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Journal articles on the topic 'Weighted least squares'

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Author: Grafiati

Published: 4 June 2021

Last updated: 28 January 2023

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1

Bloch, Daniel A., and Lincoln E. Moses. "Nonoptimally Weighted Least Squares." American Statistician 42, no. 1 (February 1988): 50. http://dx.doi.org/10.2307/2685260.

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2

Bloch, Daniel A., and Lincoln E. Moses. "Nonoptimally Weighted Least Squares." American Statistician 42, no. 1 (February 1988): 50–53. http://dx.doi.org/10.1080/00031305.1988.10475521.

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3

Romano, Joseph P., and Michael Wolf. "Resurrecting weighted least squares." Journal of Econometrics 197, no. 1 (March 2017): 1–19. http://dx.doi.org/10.1016/j.jeconom.2016.10.003.

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4

Kiers, Henk A. L. "Weighted least squares fitting using ordinary least squares algorithms." Psychometrika 62, no. 2 (June 1997): 251–66. http://dx.doi.org/10.1007/bf02295279.

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5

Amiri-Simkooei, A., and S. Jazaeri. "Weighted total least squares formulated by standard least squares theory." Journal of Geodetic Science 2, no. 2 (January 1, 2012): 113–24. http://dx.doi.org/10.2478/v10156-011-0036-5.

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Weighted total least squares formulated by standard least squares theoryThis contribution presents a simple, attractive, and flexible formulation for the weighted total least squares (WTLS) problem. It is simple because it is based on the well-known standard least squares theory; it is attractive because it allows one to directly use the existing body of knowledge of the least squares theory; and it is flexible because it can be used to a broad field of applications in the error-invariable (EIV) models. Two empirical examples using real and simulated data are presented. The first example, a linear regression model, takes the covariance matrix of the coefficient matrix asQA=Qn⊗Qm, while the second example, a 2-D affine transformation, takes a general structure of the covariance matrixQA.The estimates for the unknown parameters along with their standard deviations of the estimates are obtained for the two examples. The results are shown to be identical to those obtained based on thenonlinearGauss-Helmert model (GHM). We aim to have an impartial evaluation of WTLS and GHM. We further explore the high potential capability of the presented formulation. One can simply obtain the covariance matrix of the WTLS estimates. In addition, one can generalize the orthogonal projectors of the standard least squares from which estimates for the residuals and observations (along with their covariance matrix), and the variance of the unit weight can directly be derived. Also, the constrained WTLS, variance component estimation for an EIV model, and the theory of reliability and data snooping can easily be established, which are in progress for future publications.

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6

Cohen, Albert, and Giovanni Migliorati. "Optimal weighted least-squares methods." SMAI journal of computational mathematics 3 (October 1, 2017): 181–203. http://dx.doi.org/10.5802/smai-jcm.24.

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7

Park, Sungwoo, and Dianne P. O’Leary. "Implicitly-weighted total least squares." Linear Algebra and its Applications 435, no. 3 (August 2011): 560–77. http://dx.doi.org/10.1016/j.laa.2010.06.020.

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8

Kraus, F. J., and M. F. Senning. "Parameter Weighted Least Squares Fitting." IFAC Proceedings Volumes 18, no. 11 (September 1985): 501–6. http://dx.doi.org/10.1016/s1474-6670(17)60174-5.

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9

Magnus, Jan R., Wendun Wang, and Xinyu Zhang. "Weighted-Average Least Squares Prediction." Econometric Reviews 35, no. 6 (October 20, 2014): 1040–74. http://dx.doi.org/10.1080/07474938.2014.977065.

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10

Chen, Jiahua, and Jun Shao. "Iterative Weighted Least Squares Estimators." Annals of Statistics 21, no. 2 (June 1993): 1071–92. http://dx.doi.org/10.1214/aos/1176349165.

