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Journal articles on the topic 'Least squares'

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Published: 4 June 2021
Last updated: 31 July 2024

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1

AL-CHALABI, M. "WHEN LEAST-SQUARES SQUARES LEAST1." Geophysical Prospecting 40, no. 3 (April 1992): 359–78. http://dx.doi.org/10.1111/j.1365-2478.1992.tb00380.x.

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2

Fearn, Tom. "Least Squares." NIR news 10, no. 1 (February 1999): 7–13. http://dx.doi.org/10.1255/nirn.502.

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3

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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4

Petras, Ivo, and Igor Podlubny. "Least Squares or Least Circles?" CHANCE 23, no. 2 (March 2010): 38–42. http://dx.doi.org/10.1080/09332480.2010.10739804.

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5

Petras, Ivo, and Igor Podlubny. "Least squares or least circles?" CHANCE 23, no. 2 (April 24, 2010): 38–42. http://dx.doi.org/10.1007/s00144-010-0021-2.

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6

Ward, J. "Revisiting least squares." Teaching Mathematics and its Applications 17, no. 1 (March 1, 1998): 19–21. http://dx.doi.org/10.1093/teamat/17.1.19.

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7

Qiu, Peihua. "Generalized Least Squares." Technometrics 47, no. 4 (November 2005): 519. http://dx.doi.org/10.1198/tech.2005.s323.

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8

GRANT, IAN H. W. M. "Recursive Least Squares." Teaching Statistics 9, no. 1 (January 1987): 15–18. http://dx.doi.org/10.1111/j.1467-9639.1987.tb00614.x.

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9

Hansen, Bruce E. "Perpendicular Least Squares." Econometric Theory 6, no. 4 (December 1990): 485. http://dx.doi.org/10.1017/s0266466600005491.

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10

Goerlich, Francisco. "Perpendicular Least Squares." Econometric Theory 8, no. 01 (March 1992): 147–48. http://dx.doi.org/10.1017/s0266466600010860.

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11

Robins, James. "Partial-Least Squares." Long Range Planning 45, no. 5-6 (October 2012): 309–11. http://dx.doi.org/10.1016/j.lrp.2012.10.002.

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12

Diamond, Phil. "Fuzzy least squares." Information Sciences 46, no. 3 (December 1988): 141–57. http://dx.doi.org/10.1016/0020-0255(88)90047-3.

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13

Fearn, Tom. "Classical Least Squares." NIR news 21, no. 7 (November 2010): 16–17. http://dx.doi.org/10.1255/nirn.1209.

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14

Kaufman, L. "Maximum likelihood, least squares, and penalized least squares for PET." IEEE Transactions on Medical Imaging 12, no. 2 (June 1993): 200–214. http://dx.doi.org/10.1109/42.232249.

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15

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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16

Boswijk, Peter, and Heinz Neudecker. "An Inequality Between Perpendicular Least-Squares and Ordinary Least-Squares." Econometric Theory 10, no. 2 (June 1994): 441–42. http://dx.doi.org/10.1017/s0266466600008537.

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17

Farebrother, R. W. "An Inequality between Perpendicular Least Squares and Ordinary Least Squares." Econometric Theory 11, no. 4 (August 1995): 807–8. http://dx.doi.org/10.1017/s0266466600009853.

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18

Becker, William, and Peter Kennedy. "A Lesson in Least Squares and R Squared." American Statistician 46, no. 4 (November 1992): 282. http://dx.doi.org/10.2307/2685313.

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19

Liu, Qiaohua, Chuge Li, and Yimin Wei. "Condition numbers of multidimensional mixed least squares-total least squares problems." Applied Numerical Mathematics 178 (August 2022): 52–68. http://dx.doi.org/10.1016/j.apnum.2022.03.014.

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20

Kalsi, Anoop, and Dianne P. O'Leary. "Fast Algorithms for Structured Least Squares and Total Least Squares Problems." Journal of Research of the National Institute of Standards and Technology 111, no. 2 (March 2006): 113. http://dx.doi.org/10.6028/jres.111.010.

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21

Van Huffel, Sabine, and Joos Vandewalle. "Algebraic connections between the least squares and total least squares problems." Numerische Mathematik 55, no. 4 (July 1989): 431–49. http://dx.doi.org/10.1007/bf01396047.

