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Journal articles on the topic 'Monotone splines'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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1

Bergersen, Linn Cecilie, Kukatharmini Tharmaratnam, and Ingrid K. Glad. "Monotone splines lasso." Computational Statistics & Data Analysis 77 (September 2014): 336–51. http://dx.doi.org/10.1016/j.csda.2014.03.013.

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2

Maad Sasane, Sara. "Monotone Smoothing Splines with Bounds." Acta Applicandae Mathematicae 169, no. 1 (February 3, 2020): 613–27. http://dx.doi.org/10.1007/s10440-020-00314-0.

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Abstract The problem of monotone smoothing splines with bounds is formulated as a constrained minimization problem of the calculus of variations. Existence and uniqueness of solutions of this problem is proved, as well as the equivalence of it to a finite dimensional but nonlinear optimization problem. A new algorithm for computing the solution which is a spline curve, using a branch and bound technique, is presented. The method is applied to examples in neuroscience and for fitting cumulative distribution functions from data.

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3

BELIAKOV, G. "MONOTONE APPROXIMATION OF AGGREGATION OPERATORS USING LEAST SQUARES SPLINES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, no. 06 (December 2002): 659–76. http://dx.doi.org/10.1142/s0218488502001715.

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The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexbility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.

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4

Ramsay, J. O. "Monotone Regression Splines in Action." Statistical Science 3, no. 4 (November 1988): 425–41. http://dx.doi.org/10.1214/ss/1177012761.

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5

Fujioka, Hiroyuki, and Hiroyuki Kano. "Monotone Smoothing Spline Curves Using Normalized Uniform Cubic B-splines." Transactions of the Institute of Systems, Control and Information Engineers 26, no. 11 (2013): 389–97. http://dx.doi.org/10.5687/iscie.26.389.

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6

Fujioka, Hiroyuki, and Hiroyuki Kano. "Monotone Smoothing Spline Curves Using Normalized Uniform Cubic B-splines." Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 2013 (May 5, 2013): 152–57. http://dx.doi.org/10.5687/sss.2013.152.

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7

Breiman, Leo. "[Monotone Regression Splines in Action]: Comment." Statistical Science 3, no. 4 (November 1988): 442–45. http://dx.doi.org/10.1214/ss/1177012762.

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8

Eubank, Randy. "[Monotone Regression Splines in Action]: Comment." Statistical Science 3, no. 4 (November 1988): 446–50. http://dx.doi.org/10.1214/ss/1177012763.

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9

Hastie, Trevor, and Robert Tibshirani. "[Monotone Regression Splines in Action]: Comment." Statistical Science 3, no. 4 (November 1988): 450–56. http://dx.doi.org/10.1214/ss/1177012764.

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10

Wahba, Grace. "[Monotone Regression Splines in Action]: Comment." Statistical Science 3, no. 4 (November 1988): 456–58. http://dx.doi.org/10.1214/ss/1177012765.

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11

Ramsay, J. O. "[Monotone Regression Splines in Action]: Rejoinder." Statistical Science 3, no. 4 (November 1988): 459–61. http://dx.doi.org/10.1214/ss/1177012766.

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12

Nagahara, Masaaki, and Clyde F. Martin. "Monotone Smoothing Splines using General Linear Systems." Asian Journal of Control 15, no. 2 (June 26, 2012): 461–68. http://dx.doi.org/10.1002/asjc.557.

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13

Andersson, Lars-Erik, and Tommy Elfving. "Interpolation and approximation by monotone cubic splines." Journal of Approximation Theory 66, no. 3 (September 1991): 302–33. http://dx.doi.org/10.1016/0021-9045(91)90033-7.

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14

Yuan, Yuan, Nan Chen, and Shiyu Zhou. "Modeling Regression Quantile Process Using Monotone B-Splines." Technometrics 59, no. 3 (April 13, 2017): 338–50. http://dx.doi.org/10.1080/00401706.2016.1211553.

