Journal articles: 'Mathematics Estimation theory'

1

Girko, Vyacheslav L. "Spectral theory of minimax estimation." Acta Applicandae Mathematicae 43, no. 1 (April 1996): 59–69. http://dx.doi.org/10.1007/bf00046987.

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Chan, Hock Peng, Chiang-Wee Heng, and Ajay Jasra. "Theory of segmented particle filters." Advances in Applied Probability 48, no. 1 (March 2016): 69–87. http://dx.doi.org/10.1017/apr.2015.7.

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AbstractWe study the asymptotic behavior of a new particle filter approach for the estimation of hidden Markov models. In particular, we develop an algorithm where the latent-state sequence is segmented into multiple shorter portions, with an estimation technique based upon a separate particle filter in each portion. The partitioning facilitates the use of parallel processing, which reduces the wall-clock computational time. Based upon this approach, we introduce new estimators of the latent states and likelihood which have similar or better variance properties compared to estimators derived from standard particle filters. We show that the likelihood function estimator is unbiased, and show asymptotic normality of the underlying estimators.

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3

Ziegel, Eric R., E. L. Lehmann, and George Casella. "Theory of Point Estimation." Technometrics 41, no. 3 (August 1999): 274. http://dx.doi.org/10.2307/1270597.

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4

Yang, Da. "Interval Estimation and Hypothesis Testing." Applied Mechanics and Materials 543-547 (March 2014): 1717–20. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1717.

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Mathematical statistics is a branch of mathematics has extensive application of interval estimation and hypothesis testing, which are two important problems of statistical inference. As two important statistical inference methods, interval estimation and hypothesis testing problem is more and more widely used in the field of economic management, finance and insurance, scientific research, engineering technology, the science of decision functions are recognized by more and more people. Can go further to establish mutual influence and communication between the interval estimation and hypothesis testing, can use the theory to explain the problem of interval estimation of parameter hypothesis test, this is an important problem to improve the statistical inference theory. Therefore, the basis on the internal relations between the interval estimation and hypothesis test for deep research, explain the problem of hypothesis testing and interval estimation from the point of view, discusses the difference and connection between the two.

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Rovigatti, Gabriele, and Vincenzo Mollisi. "Theory and Practice of Total-Factor Productivity Estimation: The Control Function Approach using Stata." Stata Journal: Promoting communications on statistics and Stata 18, no. 3 (September 2018): 618–62. http://dx.doi.org/10.1177/1536867x1801800307.

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Alongside instrumental-variables and fixed-effects approaches, the control function approach is the most widely used in production function estimation. Olley and Pakes (1996, Econometrica 64: 1263–1297), Levinsohn and Petrin (2003, Review of Economic Studies 70: 317–341), and Ackerberg, Caves, and Frazer (2015, Econometrica 83: 2411–2451) have all contributed to the field by proposing two-step estimation procedures, whereas Wooldridge (2009, Economics Letters 104: 112–114) showed how to perform a consistent estimation within a single-step generalized method of moments framework. In this article, we propose a new estimator based on Wooldridge's estimation procedure, using dynamic panel instruments à la Blundell and Bond (1998, Journal of Econometrics 87: 115–143), and we evaluate its performance by using Monte Carlo simulations. We also present the new command prodest for production function estimation, and we show its main features and strengths in a comparative analysis with other community-contributed commands. Finally, we provide evidence of the numerical challenges faced when using the Olley–Pakes and Levinsohn–Petrin estimators with the Ackerberg–Caves–Frazer correction in empirical applications, and we document how the generalized method of moments estimates vary depending on the optimizer or starting points used.

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6

Narens, Louis. "A Theory of Ratio Magnitude Estimation." Journal of Mathematical Psychology 40, no. 2 (June 1996): 109–29. http://dx.doi.org/10.1006/jmps.1996.0011.

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7

Penskaya, M. Ya. "Application of regularizing operators in estimation theory." Journal of Soviet Mathematics 53, no. 6 (March 1991): 655–60. http://dx.doi.org/10.1007/bf01095377.

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8

Wang, Alan P. "Scattering theory and linear state-space estimation." Journal of Mathematical Analysis and Applications 120, no. 2 (December 1986): 397–415. http://dx.doi.org/10.1016/0022-247x(86)90165-4.

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9

Yang, L. X., D. N. Hào, and H. Sahli. "Motion estimation by hybrid diffusion: theory and implementation." Journal of Inverse and Ill-posed Problems 14, no. 3 (May 2006): 307–30. http://dx.doi.org/10.1515/156939406777340900.

