Relevant bibliographies by topics / Monotone splines

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Monotone splines'

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Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Monotone splines"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Monotone splines"

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Schiavon, Laurent. "Conditions de monotonie de la courbure pour les courbes et splines d'interpolation." Valenciennes, 2002. https://ged.uphf.fr/nuxeo/site/esupversions/ebd449f2-087e-4588-b4a1-bedcc9b86660.

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Pour une courbe, la courbure est une grandeur géométrique déterminante pour sa forme. Dans de nombreuses applications de la CAO (automobile, aéronautique), les courbes que l'on cherche à modéliser doivent être à courbure monotone, dans le but d'obtenir des formes aérodynamiques et esthétiques. Dans ce travail, nous apportons des solutions via les courbes polynomiales cubiques et rationnelles quadratiques (arcs coniques) quisont controlées par un ensemble de points (et de masses dans le cas rationnel)
For a curve, the curvature is a deciding geometric feature for its shape. For some applications of CAD (automotive, aeronautics), it is important to maintain monotone curvature along the curve we aim to modelize in order to obtain aerodynamic and aesthetic shapes. In this work, solutions are given via the cubic polynomial curves and the quadratic rational curves (conic segments) which are controlled by a set of points (and weights in the rational case)
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Hua, Lei. "Spline-based sieve semiparametric generalized estimating equation for panel count data." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/517.

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In this thesis, we propose to analyze panel count data using a spline-based sieve generalized estimating equation method with a semiparametric proportional mean model E(N(t)|Z) = Λ0(t) eβT0Z. The natural log of the baseline mean function, logΛ0(t), is approximated by a monotone cubic B-spline function. The estimates of regression parameters and spline coefficients are the roots of the spline based sieve generalized estimating equations (sieve GEE). The proposed method avoids assumingany parametric structure of the baseline mean function and the underlying counting process. Selection of an appropriate covariance matrix that represents the true correlation between the cumulative counts improves estimating efficiency. In addition to the parameters existing in the proportional mean function, the estimation that accounts for the over-dispersion and autocorrelation involves an extra nuisance parameter σ2, which could be estimated using a method of moment proposed by Zeger (1988). The parameters in the mean function are then estimated by solving the pseudo generalized estimating equation with σ2 replaced by its estimate, σ2n. We show that the estimate of (β0,Λ0) based on this two-stage approach is still consistent and could converge at the optimal convergence rate in the nonparametric/semiparametric regression setting. The asymptotic normality of the estimate of β0 is also established. We further propose a spline-based projection variance estimating method and show its consistency. Simulation studies are conducted to investigate finite sample performance of the sieve semiparametric GEE estimates, as well as different variance estimating methods with different sample sizes. The covariance matrix that accounts for the overdispersion generally increases estimating efficiency when overdispersion is present in the data. Finally, the proposed method with different covariance matrices is applied to a real data from a bladder tumor clinical trial.
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Lu, Wenjing. "Monotone spline-based nonparametric estimation of longitudinal data with mixture distributions." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/6188.

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In the dissertation, a monotone spline-based nonparametric estimation method is proposed for analyzing longitudinal data with mixture distributions. The innovative and efficient algorithm combining the concept of projected Newton-Raphson algorithm with linear mixed model estimation method is developed to obtain the nonparametric estimation of monotone B-spline functions. This algorithm provides an efficient and flexible approach for modeling longitudinal data monotonically. An iterative 'one-step-forward' algorithm based on the K-means clustering is then proposed to classify mixture distributions of longitudinal data. This algorithm is computationally efficient, especially for data with a large number of underlying distributions. To quantify the disparity of underlying distributions of longitudinal data, we also propose an index measure on the basis of the aggregated areas under the curve (AAUC), which makes no distributional assumptions and fits the theme of nonparametric analysis. An extensive simulation study is conducted to assess the empirical performance of our method under different AAUC values, covariance structures, and sample sizes. Finally, we apply the new approach in the PREDICT-HD study, a multi-site observational study of Huntington Disease (HD), to explore and assess clinical markers in motor and cognitive domains for the purpose of distinguishing participants at risk of HD from healthy subjects.
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Wu, Yuan. "The partially monotone tensor spline estimation of joint distribution function with bivariate current status data." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/762.