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15

Cessie, S. Le, and E. J. Balder. "A note on monotone interpolation and smoothing splines." Numerical Functional Analysis and Optimization 15, no. 1-2 (January 1994): 47–54. http://dx.doi.org/10.1080/01630569408816548.

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16

Kvasov, B. I. "Monotone and convex interpolation by weighted cubic splines." Computational Mathematics and Mathematical Physics 53, no. 10 (October 2013): 1428–39. http://dx.doi.org/10.1134/s0965542513100102.

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17

Ramsay, J. O., and M. Abrahamowicz. "Binomial Regression with Monotone Splines: A Psychometric Application." Journal of the American Statistical Association 84, no. 408 (December 1989): 906–15. http://dx.doi.org/10.1080/01621459.1989.10478854.

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18

Schmidt, J. W. "Monotone Data Smoothing by Quadratic Splines via Dualization." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 70, no. 8 (1990): 299–307. http://dx.doi.org/10.1002/zamm.19900700802.

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19

Kopotun, Kirill, and Alexei Shadrin. "On k-Monotone Approximation by Free Knot Splines." SIAM Journal on Mathematical Analysis 34, no. 4 (January 2003): 901–24. http://dx.doi.org/10.1137/s0036141002358514.

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20

Kvasov, Boris I. "Monotone and convex interpolation by weighted quadratic splines." Advances in Computational Mathematics 40, no. 1 (April 19, 2013): 91–116. http://dx.doi.org/10.1007/s10444-013-9300-9.

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21

Zhang, Jin-Ting. "A simple and efficient monotone smoother using smoothing splines." Journal of Nonparametric Statistics 16, no. 5 (October 2004): 779–96. http://dx.doi.org/10.1080/10485250410001681167.

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22

Manni, C. "Monotone interpolation of order 3 by C2 cubic splines." IMA Journal of Numerical Analysis 17, no. 2 (April 1, 1997): 305–20. http://dx.doi.org/10.1093/imanum/17.2.305.

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23

Ideon, Erge, and Peeter Oja. "LINEAR/LINEAR RATIONAL SPLINE INTERPOLATION." Mathematical Modelling and Analysis 15, no. 4 (November 15, 2010): 447–55. http://dx.doi.org/10.3846/1392-6292.2010.15.447-455.

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For a strictly monotone function y on [a, b] we describe the construction of an interpolating linear/linear rational spline S of smoothness class C 1. We show that for the linear/linear rational splines we obtain ¦S(xi ) − y(xi )¦8 = O(h 4) on uniform mesh xi = a + ih, i = 0,…, n. We prove also the superconvergence of order h3 for the first derivative and of order h2 for the second derivative of S in certain points. Numerical examples support the obtained theoretical results. This work was supported by the Estonian Science Foundation grant 8313.

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24

Costantini, Paolo. "Co-Monotone Interpolating Splines of Arbitrary Degree—a Local Approach." SIAM Journal on Scientific and Statistical Computing 8, no. 6 (November 1987): 1026–34. http://dx.doi.org/10.1137/0908083.

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25

DETTE, HOLGER, and DANIEL ZIGGEL. "DISCOUNT CURVE ESTIMATION BY MONOTONIZING MCCULLOCH SPLINES." International Journal of Theoretical and Applied Finance 11, no. 05 (August 2008): 529–44. http://dx.doi.org/10.1142/s0219024908004919.

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In this paper a new method for monotone estimation of discount curves is proposed. The main idea of this approach is a simple modification of the commonly used (unconstrained) McCulloch Spline. We construct an integrated density estimate from the predicted values of the discount curve. It can be shown that this statistic is an estimate of the inverse of the discount function and the final estimate can be obtained by a numerical inversion. The resulting procedure is simple and we have implemented it in Excel and VBA, respectively. The performance is illustrated by several examples, in which the curve was previously estimated with an unconstrained McCulloch Spline.

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26

Konovalov, V. N., and D. Leviatan. "Freeknot splines approximation of Sobolev-type classes of s-monotone functions." Advances in Computational Mathematics 27, no. 2 (March 23, 2007): 211–36. http://dx.doi.org/10.1007/s10444-007-9032-9.