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11

Shao, Jun. "Jackknifing Weighted Least Squares Estimators." Journal of the Royal Statistical Society: Series B (Methodological) 51, no. 1 (September 1989): 139–56. http://dx.doi.org/10.1111/j.2517-6161.1989.tb01755.x.

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12

DiCiccio, Cyrus J., Joseph P. Romano, and Michael Wolf. "Improving weighted least squares inference." Econometrics and Statistics 10 (April 2019): 96–119. http://dx.doi.org/10.1016/j.ecosta.2018.06.005.

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13

Shao, Jun. "Ordinary and weighted least-squares estimators." Canadian Journal of Statistics 18, no. 4 (December 1990): 327–36. http://dx.doi.org/10.2307/3315839.

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14

Li, Yifan, Ingmar Nolte, Michalis Vasios, Valeri Voev, and Qi Xu. "Weighted Least Squares Realized Covariation Estimation." Journal of Banking & Finance 137 (April 2022): 106420. http://dx.doi.org/10.1016/j.jbankfin.2022.106420.

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15

Chatterjee, samprit, and Martin Mächler. "Robust regression:a weighted least squares approach." Communications in Statistics - Theory and Methods 26, no. 6 (January 1997): 1381–94. http://dx.doi.org/10.1080/03610929708831988.

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16

Kleijnen, Jack P. C., Peter C. A. Karremans, Wim K. Oortwijn, and Willem J. H. Van Groenendaal. "Jackknifing estimated weighted least squares: Jewls." Communications in Statistics - Theory and Methods 16, no. 3 (January 1987): 747–64. http://dx.doi.org/10.1080/03610928708829400.

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17

Magee, Lonnie. "Improving survey-weighted least squares regression." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 60, no. 1 (1998): 115–26. http://dx.doi.org/10.1111/1467-9868.00112.

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18

Haji-Ali, Abdul-Lateef, Fabio Nobile, Raúl Tempone, and Sören Wolfers. "Multilevel weighted least squares polynomial approximation." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 2 (March 2020): 649–77. http://dx.doi.org/10.1051/m2an/2019045.

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Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

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19

Ruppert, D., and M. P. Wand. "Multivariate Locally Weighted Least Squares Regression." Annals of Statistics 22, no. 3 (September 1994): 1346–70. http://dx.doi.org/10.1214/aos/1176325632.

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20

XU, L., J. JIANG, W. LIN, Y. ZHOU, H. WU, G. SHEN, and R. YU. "Optimized sample-weighted partial least squares." Talanta 71, no. 2 (February 15, 2007): 561–66. http://dx.doi.org/10.1016/j.talanta.2006.04.039.

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21

Green, Peter J. "Regression, curvature and weighted least squares." Mathematical Programming 42, no. 1-3 (April 1988): 41–51. http://dx.doi.org/10.1007/bf01589391.

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22

Víšek, Jan Ámos. "REPRESENTATION OF THE LEAST WEIGHTED SQUARES." Advances and Applications in Statistics 47, no. 2 (December 18, 2015): 91–144. http://dx.doi.org/10.17654/adasnov2015_091_144.

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23

Jian, Xiaodong, Ricardo A. Olea, and Yun-Sheng Yu. "Semivariogram modeling by weighted least squares." Computers & Geosciences 22, no. 4 (May 1996): 387–97. http://dx.doi.org/10.1016/0098-3004(95)00095-x.

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24

Zhou, Y., and X. Fang. "A mixed weighted least squares and weighted total least squares adjustment method and its geodetic applications." Survey Review 48, no. 351 (March 30, 2016): 421–29. http://dx.doi.org/10.1179/1752270615y.0000000040.

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25

Chen, Chuanfa, Changqing Yan, and Yanyan Li. "A robust weighted least squares support vector regression based on least trimmed squares." Neurocomputing 168 (November 2015): 941–46. http://dx.doi.org/10.1016/j.neucom.2015.05.031.