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22

Giloni, A., and M. Padberg. "Least trimmed squares regression, least median squares regression, and mathematical programming." Mathematical and Computer Modelling 35, no. 9-10 (May 2002): 1043–60. http://dx.doi.org/10.1016/s0895-7177(02)00069-9.

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23

Chen, Keh-Wei, and A. S. Papadoupoulos. "Comparison of the linear least squares and nonlinear least squares spheres." Microelectronics Reliability 36, no. 1 (January 1996): 37–46. http://dx.doi.org/10.1016/0026-2714(95)00060-f.

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24

Paige, Christopher C., and Zdenek Strakoš. "Bounds for the least squares distance using scaled total least squares." Numerische Mathematik 91, no. 1 (March 1, 2002): 93–115. http://dx.doi.org/10.1007/s002110100317.

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25

Yang, Zhanshan. "An analysis of the mixed least squares-total least squares problems." Filomat 36, no. 12 (2022): 4195–209. http://dx.doi.org/10.2298/fil2212195y.

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In this paper, we first get further consideration of the first order perturbation with normwise condition number of the MTLS problem. For easy estimation, we show a lower bound for the normwise condition number which is proved to be optimal. In order to overcome the problems encountered in calculating the normwise condition number, we give an upper bound for computing more effectively and nonstandard and unusual perturbation bounds for the MTLS problem. Both of the two types of the perturbation bounds can enjoy storage and computational advantages. For getting more insight into the sensitivity of the MTLS technique with respect to perturbations in all data, we analyze the corrections applied by MTLS to the data in Ax ? b to make the set compatible and indicate how closely the data A, b fit the so-called general errors-in-variables model. On how to estimate the conditioning of the MTLS problem more effectively, we propose statistical algorithms by taking advantage of the superiority of small sample statistical condition estimation (SCE) techniques.
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26

Erkut, Erhan, and Armann Ingolfsson. "Let's Put the Squares in Least-Squares." INFORMS Transactions on Education 1, no. 1 (September 2000): 47–50. http://dx.doi.org/10.1287/ited.1.1.47.

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27

SUGIYAMA, Masashi, and Taiji SUZUKI. "Least-Squares Independence Test." IEICE Transactions on Information and Systems E94-D, no. 6 (2011): 1333–36. http://dx.doi.org/10.1587/transinf.e94.d.1333.

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28

Glaister, P. "85.13 Least Squares Revisited." Mathematical Gazette 85, no. 502 (March 2001): 104. http://dx.doi.org/10.2307/3620485.

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29

Máca, Jaromír, and Bohus Leitner. "Nonlinear least squares method." Communications - Scientific letters of the University of Zilina 1, no. 2 (June 30, 1999): 52–58. http://dx.doi.org/10.26552/com.c.1999.2.52-58.

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30

Ripa, P. "Least squares data fitting." Ciencias Marinas 28, no. 1 (February 1, 2002): 79–105. http://dx.doi.org/10.7773/cm.v28i1.204.

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31

Teunissen, P. J. G., and E. H. Knickmeyer. "NONLINEARITY AND LEAST SQUARES." CISM journal 42, no. 4 (January 1988): 321–30. http://dx.doi.org/10.1139/geomat-1988-0027.

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Since almost all functional relations in our geodetic models are nonlinear, it is important, especially from a statistical inference point of view, to know how nonlinearity manifests itself at the various stages of an adjustment. In this paper particular attention is given to the effect of nonlinearity on the first two moments of least squares estimators. Expressions for the moments of least squares estimators of parameters, residuals and functions derived from parameters, are given. The measures of nonlinearity are discussed both from a statistical and differential geometric point of view. Finally, our results are applied to the 2D symmetric Helmert transformation with a rotational invariant covariance structure.
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32

RAO SRIPADA, N., and D. GRANT FISHER. "Improved least squares identification." International Journal of Control 46, no. 6 (December 1987): 1889–913. http://dx.doi.org/10.1080/00207178708934023.

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33

Zoia, Maria Grazia. "Restricted least squares revisited." Journal of Statistics and Management Systems 6, no. 1 (January 2003): 95–100. http://dx.doi.org/10.1080/09720510.2003.10701071.

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34

Gatto, Marta, and Fabio Marcuzzi. "Unbiased Least-Squares Modelling." Mathematics 8, no. 6 (June 16, 2020): 982. http://dx.doi.org/10.3390/math8060982.