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10

Wechsler, H., Z. Duric, F. Li, and V. Cherkassky. "Motion estimation using statistical learning theory." IEEE Transactions on Pattern Analysis and Machine Intelligence 26, no. 4 (April 2004): 466–78. http://dx.doi.org/10.1109/tpami.2004.1265862.

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11

Gao, Feng. "A probabilistic theory for error estimation in automatic integration." Numerische Mathematik 56, no. 4 (April 1989): 309–29. http://dx.doi.org/10.1007/bf01396607.

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12

Hidayati, Lilik, Nur Chamidah, and I. Nyoman Budiantara. "ESTIMASI SELANG KEPERCAYAAN NILAI UJIAN NASIONAL BERBASIS KOMPETENSI BERDASARKAN MODEL REGRESI SEMIPARAMETRIK MULTIRESPON TRUNCATED SPLINE." MEDIA STATISTIKA 13, no. 1 (June 25, 2020): 92–103. http://dx.doi.org/10.14710/medstat.13.1.92-103.

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Confidence interval estimation is important in statistical inference for the parameters of the regression model, but the theory of confidence interval estimation for multi-response semiparametric regression model parameters based on the truncated spline estimator has not been examined. In this study, we estimate the confidence interval of the multi-response semiparametric regression model based on the truncated spline estimator by using pivotal quantity method with the central limit theorem approach. This confidence interval theory is applied to data of competency-based national exam (UNBK) scores in West Nusa Tenggara Province where its UNBK in the lowest position among other provinces in Indonesia. The method used for estimating parameters is weighted least square. The best model is determined based on the Generalized Cross Validation (GCV) minimum value. Based on the estimated 95% confidence interval of parameters of the multi-response truncated spline semiparametric regression model, the results showed that the insignificant factors affecting the UNBK scores were gender and parental education duration while the report card of scores and USBK scores had a positive effect on the UNBK scores but only the UNBK scores of mathematics that report card of scores factor has a negative effect on it.

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13

Bourgain, Jean. "Estimation of certain exponential sums arising in complexity theory." Comptes Rendus Mathematique 340, no. 9 (May 2005): 627–31. http://dx.doi.org/10.1016/j.crma.2005.03.008.

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14

Durot, Cécile, and Hendrik P. Lopuhaä. "Limit Theory in Monotone Function Estimation." Statistical Science 33, no. 4 (November 2018): 547–67. http://dx.doi.org/10.1214/18-sts664.

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15

Ponosov, Arcady, Anna Machina, and Valeria Tafintseva. "Piecewise synergetic systems and applications in biochemical systems theory." Georgian Mathematical Journal 24, no. 1 (March 1, 2017): 135–48. http://dx.doi.org/10.1515/gmj-2016-0065.

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AbstractWe study piecewise synergetic systems originating from Biochemical Systems Theory. In the first part of the paper, the emphasis is put on practical calculations with such systems. We consider four examples: calculation of trajectories and steady states, solution of an optimization problem and a method of estimation of parameters (kinetic orders), all examples being biologically motivated. In the second part of the paper, we study convergence of solutions, in particularly, steady states, of a sequence of piecewise synergetic systems approximating an arbitrary compartment model. This convergence analysis is then applied to the optimization problem and the method of estimating sensitivities (kinetic orders) in a generic compartment model. In this paper we put forward arguments for the importance of the theoretical and numerical analysis of piecewise synergetic systems.

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16

MAK, T. K. "Interpretation and estimation in ranking theory." Biometrika 72, no. 1 (1985): 227–29. http://dx.doi.org/10.1093/biomet/72.1.227.

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17

Nilsson, Håkan, Jörg Rieskamp, and Eric-Jan Wagenmakers. "Hierarchical Bayesian parameter estimation for cumulative prospect theory." Journal of Mathematical Psychology 98 (September 2020): 102429. http://dx.doi.org/10.1016/j.jmp.2020.102429.

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18

Sadeghnejad, Saeid, Mohsen Masihi, Mahmoudreza Pishvaie, and Peter R. King. "Rock Type Connectivity Estimation Using Percolation Theory." Mathematical Geosciences 45, no. 3 (February 28, 2013): 321–40. http://dx.doi.org/10.1007/s11004-013-9446-5.

