Optimal designs for spline wavelet regression models

Maronge, Jacob M; Zhai, Yi; Wiens, Douglas P.; Fang, Zhide

doi:10.1016/j.jspi.2016.11.005

Cited by 6 publications

(4 citation statements)

References 18 publications

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“…Polynomial slices play an important role in approximation theory and statistics. Polynomial slices are flexible and effective in dealing with local properties of a function or data [18][19][20]. One of the most important types of polynomial slices is the spline polynomial.…”

Section: Spline Functionmentioning

confidence: 99%

Spline Model in The Case of Cervical Cancer Patient Resilience

Hidayat

Ilyas²,

Yuliani³

2023

Trends Sci

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Cervical cancer ranks highest in developing countries, and ranks 10th in developed countries as a cause of death for women. In Indonesia, cervical cancer ranks second out of the 10 most common cancers based on Anatomical Pathology data in 2010 with an incidence rate of 20 %. The number of new women with cervical cancer ranges from 90 - 100 cases per 100,000 population and every year there are 40 thousand cases of cervical cancer. Cervical cancer is a gynecological disease that has a high level of malignancy and is caused by the Human Papilloma Virus (HPV). One method that can be used in the analysis of human survival is survival analysis using the Cox proportional hazard model. This research will use the development of the Cox model using the Spline function as its basis. Based on the results obtained, the developed model can model the data well and give a low MSE. Based on the developed model, it is found that the variables that influence the survival rate of cervical cancer patients are age, stage, type of PRC transfusion treatment and comorbidities. HIGHLIGHTS Due to in silico study such as molecular docking, molecular dynamic simulation is an important computational method for drug design. It can be used to predict the binding orientation of small molecule drug candidates to their protein targets. In addition, docking is also can be applied to predict small molecule affinity and activity. Thus, molecular docking has an important role in drug discovery and rational design The ligand interaction with the receptor was more stable due to the decreased binding free energy value The lowest binding free energy and lowest RMSD value of this molecule, which may presumably cause compound 3 to has better binding affinity compare to other compounds GRAPHICAL ABSTRACT

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Section: Spline Functionmentioning

confidence: 99%

Spline Model in The Case of Cervical Cancer Patient Resilience

Hidayat

Ilyas²,

Yuliani³

2023

Trends Sci

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“…Haar wavelets [Maronge et al, 2017] or B-splines [Grove et al, 2004]. One of the classical estimators for β in (2.1) is the Gauss-Markov estimator, corresponding to the best unbiased linear estimator.…”

Section: Optimal Design For Linear Modelsmentioning

confidence: 99%

On proportional volume sampling for experimental design in general spaces

Poinas¹,

Bardenet²

2020

Preprint

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Optimal experimental design for linear regression is a fundamental research topic in statistics and related fields. For finite design spaces, recent progress has shown that random designs drawn using proportional volume sampling (PVS) lead to approximation guarantees for A-optimal design. Proportional volume sampling strikes the balance between forcing the design nodes to jointly fill the design space, while marginally staying in regions of high mass under the solution of a relaxed convex version of the optimal problem. In this paper, we examine some of the statistical implications of PVS. First, we extend PVS to generic Polish design spaces, and we show that not only are the A-optimality approximation guarantees preserved, but we obtain similar guarantees for D-optimal design. Through a connection with determinantal point processes, another type of repulsive random design, we show that PVS can be sampled in polynomial time. Unfortunately, in spite of its mathematical elegance and computational tractability, we demonstrate on a simple example that the practical implications of general PVS are likely limited. In the second part of the paper, we focus on applications and rather investigate the use of PVS as a subroutine for stochastic search heuristics. We demonstrate that PVS is a robust addition to the practitioner's toolbox, especially when the regression functions are nonstandard and the design space is low-dimensional but has a complicated shape (e.g., nonlinear boundaries, several connected components).

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“…To date, researchers have investigated various functions for estimating the regression curve in nonparametric regression, such as spline [3][4][5][6], Fourier series [7][8][9], kernel [10][11][12], polynomial [13][14][15], and wavelet [16][17][18] functions. The present study explores the nonparametric regression approach to analyzing spatial data, i.e., the use of the nonparametric truncated spline function in geographically weighted regression [19,20].…”

Section: Introductionmentioning

confidence: 99%

The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression

2021

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Nonparametric regression becomes a potential solution if the parametric regression assumption is too restrictive while the regression curve is assumed to be known. In multivariable nonparametric regression, the pattern of each predictor variable’s relationship with the response variable is not always the same; thus, a combined estimator is recommended. In addition, regression modeling sometimes involves more than one response, i.e., multiresponse situations. Therefore, we propose a new estimation method of performing multiresponse nonparametric regression with a combined estimator. The objective is to estimate the regression curve using combined truncated spline and Fourier series estimators for multiresponse nonparametric regression. The regression curve estimation of the proposed model is obtained via two-stage estimation: (1) penalized weighted least square and (2) weighted least square. Simulation data with sample size variation and different error variance were applied, where the best model satisfied the result through a large sample with small variance. Additionally, the application of the regression curve estimation to a real dataset of human development index indicators in East Java Province, Indonesia, showed that the proposed model had better performance than uncombined estimators. Moreover, an adequate coefficient of determination of the best model indicated that the proposed model successfully explained the data variation.

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Optimal designs for spline wavelet regression models

Cited by 6 publications

References 18 publications

Spline Model in The Case of Cervical Cancer Patient Resilience

Spline Model in The Case of Cervical Cancer Patient Resilience

On proportional volume sampling for experimental design in general spaces

The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression

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