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In this paper we analyze the bias in a general linear least-squares parameter estimation problem, when it is caused by deterministic variables that have not been included in the model. We propose a method to substantially reduce this bias, under the hypothesis that some a-priori information on the magnitude of the modelled and unmodelled components of the model is known. We call this method Unbiased Least-Squares (ULS) parameter estimation and present here its essential properties and some numerical results on an applied example.
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35

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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36

Hayes, Kevin, and John Haslett. "Simplifying General Least Squares." American Statistician 53, no. 4 (November 1999): 376. http://dx.doi.org/10.2307/2686060.

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37

Tofallis, Chris. "Least Squares Percentage Regression." Journal of Modern Applied Statistical Methods 7, no. 2 (November 1, 2008): 526–34. http://dx.doi.org/10.22237/jmasm/1225513020.

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38

Passi, Ranjit M., and Claude Morel. "Least squares adaptive polynomials." Communications in Statistics - Theory and Methods 18, no. 1 (January 1989): 315–29. http://dx.doi.org/10.1080/03610928908829900.

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39

Manson, Josiah, and Scott Schaefer. "Moving Least Squares Coordinates." Computer Graphics Forum 29, no. 5 (September 21, 2010): 1517–24. http://dx.doi.org/10.1111/j.1467-8659.2010.01760.x.

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40

Boyé, S., G. Guennebaud, and C. Schlick. "Least Squares Subdivision Surfaces." Computer Graphics Forum 29, no. 7 (September 2010): 2021–28. http://dx.doi.org/10.1111/j.1467-8659.2010.01788.x.

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41

Kavan, L., A. W. Bargteil, and P. P. Sloan. "Least Squares Vertex Baking." Computer Graphics Forum 30, no. 4 (June 2011): 1319–26. http://dx.doi.org/10.1111/j.1467-8659.2011.01991.x.

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42

Heller, René, Kai Rodenbeck, and Michael Hippke. "Transit least-squares survey." Astronomy & Astrophysics 625 (May 2019): A31. http://dx.doi.org/10.1051/0004-6361/201935276.

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We apply for the first time the transit least-squares (TLS) algorithm to search for new transiting exoplanets. TLS has been developed as a successor to the box least-squares (BLS) algorithm, which has served as a standard tool for the detection of periodic transits. In this proof-of-concept paper, we demonstrate that TLS finds small planets that have previously been missed. We show the capabilities of TLS using the K2 EVEREST-detrended light curve of the star K2-32 (EPIC 205071984), which has been known to have three transiting planets. TLS detects these known Neptune-sized planets K2-32 b, d, and c in an iterative search and finds an additional transit signal with a high signal detection efficiency (SDETLS) of 26.1 at a period of 4.34882−0.00075+0.00069 d. We show that this additional signal remains detectable (SDETLS = 13.2) with TLS in the K2SFF light curve of K2-32, which includes a less optimal detrending of the systematic trends. The signal is below common detection thresholds if searched with BLS in the K2SFF light curve (SDEBLS = 8.9), however, as in previous searches. Markov chain Monte Carlo sampling with the emcee software shows that the radius of this candidate is 1.01−0.09+0.10 R⊕. We analyzed its phase-folded transit light curve using the vespa software and calculated a false-positive probability FPP = 3.1 × 10−3. Taking into account the multiplicity boost of the system, we estimate an FPP < 3.1 × 10−4, which formally validates K2-32 e as a planet. K2-32 now hosts at least four planets that are very close to a 1:2:5:7 mean motion resonance chain. The offset of the orbital periods of K2-32 e and b from a 1:2 mean motion resonance agrees very well with the sample of transiting multiplanet systems from Kepler, lending further credence to the planetary nature of K2-32 e. We expect that TLS can find many more transits of Earth-sized and even smaller planets in the Kepler and K2 data that have so far remained undetected with algorithms that search for box-like signals.
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43

Wu, Yong, Jun Wang, and Pei‐Chuan Zhang. "Least‐squares particle filter." Electronics Letters 50, no. 24 (November 2014): 1881–82. http://dx.doi.org/10.1049/el.2014.2980.