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19

Embrechts, Paul, and Harro Walk. "Recursive estimation of distributional fix-points." Journal of Applied Probability 37, no. 01 (March 2000): 73–87. http://dx.doi.org/10.1017/s0021900200015266.

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In various stochastic models the random equation of implicit renewal theory appears where the real random variable S and the stochastic process Ψ with index space and state space R are independent. By use of stochastic approximation the distribution function of S is recursively estimated on the basis of independent or ergodic copies of Ψ. Under integrability assumptions almost sure L 1-convergence is proved. The choice of gains in the recursion is discussed. Applications are given to insurance mathematics (perpetuities) and queueing theory (stationary waiting and queueing times).

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20

Xia, Xintao, Zhongyu Wang, and Yongsheng Gao. "Estimation of non-statistical uncertainty using fuzzy-set theory." Measurement Science and Technology 11, no. 4 (March 10, 2000): 430–35. http://dx.doi.org/10.1088/0957-0233/11/4/314.

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21

Embrechts, Paul, and Harro Walk. "Recursive estimation of distributional fix-points." Journal of Applied Probability 37, no. 1 (March 2000): 73–87. http://dx.doi.org/10.1239/jap/1014842269.

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In various stochastic models the random equation of implicit renewal theory appears where the real random variable S and the stochastic process Ψ with index space and state space R are independent. By use of stochastic approximation the distribution function of S is recursively estimated on the basis of independent or ergodic copies of Ψ. Under integrability assumptions almost sure L1-convergence is proved. The choice of gains in the recursion is discussed. Applications are given to insurance mathematics (perpetuities) and queueing theory (stationary waiting and queueing times).

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22

Sengupta, Sailes K., and Steven M. Kay. "Fundamentals of Statistical Signal Processing: Estimation Theory." Technometrics 37, no. 4 (November 1995): 465. http://dx.doi.org/10.2307/1269750.

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23

Ramsay, Philip H., and David W. Scott. "Multivariate Density Estimation, Theory, Practice, and Visualization." Technometrics 35, no. 4 (November 1993): 451. http://dx.doi.org/10.2307/1270280.

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24

Wang, Ting, Hang Zhang, and Yan-long Zhao. "Parameter Estimation Based on Set-valued Signals: Theory and Application." Acta Mathematicae Applicatae Sinica, English Series 35, no. 2 (April 2019): 255–63. http://dx.doi.org/10.1007/s10255-019-0822-x.

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25

Li, Bicao, Guanyu Yang, Zhoufeng Liu, Jean Louis Coatrieux, and Huazhong Shu. "Multimodal Medical Image Registration Based on an Information-Theory Measure with Histogram Estimation of Continuous Image Representation." Mathematical Problems in Engineering 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/2135453.

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This work presents a novel method for multimodal medical registration based on histogram estimation of continuous image representation. The proposed method, regarded as “fast continuous histogram estimation,” employs continuous image representation to estimate the joint histogram of two images to be registered. The Jensen–Arimoto (JA) divergence is a similarity measure to measure the statistical dependence between medical images from different modalities. The estimated joint histogram is exploited to calculate the JA divergence in multimodal medical image registration. In addition, to reduce the grid effect caused by the grid-aligning transformations between two images and improve the implementation speed of the registration method, random samples instead of all pixels are extracted from the images to be registered. The goal of the registration is to optimize the JA divergence, which would be maximal when two misregistered images are perfectly aligned using the downhill simplex method, and thus to get the optimal geometric transformation. Experiments are conducted on an affine registration of 2D and 3D medical images. Results demonstrate the superior performance of the proposed method compared to standard histogram, Parzen window estimations, particle filter, and histogram estimation based on continuous image representation without random sampling.

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26

Metz, Charles E., and Xiaochuan Pan. "“Proper” Binormal ROC Curves: Theory and Maximum-Likelihood Estimation." Journal of Mathematical Psychology 43, no. 1 (March 1999): 1–33. http://dx.doi.org/10.1006/jmps.1998.1218.

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27

Lavergne, Pascal, and Valentin Patilea. "Smooth minimum distance estimation and testing with conditional estimating equations: Uniform in bandwidth theory." Journal of Econometrics 177, no. 1 (November 2013): 47–59. http://dx.doi.org/10.1016/j.jeconom.2013.05.006.

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28

Mahmoud, Magdi S. "Robust stability and ℋ∞-estimation for uncertain discrete systems with state-delay." Mathematical Problems in Engineering 7, no. 5 (2001): 393–412. http://dx.doi.org/10.1155/s1024123x01001703.

