison of spectral estimators for characterizing fractionated atrial electrograms." BioMedical Engineering OnLine 12, no. 1 (2013): 72. http://dx.doi.org/10.1186/1475-925x-12-72.

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50

Alty, S. R., A. Jakobsson, and E. G. Larsson. "Efficient time-recursive implementation of matched filterbank spectral estimators." IEEE Transactions on Circuits and Systems I: Regular Papers 52, no. 3 (March 2005): 516–21. http://dx.doi.org/10.1109/tcsi.2004.842876.

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