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27

Cai, Bo, Xiaoyan Lin, and Lianming Wang. "Bayesian proportional hazards model for current status data with monotone splines." Computational Statistics & Data Analysis 55, no. 9 (September 2011): 2644–51. http://dx.doi.org/10.1016/j.csda.2011.03.013.

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28

Lu, Minggen, Yan Liu, and Chin-Shang Li. "Efficient estimation of a linear transformation model for current status data via penalized splines." Statistical Methods in Medical Research 29, no. 1 (December 28, 2018): 3–14. http://dx.doi.org/10.1177/0962280218820406.

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We propose a flexible and computationally efficient penalized estimation method for a semi-parametric linear transformation model with current status data. To facilitate model fitting, the unknown monotone function is approximated by monotone B-splines, and a computationally efficient hybrid algorithm involving the Fisher scoring algorithm and the isotonic regression is developed. A goodness-of-fit test and model diagnostics are also considered. The asymptotic properties of the penalized estimators are established, including the optimal rate of convergence for the function estimator and the semi-parametric efficiency for the regression parameter estimators. An extensive numerical experiment is conducted to evaluate the finite-sample properties of the penalized estimators, and the methodology is further illustrated with two real studies.

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29

Shen, Jinglai, and Xiao Wang. "Estimation of Monotone Functions via P-Splines: A Constrained Dynamical Optimization Approach." SIAM Journal on Control and Optimization 49, no. 2 (January 2011): 646–71. http://dx.doi.org/10.1137/090774513.

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30

Bantis, Leonidas E., John V. Tsimikas, and Stelios D. Georgiou. "Survival estimation through the cumulative hazard function with monotone natural cubic splines." Lifetime Data Analysis 18, no. 3 (March 8, 2012): 364–96. http://dx.doi.org/10.1007/s10985-012-9218-4.

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31

Bremnes, John Bjørnar. "Constrained Quantile Regression Splines for Ensemble Postprocessing." Monthly Weather Review 147, no. 5 (May 1, 2019): 1769–80. http://dx.doi.org/10.1175/mwr-d-18-0420.1.

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Abstract Statistical postprocessing of ensemble forecasts is widely applied to make reliable probabilistic weather forecasts. Motivated by the fact that nature imposes few restrictions on the shape of forecast distributions, a flexible quantile regression method based on constrained spline functions (CQRS) is proposed and tested on ECMWF Ensemble Prediction System (ENS) wind speed forecasting data at 125 stations in Norway. First, it is demonstrated that constraining quantile functions to be monotone and bounded is preferable. Second, combining an ensemble quantile with the ensemble mean proved to be a good covariate for the respective quantile. Third, CQRS only needs to be applied to about 10 equidistant quantiles, while those between can be obtained by interpolation. A comparison of CQRS versus a mixture model of truncated and lognormal distributions showed slight overall improvements in quantile score (less than 1%), reliability, and to some extent also sharpness. For strong wind speed forecasts the quantile score was improved by up to 4.5% depending on lead time.

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32

Lu, M., Y. Zhang, and J. Huang. "Estimation of the mean function with panel count data using monotone polynomial splines." Biometrika 94, no. 3 (August 5, 2007): 705–18. http://dx.doi.org/10.1093/biomet/asm057.

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33

Schmidt, Jochen W., and Walter Heß. "S-convex, monotone, and positive interpolation with rational bicubic splines of C2-continuity." BIT 33, no. 3 (September 1993): 496–511. http://dx.doi.org/10.1007/bf01990531.

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34

Kopotun, K. A., D. Leviatan, and A. V. Prymak. "Nearly monotone and nearly convex approximation by smooth splines in Lp, p>0." Journal of Approximation Theory 160, no. 1-2 (September 2009): 103–12. http://dx.doi.org/10.1016/j.jat.2008.02.004.