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In this paper, we investigate the problems of robust stability and ℋ∞-estimation for a class of linear discrete-time systems with time-varying norm-bounded parameter uncertainty and unknown state-delay. We provide complete results for robust stability with prescribed performance measure and establish a version of the discrete Bounded Real Lemma. Then, we design a linear estimator such that the estimation error dynamics is robustly stable with a guaranteed ℋ∞-performance irrespective of the parameteric uncertainties and unknown state delays. A numerical example is worked out to illustrate the developed theory.

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29

Ramya, R., and P. Chandrasekaran. "NONLINEAR STRUCTURAL ESTIMATION OF LOCALIZED NETWORK USING HOMOTOPHIC TOPOLOGICAL (2(N)+1) DIMENSIONAL FOR DISTANCE THEORY (HTD-DT)." Advances in Mathematics: Scientific Journal 10, no. 5 (May 7, 2021): 2419–31. http://dx.doi.org/10.37418/amsj.10.5.10.

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A Nonlinear Structural Equation Model (NLSEM) is formed on the basis of various dimension in normal mutual estimation depending on Distance Estimation Theory (DET) and its complex networks structure. The homotophy linear topography analyze the dimension of formal network in hidden paths to consider the linear structure. However, dimension theory is a linear dependence between the variables for observation is problem in nature of distance estimation along the node and these approaches have limitations to form shortest communication. This paper proposes the Nonlinear structural estimation of localized network using homotphic topological (2 (n)+1) dimensional for distance theory Structure equation model based on the Probability distribution theory of evaluation model (PDTE) that compensates for the potential innumerable dependencies between network points. For this unstructural reason, network densities are provided to take advantage of the lower specific margins of density that are present in most real-world networks. The Gambier IV order $(y \frac{d^2 y}{dt^2} (\alpha, \beta)$, complex constant) is used to optimize the Painleve I order $(X’=X’^{(dy/dt)}y^2 + t)$ equation to derive the neighborhood singularities to estimate the distance. This computational provides an efficient integration to the diagonal gradient algorithm has been developed to estimate the SEM coefficients of polymorphic formation and therefore infer the edge structures on distance estimation. Preliminary testing of simulated data demonstrates the effectiveness of the new approach produce high estimation with lower redundancy steps of mathematical solvation.

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30

Sharia, Teo. "Rate of Convergence in Recursive Parameter Estimation Procedures." gmj 14, no. 4 (December 2007): 721–36. http://dx.doi.org/10.1515/gmj.2007.721.

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Abstract This paper is concerned with the rate of convergence of recursive estimation procedures for parameters of discrete time stochastic processes. Applications to estimation of parameters in several models are presented to illustrate the theory.

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31

Schipp, Bernhard, and Markus Brechtmann. "Minimax estimation with random coefficients: Theory and application to stock returns." Acta Applicandae Mathematicae 43, no. 1 (April 1996): 113–26. http://dx.doi.org/10.1007/bf00046992.

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32

Dudewicz, Edward J., and Ishwari D. Dhariyal. "Estimation Theory of Selective Reporting: The Best-1-of-k Report." SIAM Journal on Applied Mathematics 46, no. 3 (June 1986): 406–16. http://dx.doi.org/10.1137/0146028.

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33

Karoblis, Antanas. "The Approximation of Sum of Independent Distributions by the Erlang Distribution Function." Nonlinear Analysis: Modelling and Control 7, no. 1 (June 5, 2002): 55–60. http://dx.doi.org/10.15388/na.2002.7.1.15202.

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The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

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34

Chen, D. G. "Bootstrapping estimation for estimating relative potency in combinations of bioassays." Computational Statistics & Data Analysis 51, no. 9 (May 2007): 4597–604. http://dx.doi.org/10.1016/j.csda.2006.07.040.

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35

Wu, Wei Biao, Yinxiao Huang, and Yibi Huang. "Kernel estimation for time series: An asymptotic theory." Stochastic Processes and their Applications 120, no. 12 (December 2010): 2412–31. http://dx.doi.org/10.1016/j.spa.2010.08.001.

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36

Talantzis, F., A. G. Constantinides, and L. C. Polymenakos. "Estimation of direction of arrival using information theory." IEEE Signal Processing Letters 12, no. 8 (August 2005): 561–64. http://dx.doi.org/10.1109/lsp.2005.849546.