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26

Bewley, Ronald. "Weighted Least Squares Estimation from Grouped Observations." Review of Economics and Statistics 71, no. 1 (February 1989): 187. http://dx.doi.org/10.2307/1928070.

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27

Hwang, Changha, and Jooyong Shim. "Geographically weighted least squares-support vector machine." Journal of the Korean Data and Information Science Society 28, no. 1 (January 31, 2017): 227–35. http://dx.doi.org/10.7465/jkdi.2017.28.1.227.

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28

Jeng, Yih Nen, and Wu Sheng Lin. "Weighted least squares method of grid generation." AIAA Journal 33, no. 2 (February 1995): 364–65. http://dx.doi.org/10.2514/3.12396.

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29

Lee, Jaechoul. "A Reformulation of Weighted Least Squares Estimators." American Statistician 63, no. 1 (February 2009): 49–55. http://dx.doi.org/10.1198/tast.2009.0011.

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30

Nja, M. "A Modified Iterative Weighted Least Squares Method." British Journal of Mathematics & Computer Science 4, no. 6 (January 10, 2014): 849–57. http://dx.doi.org/10.9734/bjmcs/2014/7442.

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31

Magnus, Jan R., and Giuseppe De Luca. "WEIGHTED-AVERAGE LEAST SQUARES (WALS): A SURVEY." Journal of Economic Surveys 30, no. 1 (November 4, 2014): 117–48. http://dx.doi.org/10.1111/joes.12094.

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32

Wang, Jin, Gwanggil Jeon, and Jechang Jeong. "De-Interlacing Algorithm Using Weighted Least Squares." IEEE Transactions on Circuits and Systems for Video Technology 24, no. 1 (January 2014): 39–48. http://dx.doi.org/10.1109/tcsvt.2013.2280068.

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33

Ping-Teng Chang and E. Stanley Lee. "A generalized fuzzy weighted least-squares regression." Fuzzy Sets and Systems 82, no. 3 (September 1996): 289–98. http://dx.doi.org/10.1016/0165-0114(95)00284-7.

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34

Zhang, M. H., Q. S. Xu, and D. L. Massart. "Averaged and weighted average partial least squares." Analytica Chimica Acta 504, no. 2 (February 2004): 279–89. http://dx.doi.org/10.1016/j.aca.2003.10.056.

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35

Yamada, Koichi M. T. "Standard deviations in weighted least-squares analyses." Journal of Molecular Spectroscopy 156, no. 2 (December 1992): 512–16. http://dx.doi.org/10.1016/0022-2852(92)90252-j.

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36

Chinn, G., and Sung-Cheng Huang. "Weighted least-squares filtered backprojection tomographic reconstruction." IEEE Signal Processing Letters 2, no. 3 (March 1995): 49–50. http://dx.doi.org/10.1109/97.372914.

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37

WU, WEN-TENG, Y. T. CHU, and KUO-CHIEH CHEN. "Moving identification via weighted least-squares estimation." International Journal of Systems Science 18, no. 3 (January 1987): 477–86. http://dx.doi.org/10.1080/00207728708963981.

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38

Hough, Patricia D., and Stephen A. Vavasis. "Complete Orthogonal Decomposition for Weighted Least Squares." SIAM Journal on Matrix Analysis and Applications 18, no. 2 (April 1997): 369–92. http://dx.doi.org/10.1137/s089547989528079x.

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39

Carlson, B. D., and D. Willner. "Antenna pattern synthesis using weighted least squares." IEE Proceedings H Microwaves, Antennas and Propagation 139, no. 1 (1992): 11. http://dx.doi.org/10.1049/ip-h-2.1992.0003.

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40

Cressie, Noel. "Fitting variogram models by weighted least squares." Journal of the International Association for Mathematical Geology 17, no. 5 (July 1985): 563–86. http://dx.doi.org/10.1007/bf01032109.