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35

Jatmiko, Yogo Aryo. "Analisis Regresi Kuantil B-Splines Monoton Naik pada Hubungan Rata-Rata Lama Sekolah dan Pengeluaran Rumah Tangga Per Kapita di Provinsi Yogyakarta." Jurnal Matematika "MANTIK" 4, no. 2 (October 31, 2018): 128–36. http://dx.doi.org/10.15642/mantik.2018.4.2.128-136.

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The multidimensional problem in various countries that is always become the government's attention is the problem of poverty, Indonesia is no exception. Poverty is often associated with the education sector due to the function of education as a driving force of the transformation of society to break the chain of poverty. The pattern of relations between poverty and the education sector can be seen from the relationship between the level of education (mean years of schooling) and poverty level (per capita household expenditure). DI Yogyakarta is still the province with the largest percentage of poverty on the Java island despite showing a downward trend since 2007. This study aims to look at the relationship between the level of education (mean years of schooling) and poverty level (per capita household expenditure) in DI Yogyakarta Province 2016. The model that is suitable for determining household characteristics is quantile regression with the Increased monotone B-Splines method that links the mean years of schooling and per capita household expenditure. Estimation results based on the quantile regression model with Increased monotone B-Splines method found that households with the lowest education level are said to be very poor households if monthly per capita expenditure is less than 322,205 rupiah and is said to be a poor household if monthly per capita expenditure is between 322,205 rupiah to 426,666 rupiah. Meanwhile, households with the highest level of education are said to be very poor households if monthly per capita expenditure is less than 3,410,965 rupiahs and is said to be a poor household if monthly per capita expenditure is between 3,410,965 rupiahs up to 4,676,718 rupiahs

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36

Kwessi, Eddy, and Brice M. Nguelifack. "Signed-rank analysis of a partial linear model with B-splines estimated monotone non parametric function." Communications in Statistics - Theory and Methods 46, no. 10 (May 24, 2016): 4843–54. http://dx.doi.org/10.1080/03610926.2015.1089289.

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37

Bantis, Leonidas E., John V. Tsimikas, and Stelios D. Georgiou. "Survival estimation through the cumulative hazard with monotone natural cubic splines using convex optimization-the HCNS approach." Computer Methods and Programs in Biomedicine 190 (July 2020): 105357. http://dx.doi.org/10.1016/j.cmpb.2020.105357.

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38

Bacigál, Tomáš, and Mária Ždímalová. "Convergence of Linear Approximation of Archimedean Generator from Williamson’s Transform in Examples." Tatra Mountains Mathematical Publications 69, no. 1 (June 27, 2017): 1–18. http://dx.doi.org/10.1515/tmmp-2017-0010.

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Abstract We discuss a new construction method for obtaining additive generators of Archimedean copulas proposed by McNeil, A. J.-Nešlehová, J.: Multivariate Archimedean copulas, d-monotone functions and l1-norm symmetric distributions, Ann. Statist. 37 (2009), 3059-3097, the so-called Williamson n-transform, and illustrate it by several examples. We show that due to the equivalence of convergences of positive distance functions, additive generators and copulas, we may approximate any n-dimensional Archimedean copula by an Archimedean copula generated by a transformation of weighted sum of Dirac functions concentrated in certain suitable points. Specifically, in two dimensional case this means that any Archimedean copula can be approximated by a piece-wise linear Archimedean copula, moreover the approximation of generator by linear splines circumvents the problem with the non-existence of explicit inverse.

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39

Bantis, Leonidas E., John V. Tsimikas, and Stelios D. Georgiou. "Smooth ROC curves and surfaces for markers subject to a limit of detection using monotone natural cubic splines." Biometrical Journal 55, no. 5 (April 3, 2013): 719–40. http://dx.doi.org/10.1002/bimj.201200158.

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40

Liu, Xinru, Yuanpeng Zhu, and Shengjun Liu. "Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface." Journal of Applied Mathematics 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/987076.

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A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.

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41

He, Xuming, and Peide Shi. "Monotone B-Spline Smoothing." Journal of the American Statistical Association 93, no. 442 (June 1998): 643. http://dx.doi.org/10.2307/2670115.