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37

Wang, Wei, and Chunyan Han. "H∞Channel Estimation for DS-CDMA Systems: A Partial Difference Equation Approach." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/307342.

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In the communications literature, a number of different algorithms have been proposed for channel estimation problems with the statistics of the channel noise and observation noise exactly known. In practical systems, however, the channel parameters are often estimated using training sequences which lead to the statistics of the channel noise difficult to obtain. Moreover, the received signals are corrupted not only by the ambient noises but also by multiple-access interferences, so the statistics of observation noises is also difficult to obtain. In this paper, we will investigate theH∞channel estimation problem for direct-sequence code-division multiple-access (DS-CDMA) communication systems with time-varying multipath fading channels. The channel estimator is designed by applying a partial difference equation approach together with the innovation analysis theory. This method can give a sufficient and necessary condition for the existence of anH∞channel estimator.

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38

Schmid, Friedrich, and Axel Schmidt. "Nonparametric estimation of the coefficient of overlapping—theory and empirical application." Computational Statistics & Data Analysis 50, no. 6 (March 2006): 1583–96. http://dx.doi.org/10.1016/j.csda.2005.01.014.

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39

Baker, F. B. "Item Response Theory: Parameter Estimation Techniques." Biometrics 50, no. 3 (September 1994): 896. http://dx.doi.org/10.2307/2532822.

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40

Prasad, K. Venkatesh. "Fundamentals of statistical signal processing: Estimation theory." Control Engineering Practice 2, no. 4 (August 1994): 728. http://dx.doi.org/10.1016/0967-0661(94)90195-3.

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41

Repin, S. I. "A posteriori error estimation for nonlinear variational problems by duality theory." Journal of Mathematical Sciences 99, no. 1 (March 2000): 927–35. http://dx.doi.org/10.1007/bf02673600.

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42

Yang, Le. "Riemannian median and its estimation." LMS Journal of Computation and Mathematics 13 (December 2010): 461–79. http://dx.doi.org/10.1112/s1461157020090531.

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AbstractIn this paper, we define the geometric median for a probability measure on a Riemannian manifold, give its characterization and a natural condition to ensure its uniqueness. In order to compute the geometric median in practical cases, we also propose a subgradient algorithm and prove its convergence as well as estimating the error of approximation and the rate of convergence. The convergence property of this subgradient algorithm, which is a generalization of the classical Weiszfeld algorithm in Euclidean spaces to the context of Riemannian manifolds, also improves a recent result of P. T. Fletcheret al. [NeuroImage45 (2009) S143–S152].

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43

Karabatsos, George, and William H. Batchelder. "Markov chain estimation for test theory without an answer key." Psychometrika 68, no. 3 (September 2003): 373–89. http://dx.doi.org/10.1007/bf02294733.

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44

Nolan, John P. "Multivariate elliptically contoured stable distributions: theory and estimation." Computational Statistics 28, no. 5 (January 30, 2013): 2067–89. http://dx.doi.org/10.1007/s00180-013-0396-7.

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45

KIMELBLAT, VLADIMIR. "APPLYING 1/F NOISE FOR DRIFT ESTIMATION." Fluctuation and Noise Letters 10, no. 02 (June 2011): 181–88. http://dx.doi.org/10.1142/s021947751100051x.

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The work introduces a new 1/f noise theory that focuses on limited signals. Usually, 1/f noise represents drift, because 1/f noise is the spectral power density of the drift. The subjects of the new theory are signals that have limited value and duration. Therefore the basis of the new theory of 1/f noise corresponds to the real properties of any device and signal comprising 1/f noise. On this basis, the standard deviation of 1/f noise was derived, which is the most important parameter of 1/f noise. This standard deviation has good consistency with (a) the widely used Hurst approximation, (b) the square root of time dependence of Brownian motion displacement, and (c) theoretically derived Brownian displacement. Comparison of an existing 1/f noise theory and the new one shows that both theories are incompatible because subjects of the existing 1/f noise theory are limitless signals, which do not exist.

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46

Crisan, Dan. "The stochastic filtering problem: a brief historical account." Journal of Applied Probability 51, A (December 2014): 13–22. http://dx.doi.org/10.1239/jap/1417528463.