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44

Zhao, Yiyuan. "Least squares optimal linearization." Journal of Guidance, Control, and Dynamics 17, no. 5 (September 1994): 990–97. http://dx.doi.org/10.2514/3.21300.

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45

Heller, René, Michael Hippke, and Kai Rodenbeck. "Transit least-squares survey." Astronomy & Astrophysics 627 (July 2019): A66. http://dx.doi.org/10.1051/0004-6361/201935600.

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The extended Kepler mission (K2) has revealed more than 500 transiting planets in roughly 500 000 stellar light curves. All of these were found either with the box least-squares algorithm or by visual inspection. Here we use our new transit least-squares (TLS) algorithm to search for additional planets around all K2 stars that are currently known to host at least one planet. We discover and statistically validate 17 new planets with radii ranging from about 0.7 Earth radii (R⊕) to roughly 2.2 R⊕ and a median radius of 1.18 R⊕. EPIC 201497682.03, with a radius of 0.692+0.059−0.048, is the second smallest planet ever discovered with K2. The transit signatures of these 17 planets are typically 200 ppm deep (ranging from 100 ppm to 2000 ppm), and their orbital periods extend from about 0.7 d to 34 d with a median value of about 4 d. Fourteen of these 17 systems only had one known planet before, and they now join the growing number of multi-planet systems. Most stars in our sample have subsolar masses and radii. The small planetary radii in our sample are a direct result of the higher signal detection efficiency that TLS has compared to box-fitting algorithms in the shallow-transit regime. Our findings help in populating the period-radius diagram with small planets. Our discovery rate of about 3.7% within the group of previously known K2 systems suggests that TLS can find over 100 additional Earth-sized planets in the data of the Kepler primary mission.
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46

Heller, René, Michael Hippke, Jantje Freudenthal, Kai Rodenbeck, Natalie M. Batalha, and Steve Bryson. "Transit least-squares survey." Astronomy & Astrophysics 638 (June 2020): A10. http://dx.doi.org/10.1051/0004-6361/201936929.

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The Sun-like star Kepler-160 (KOI-456) has been known to host two transiting planets, Kepler-160 b and c, of which planet c shows substantial transit-timing variations (TTVs). We studied the transit photometry and the TTVs of this system in our search for a suspected third planet. We used the archival Kepler photometry of Kepler-160 to search for additional transiting planets using a combination of our Wōtan detrending algorithm and our transit least-squares detection algorithm. We also used the Mercury N-body gravity code to study the orbital dynamics of the system in trying to explain the observed TTVs of planet c. First, we recovered the known transit series of planets Kepler-160 b and c. Then we found a new transiting candidate with a radius of 1.91−0.14+0.17 Earth radii (R⊕), an orbital period of 378.417−0.025+0.028 d, and Earth-like insolation. The vespa software predicts that this signal has an astrophysical false-positive probability of FPP3 = 1.8 × 10−3 when the multiplicity of the system is taken into account. Kepler vetting diagnostics yield a multiple event statistic of MES = 10.7, which corresponds to an ~85% reliability against false alarms due to instrumental artifacts such as rolling bands. We are also able to explain the observed TTVs of planet c with the presence of a previously unknown planet. The period and mass of this new planet, however, do not match the period and mass of the new transit candidate. Our Markov chain Monte Carlo simulations of the TTVs of Kepler-160 c can be conclusively explained by a new nontransiting planet with a mass between about 1 and 100 Earth masses and an orbital period between about 7 and 50 d. We conclude that Kepler-160 has at least three planets, one of which is the nontransiting planet Kepler-160 d. The expected stellar radial velocity amplitude caused by this new planet ranges between about 1 and 20 m s−1. We also find the super-Earth-sized transiting planet candidate KOI-456.04 in the habitable zone of this system, which could be the fourth planet.
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47

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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48

Hayes, Kevin, and John Haslett. "Simplifying General Least Squares." American Statistician 53, no. 4 (November 1999): 376–81. http://dx.doi.org/10.1080/00031305.1999.10474493.

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49

Asensio Ramos, A., and P. Petit. "Bayesian least squares deconvolution." Astronomy & Astrophysics 583 (October 27, 2015): A51. http://dx.doi.org/10.1051/0004-6361/201526401.

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50

Iona, Mario. "Least squares of What?" Physics Teacher 26, no. 4 (April 1988): 201. http://dx.doi.org/10.1119/1.2342484.

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