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42

Yu, X. M., and S. P. Zhou. "On Monotone Spline Approximation." SIAM Journal on Mathematical Analysis 25, no. 4 (July 1994): 1227–39. http://dx.doi.org/10.1137/s0036141092228258.

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43

Dzyubenko, G. A., K. A. Kopotun, and A. V. Prymak. "Three-monotone spline approximation." Journal of Approximation Theory 162, no. 12 (December 2010): 2168–83. http://dx.doi.org/10.1016/j.jat.2010.07.004.

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44

He, Xuming, and Peide Shi. "MonotoneB-Spline Smoothing." Journal of the American Statistical Association 93, no. 442 (June 1998): 643–50. http://dx.doi.org/10.1080/01621459.1998.10473717.

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45

RAMPONI, ALESSANDRO. "ADAPTIVE AND MONOTONE SPLINE ESTIMATION OF THE CROSS-SECTIONAL TERM STRUCTURE." International Journal of Theoretical and Applied Finance 06, no. 02 (March 2003): 195–212. http://dx.doi.org/10.1142/s0219024903001840.

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A number of numerical methods based on a piecewise polynomial approximation have been proposed for the estimation of the term structure of interest rates. Some drawbacks have been pointed out, such as a possible non monotonic estimated discount function and a highly fluctuating spot and forward rates. In order to overcome these kind of problems, we study the feasibility of an adaptive regression spline technique which use a monotone basis together with two alternative knot location procedures: a deterministic greedy algorithm and its randomized version in a simulated annealing framework. The features of the proposed method are tested on a set of data.

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46

Abrahamowicz, Michal. "Monotone spline additive-risks model." Controlled Clinical Trials 12, no. 5 (October 1991): 619. http://dx.doi.org/10.1016/0197-2456(91)90075-w.

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47

Fuhr, Richard D., and Michael Kallay. "Monotone linear rational spline interpolation." Computer Aided Geometric Design 9, no. 4 (September 1992): 313–19. http://dx.doi.org/10.1016/0167-8396(92)90038-q.

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48

Sparling, B., and T. Rezansoff. "The effect of confinement on lap splices in reversed cyclic loading." Canadian Journal of Civil Engineering 13, no. 6 (December 1, 1986): 681–92. http://dx.doi.org/10.1139/l86-103.

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Twelve large-scale tests (7 m beams with 30 mm main reinforcement) were made to investigate the performance of lap splices in reinforced concrete beams subjected to reversed cyclic loading which produced yielding in the main reinforcement. Load history and various configurations of splice confinement were the major parameters considered. Performance was judged on the basis of strength, ductility, and several degradation indicators.Behavior was dependent on the degree of splice confinement. Specimens containing superior splice confinement, provided either by closely spaced stirrups or by closely fitting spirals, were more ductile and sustained more load cycles, on average, prior to failure. It was advantageous to provide more splice confinement than the amount considered to be effective under static loading. Tensile splices designed with superior confinement according to proposed seismic specifications achieved ductility ratios (failure deflection divided by first yield deflection with no splice) which averaged 2.66.Reversed cyclic loading was more damaging than repeated unidirectional or monotonic loading. The number of reversed load cycles to failure decreased as the intensity of loading increased. Under load reversals, the reduction in stiffness, the increase in energy dissipation, and the gain in damping capacity were used to examine the degradation that could be sustained before failure. Key words: reinforced concrete, beams, bond, splices, cyclic loads, ductility, seismic design, joints, deflection, strength, stiffness, damping.

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49

Costantini, Paolo. "On monotone and convex spline interpolation." Mathematics of Computation 46, no. 173 (January 1, 1986): 203. http://dx.doi.org/10.1090/s0025-5718-1986-0815841-7.

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50

Holtz, Markus, and Angela Kunoth. "B‐Spline‐Based Monotone Multigrid Methods." SIAM Journal on Numerical Analysis 45, no. 3 (January 2007): 1175–99. http://dx.doi.org/10.1137/050642575.

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