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Onwards from the mid-twentieth century, the stochastic filtering problem has caught the attention of thousands of mathematicians, engineers, statisticians, and computer scientists. Its applications span the whole spectrum of human endeavour, including satellite tracking, credit risk estimation, human genome analysis, and speech recognition. Stochastic filtering has engendered a surprising number of mathematical techniques for its treatment and has played an important role in the development of new research areas, including stochastic partial differential equations, stochastic geometry, rough paths theory, and Malliavin calculus. It also spearheaded research in areas of classical mathematics, such as Lie algebras, control theory, and information theory. The aim of this paper is to give a brief historical account of the subject concentrating on the continuous-time framework.

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47

Harwell, Michael R., Frank B. Baker, and Michael Zwarts. "Item Parameter Estimation Via Marginal Maximum Likelihood and an EM Algorithm: A Didactic." Journal of Educational Statistics 13, no. 3 (September 1988): 243–71. http://dx.doi.org/10.3102/10769986013003243.

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The Bock and Aitkin (1981) Marginal Maximum Likelihood/EM approach to item parameter estimation is an alternative to the classical joint maximum likelihood procedure of item response theory. Unfortunately, the complexity of the underlying mathematics and the terse nature of the existing literature has made understanding of the approach difficult. To make the approach accessible to a wider audience, the present didactic paper provides the essential mathematical details of a marginal maximum likelihood/EM solution and shows how it can be used to obtain consistent item parameter estimates. For pedagogical purposes, a short BASIC computer program is used to illustrate the underlying simplicity of the method.

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48

ODEN, J. TINSLEY, SERGE PRUDHOMME, TIM WESTERMANN, JON BASS, and MARK E. BOTKIN. "ERROR ESTIMATION OF EIGENFREQUENCIES FOR ELASTICITY AND SHELL PROBLEMS." Mathematical Models and Methods in Applied Sciences 13, no. 03 (March 2003): 323–44. http://dx.doi.org/10.1142/s0218202503002520.

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In this paper, a method for deriving computable estimates of the approximation error in eigenvalues or eigenfrequencies of three-dimensional linear elasticity or shell problems is presented. The analysis for the error estimator follows the general approach of goal-oriented error estimation for which the error is estimated in so-called quantities of interest, here the eigenfrequencies, rather than global norms. A general theory is developed and is then applied to the linear elasticity equations. For the shell analysis, it is assumed that the shell model is not completely known and additional errors are introduced due to modeling approximations. The approach is then based on recovering three-dimensional approximations from the shell eigensolution and employing the error estimator developed for linear elasticity. The performance of the error estimator is demonstrated on several test problems.

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49

Ma, Jingxin, Haisen Li, Jianjun Zhu, and Baowei Chen. "Sound Velocity Estimation of Seabed Sediment Based on Parametric Array Sonar." Mathematical Problems in Engineering 2020 (August 14, 2020): 1–6. http://dx.doi.org/10.1155/2020/9810215.

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Backscattered sound waves of seabed sediments are important information carriers in seafloor detection and acoustic characteristic parameters inversion. Most of the existing methods for estimating geoacoustic parameters are based on multiangle seabed backscattered signal processing and suitable for flat seafloor conditions with uniform sediment thickness. This usually deviates from the real field conditions and affects the accuracy of parameter estimation. In this paper, the sound ray propagation theory is studied and analysed under the condition of sloping seabed and uneven sediment thickness. Based on the phased parameter array sonar system, a method of acoustic parameters estimation of the sediment under inclined seabed conditions is proposed. The simulation results show that the new method shows good adaptability to different inclination angles of the seabed and solves the problem of accuracy of acoustic parameter estimation of the inclined seabed sediments. The model will greatly reduce the seafloor topography requirements in the sediment acoustic parameter inversion, such as velocity, layer thickness, and acoustic impedance.

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50

Crisan, Dan. "The stochastic filtering problem: a brief historical account." Journal of Applied Probability 51, A (December 2014): 13–22. http://dx.doi.org/10.1017/s002190020002115x.

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Onwards from the mid-twentieth century, the stochastic filtering problem has caught the attention of thousands of mathematicians, engineers, statisticians, and computer scientists. Its applications span the whole spectrum of human endeavour, including satellite tracking, credit risk estimation, human genome analysis, and speech recognition. Stochastic filtering has engendered a surprising number of mathematical techniques for its treatment and has played an important role in the development of new research areas, including stochastic partial differential equations, stochastic geometry, rough paths theory, and Malliavin calculus. It also spearheaded research in areas of classical mathematics, such as Lie algebras, control theory, and information theory. The aim of this paper is to give a brief historical account of the subject concentrating on the continuous-time framework.

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Journal articles on the topic 'Mathematics Estimation theory'

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