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41

Chen, Tsu-Fen. "Weighted least-squares approximationsto nonlinear hyperbolic equations." Computers & Mathematics with Applications 48, no. 7-8 (October 2004): 1059–76. http://dx.doi.org/10.1016/j.camwa.2004.10.005.

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42

Gotway, Carol A. "Fitting semivariogram models by weighted least squares." Computers & Geosciences 17, no. 1 (January 1991): 171–72. http://dx.doi.org/10.1016/0098-3004(91)90085-r.

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43

Choi, Jaesung. "Type I projection sum of squares by weighted least squares." Journal of the Korean Data and Information Science Society 25, no. 2 (March 31, 2014): 423–29. http://dx.doi.org/10.7465/jkdi.2014.25.2.423.

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44

Zang, Zhuquan, Robert R. Bitmead, and Michel Gevers. "Iterative weighted least-squares identification and weighted LQG control design." Automatica 31, no. 11 (November 1995): 1577–94. http://dx.doi.org/10.1016/0005-1098(95)00082-8.

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45

Li, Ying, Musheng Wei, Fengxia Zhang, and Jianli Zhao. "On accurate error estimates for the quaternion least squares and weighted least squares problems." International Journal of Computer Mathematics 97, no. 8 (July 18, 2019): 1662–77. http://dx.doi.org/10.1080/00207160.2019.1642469.

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46

D’Urso, Pierpaolo, and Riccardo Massari. "Weighted Least Squares and Least Median Squares estimation for the fuzzy linear regression analysis." METRON 71, no. 3 (October 23, 2013): 279–306. http://dx.doi.org/10.1007/s40300-013-0025-9.

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47

Yang, Bo, and Liang Zhang. "A Novel Sparse Weighted Least Squares Support Vector Classifier." Advanced Materials Research 842 (November 2013): 746–49. http://dx.doi.org/10.4028/www.scientific.net/amr.842.746.

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A novel sparse weighted LSSVM classifier is proposed in this paper, which is based on Suykens weighted LSSVM. Unlike Suykens weighted LSSVM, the proposed weighted method is more suitable for classification. The distance between sample and classification border is used as the sample importance measure in our weighted method. Based on this importance measure, a new weight calculating function, using which can adjust the sparseness of weight, is designed. In order to solve the imbalance problem, a kind of normalization weights calculating method is proposed. Finally, the proposed method is used on digit recognition. Comparative experiment results show that the proposed sparse weighted LSSVM can improve the recognition correct rate effectively.

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48

Choi, Sangbum, Taehwa Choi, Hyunsoon Cho, and Dipankar Bandyopadhyay. "Weighted least‐squares regression with competing risks data." Statistics in Medicine 41, no. 2 (October 23, 2021): 227–41. http://dx.doi.org/10.1002/sim.9232.

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49

Bouhlel, Noura, Ghada Feki, and Chokri Ben Amar. "Adaptive weighted least squares regression for subspace clustering." Knowledge and Information Systems 63, no. 11 (October 11, 2021): 2883–900. http://dx.doi.org/10.1007/s10115-021-01612-1.

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50

Carp, Doina, Constantin Popa, Tobias Preclik, and Ulrich Rüde. "Iterative Solution of Weighted Linear Least Squares Problems." Analele Universitatii "Ovidius" Constanta - Seria Matematica 28, no. 2 (July 1, 2020): 53–65. http://dx.doi.org/10.2478/auom-2020-0019.

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AbstractIn this report we show that the iterated regularization scheme due to Riley and Golub, sometimes also called the iterated Tikhonov regularization, can be generalized to damped least squares problems where the weights matrix D is not necessarily the identity but a general symmetric and positive definite matrix. We show that the iterative scheme approaches the same point as the unique solutions of the regularized problem, when the regularization parameter goes to 0. Furthermore this point can be characterized as the solution of a weighted minimum Euclidean norm problem. Finally several numerical experiments were performed in the field of rigid multibody dynamics supporting the theoretical claims.

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