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The analysis of joint distribution function with bivariate event time data is a challenging problem both theoretically and numerically. This thesis develops a tensor splinebased nonparametric maximum likelihood estimation method to estimate the joint distribution function with bivariate current status data. The tensor I-splines are developed to replace the traditional tensor B-splines in approximating joint distribution function in order to simplify the restricted maximum likelihood estimation problem in computing. The generalized gradient projection algorithm is used to compute the restricted optimization problem. We show that the proposed tensor spline-based nonparametric estimator is consistent and that the rate of convergence is obtained. Simulation studies with moderate sample sizes show that the finite-sample performance of the proposed estimator is generally satisfactory.
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Boschert, Sandra [Verfasser], Angela [Gutachter] Kunoth, Helmut [Gutachter] Harbrecht, and Ulrich [Gutachter] Langer. "B-Spline Based Methods: From Monotone Multigrid Schemes for American Options to Uncertain Volatility Models / Sandra Boschert ; Gutachter: Angela Kunoth, Helmut Harbrecht, Ulrich Langer." Köln : Universitäts- und Stadtbibliothek Köln, 2020. http://d-nb.info/1223091651/34.

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Patenaude, Valérie. "Utilisation de splines monotones afin de condenser des tables de mortalité dans un contexte bayésien." Thèse, 2011. http://hdl.handle.net/1866/5147.

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Dans ce mémoire, nous cherchons à modéliser des tables à deux entrées monotones en lignes et/ou en colonnes, pour une éventuelle application sur les tables de mortalité. Nous adoptons une approche bayésienne non paramétrique et représentons la forme fonctionnelle des données par splines bidimensionnelles. L’objectif consiste à condenser une table de mortalité, c’est-à-dire de réduire l’espace d’entreposage de la table en minimisant la perte d’information. De même, nous désirons étudier le temps nécessaire pour reconstituer la table. L’approximation doit conserver les mêmes propriétés que la table de référence, en particulier la monotonie des données. Nous travaillons avec une base de fonctions splines monotones afin d’imposer plus facilement la monotonie au modèle. En effet, la structure flexible des splines et leurs dérivées faciles à manipuler favorisent l’imposition de contraintes sur le modèle désiré. Après un rappel sur la modélisation unidimensionnelle de fonctions monotones, nous généralisons l’approche au cas bidimensionnel. Nous décrivons l’intégration des contraintes de monotonie dans le modèle a priori sous l’approche hiérarchique bayésienne. Ensuite, nous indiquons comment obtenir un estimateur a posteriori à l’aide des méthodes de Monte Carlo par chaînes de Markov. Finalement, nous étudions le comportement de notre estimateur en modélisant une table de la loi normale ainsi qu’une table t de distribution de Student. L’estimation de nos données d’intérêt, soit la table de mortalité, s’ensuit afin d’évaluer l’amélioration de leur accessibilité.
This master’s thesis is about the estimation of bivariate tables which are monotone within the rows and/or the columns, with a special interest in the approximation of life tables. This problem is approached through a nonparametric Bayesian regression model, in particular linear combinations of regression splines. By condensing a life table, our goal is to reduce its storage space without losing the entries’ accuracy. We will also study the reconstruction time of the table with our estimators. The properties of the reference table, specifically its monotonicity, must be preserved in the estimation. We are working with a monotone spline basis since splines are flexible and their derivatives can easily be manipulated. Those properties enable the imposition of constraints of monotonicity on our model. A brief review on univariate approximations of monotone functions is then extended to bivariate estimations. We use hierarchical Bayesian modeling to include the constraints in the prior distributions. We then explain the Markov chain Monte Carlo algorithm to obtain a posterior estimator. Finally, we study the estimator’s behaviour by applying our model on the Standard Normal table and the Student’s t table. We estimate our data of interest, the life table, to establish the improvement in data accessibility.
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Balabdaoui, Fadoua. "Estimation non-paramétrique d'une densité k-monotone: Une nouvelle théorie de distribution asymptotique." Phd thesis, 2004. http://tel.archives-ouvertes.fr/tel-00011980.

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Nous considérons l'estimation non-paramétrique d'une densité k-monotone définie sur (0,∞), pour un entier k > 0 donné, via les méthodes de maximum de vraisemblance et des moindres carrés qu'on note respectivement par MLE et LSE.

Dans l'introduction, nous présentons tout d'abord la motivation principale derrière ce problème et nous faisons l'effort d'inclure dans le cadre général de notre travail les résultats asymptotiques qui étaient déjà établis pour les cas spéciaux k=1 et k=2.

Ensuite, nous nous penchons sur l'étude des propriétés des MLE et LSE d'une densité k-monotone g_0 dans le cas où on dispose de n observations indépendantes générées de g_0. Notre étude asymptotique est locale, c'est-à-dire que nous nous intéressons uniquement aux propriétés asymptotiques des estimateurs et de leur dérivées à un point fixe, x_0. Sous certaines hypothèses que nous précisons, nous établissons d'abord les bornes inférieures minimax pour l'estimation des dérivées g^{(j)}_0(x_0), j=0,...,k-1. Les bornes obtenues indiquent que n^{-(k-j)/(2k+1)} est la vitesse de convergence optimale de n'importe quel estimateur non-paramétrique de g^{(j)}_0(x_0). Sous les mêmes hypothèses et si une certaine conjecture est vraie, nous démontrons que cette vitesse optimale est atteinte dans le cas des MLE et LSE.

Pour compléter la théorie asymptotique des estimateurs et de leur dérivées au point x_0, nous passons à la dérivation de leurs distributions limites lorsque la taille de l'échantillon n tend vers l'infini. Il s'avère que ces distributions dépendent d'un processus stochastique bien particulier défini sur l'ensemble des réels R. On note ce processus par H_k Le 3ème chapitre est consacré essentiellement à l'existence et à l'unicité de H_k, ainsi qu'à sa caractérisation. Nous démontrons que si Y_k est la primitive (k-1)-ème d'un mouvement Brownien + k!/(2k)! t^{2k}, alors H_k reste au-dessus (au-dessous) de Y_k lorsque k est pair (impair). Un simple changement de variable suffit pour reconnaître que nos résultats comprennent les cas spéciaux k=1 et k=2 où le problème se réduit à l'estimation d'une densité décroissante et d'une densité décroissante et convexe respectivement. Pour ces cas-là, la théorie asymptotique des MLE et LES a été déjà établie.

L'aspect algorithmique fait l'objet du 4ème chapitre. Les algorithmes de Splines itératifs (Iterative Spline algorithms) sont développés et implémentés afin de calculer les estimateurs et aussi pour obtenir une approximation du processus limite sur n'importe quel compact dans R. Ces algorithmes exploitent essentiellement la structure 'splineuse' des MLE, LSE et H_k, et se basent ainsi sur la suppression et l'addition itératives des noeuds de certains Splines aléatoires.
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Lapointe, Marc-Élie. "Approche bayésienne de la construction d'intervalles de crédibilité simultanés à partir de courbes simulées." Thèse, 2015. http://hdl.handle.net/1866/12576.

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Ce mémoire porte sur la simulation d'intervalles de crédibilité simultanés dans un contexte bayésien. Dans un premier temps, nous nous intéresserons à des données de précipitations et des fonctions basées sur ces données : la fonction de répartition empirique et la période de retour, une fonction non linéaire de la fonction de répartition. Nous exposerons différentes méthodes déjà connues pour obtenir des intervalles de confiance simultanés sur ces fonctions à l'aide d'une base polynomiale et nous présenterons une méthode de simulation d'intervalles de crédibilité simultanés. Nous nous placerons ensuite dans un contexte bayésien en explorant différents modèles de densité a priori. Pour le modèle le plus complexe, nous aurons besoin d'utiliser la simulation Monte-Carlo pour obtenir les intervalles de crédibilité simultanés a posteriori. Finalement, nous utiliserons une base non linéaire faisant appel à la transformation angulaire et aux splines monotones pour obtenir un intervalle de crédibilité simultané valide pour la période de retour.
This master's thesis addresses the problem of the simulation of simultaneous credible intervals in a Bayesian context. First, we will study precipation data and two functions based on these data : the empirical distribution function and the return period, a non-linear function of the empirical distribution. We will review different methods already known to obtain simultaneous confidence intervals of these functions with a polynomial basis and we will present a method to simulate simultaneous credible intervals. Second, we will explore some models of prior distributions and in the more complex one, we will need the Monte-Carlo method to simulate simultaneous posterior credible intervals. Finally, we will use a non-linear basis based on the angular transformation and on monotone splines to obtain valid simultaneous credible intervals for the return period.
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Yu, Chao Ya, and 游詔雅. "A NOTE ON MONOTONE PIECEWISE CUBIC SPLINE." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/83784414626315526206.

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碩士
逢甲大學
應用數學研究所
82
A physical quantity is often known to have a certain behav- iour, monotonic increasing (or decreasing), as a function of other quantities. Thus, there is a need for algorithms which preserving the monotonicity properties of the monotonic data as well as producing physically reasonable curves and surfaces. Fritsch and Carlson [4] derived necessary and sufficient conditions for a cubic spline to be monotonic from a set of monotonic data. Those conditions may form a basis for developi- ng a numerical method to produce a monotonic interpolation and represent approximately the physical reality.
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李垂勳. "Lapped splices for high strength concrete under monotonic and cyclic loading." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/12775276164145216888.

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Books on the topic "Monotone splines"

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On the construction of monotony preserving taper curves. Helsinki: Suomen Metsätieteellinen Seura, 1988.

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Book chapters on the topic "Monotone splines"

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Egerstedt, Magnus, and Clyde Martin. "Optimal Control and Monotone Smoothing Splines." In New Trends in Nonlinear Dynamics and Control and their Applications, 279–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-45056-6_18.

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Bainov, Drumi, Angel Dishliev, and Snezhana Hristova. "Monotone Iterative Technique for Impulsive Differential-Difference Equations with Variable Impulsive Perturbations." In Multivariate Approximation and Splines, 13–27. Basel: Birkhäuser Basel, 1997. http://dx.doi.org/10.1007/978-3-0348-8871-4_2.

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Ramirez, Donald E., and Philip W. Smith. "Applications of Smoothed Monotone Regression Splines and Smoothed Bootstrapping in Survival Analysis." In COMPSTAT, 425–30. Heidelberg: Physica-Verlag HD, 1998. http://dx.doi.org/10.1007/978-3-662-01131-7_59.

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Bellavia, Fabio, and Carlo Colombo. "Color Correction for Image Stitching by Monotone Cubic Spline Interpolation." In Pattern Recognition and Image Analysis, 165–72. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19390-8_19.

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Li, Zhong, Lizhuang Ma, Dereck Meek, Wuzheng Tan, Zhihong Mao, and Mingxi Zhao. "Curvature Monotony Condition for Rational Quadratic B-spline Curves." In Computational Science and Its Applications - ICCSA 2006, 1118–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11751540_122.

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Karim, Samsul Ariffin Abdul, and Malik Zawwar Hussain. "Retracted: Visualization of Positive and Monotone Data by Rational Quadratic Spline." In Lecture Notes in Computer Science, 436–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05036-7_41.

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Karim, Samsul Ariffin Abdul, and Malik Zawwar Hussain. "Erratum to: Visualization of Positive and Monotone Data by Rational Quadratic Spline." In Lecture Notes in Computer Science, 916. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05036-7_87.

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"Chapter Seven. Monotone Smoothing Splines." In Control Theoretic Splines, 113–32. Princeton University Press, 2009. http://dx.doi.org/10.1515/9781400833870.113.

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"Bayesian Semiparametric Regression Analysis of Interval- Censored Data with Monotone Splines." In Interval-Censored Time-to-Event Data, 177–94. Chapman and Hall/CRC, 2012. http://dx.doi.org/10.1201/b12290-14.

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"Methods of Monotone and Convex Spline Interpolation." In Methods of Shape-Preserving Spline Approximation, 97–126. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812813381_0005.

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Conference papers on the topic "Monotone splines"

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"An Algorithm for Constructing Monotone Quintic Interpolating Splines." In 2020 Spring Simulation Conference. Society for Modeling and Simulation International (SCS), 2020. http://dx.doi.org/10.22360/springsim.2020.hpc.003.

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Liu, Muye. "Approximate Growth Curve of Fetus Pancreas by Monotone Splines Regression." In international Conference on Intelligent Computing and Information Engineering (ICIE). VOLKSON PRESS, 2017. http://dx.doi.org/10.26480/icie.01.2017.41.44.

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Wolber and Alfy. "Monotonic cubic spline interpolation." In Proceedings Computer Graphics International CGI-99. IEEE, 1999. http://dx.doi.org/10.1109/cgi.1999.777953.

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Wang, Yong, Huanjun Jiang, Chen Wu, Zihui Xu, and Zhiyuan Qin. "Experimental study on seismic performance of suspended ceiling components." In IABSE Congress, Christchurch 2021: Resilient technologies for sustainable infrastructure. Zurich, Switzerland: International Association for Bridge and Structural Engineering (IABSE), 2021. http://dx.doi.org/10.2749/christchurch.2021.0496.

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<p>Suspended ceiling systems (SCSs) experienced severe damage during strong earthquakes that occurred in recent years. The capacity of the ceiling component is a crucial factor affecting the seismic performance of SCS. Therefore, a series of static tests on suspended ceiling components under monotonic and cyclic loadings were carried out to investigate the seismic performance of the ceiling components. The ceiling components include main tee splices, cross tee latches and peripheral attachments. All specimens were tested under axial loading. Additionally, the static tests of cross tee latches subjected to shear and bending loadings were performed due to their seismic vulnerability. The failure pattern, load-carrying ability, deformation capacity and energy dissipation of the ceiling components are presented in detail in this study.</p>
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Nanduri, Jagannath R., and Ismail B. Celik. "Application of Journal of Fluids Engineering CFD Verification Procedure to Flow Past Bluff Body Using Two Different Turbulence Models." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78316.

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The ASME Journal of Fluids Engineering (JFE) recently adopted the grid convergence index (GCI) method as one of the methods among others to estimate the discretization error in CFD applications. The GCI method (based on Richardson extrapolation (RE)) is applied to CFD simulations of confined flow past a bluff-body and is used to evaluate the performance of two different turbulence models in predicting the flow. Four different grid densities (coarse, fine, finer and finest) are used in a 2D axisymmetric geometry along with the RNG k-ε model and the Reynolds stress transport (RST) turbulence models to predict the flow. A spline extrapolation (SE) method for the approximate error is also used to estimate the extrapolated value of the flow variables. The two models show monotonic and oscillatory convergence in various regions of the flow field. Results from the two turbulence models show different convergence behaviors. The results from the RE method as well as the SE method are assessed by comparing to the solution obtained on the finest grid as well as experimental data. The relative advantage of each of the methods is discussed. This study is a contribution towards testing the procedure proposed by JFE.
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