• Communications for Statistical Applications and Methods
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• 제4권1호
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• pp.177-183
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• 1997

A data-adaptive order selection procedure is proposed for local polynomial nonparametric regression. For each given polynomial order, bias and variance are estimated and the adaptive polynomial order that has the smallest estimated mean squared error is selected locally at each location point. To estimate mean squared error, empirical bias estimate of Ruppert (1995) and local polynomial variance estimate of Ruppert, Wand, Wand, Holst and Hossjer (1995) are used. Since the proposed method does not require fitting polynomial model of order higher than the model order, it is simpler than the order selection method proposed by Fan and Gijbels (1995b).

• ETRI Journal
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• 제27권6호
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• pp.747-758
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• 2005

The problem of selection among competing models has been a fundamental issue in statistical data analysis. Good fits to data can be misleading since they can result from properties of the model that have nothing to do with it being a close approximation to the source distribution of interest (for example, overfitting). In this study we focus on the preference among models from a family of polynomial regressors. Three decades of research has spawned a number of plausible techniques for the selection of models, namely, Akaike's Finite Prediction Error (FPE) and Information Criterion (AIC), Schwartz's criterion (SCH), Generalized Cross Validation (GCV), Wallace's Minimum Message Length (MML), Minimum Description Length (MDL), and Vapnik's Structural Risk Minimization (SRM). The fundamental similarity between all these principles is their attempt to define an appropriate balance between the complexity of models and their ability to explain the data. This paper presents an empirical study of the above principles in the context of model selection, where the models under consideration are univariate polynomials. The paper includes a detailed empirical evaluation of the model selection methods on six target functions, with varying sample sizes and added Gaussian noise. The results from the study appear to provide strong evidence in support of the MML- and SRM- based methods over the other standard approaches (FPE, AIC, SCH and GCV).

• 디지털산업정보학회논문지
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• 제7권4호
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• pp.7-14
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• 2011

Infinite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rate per fault (hazard function). This infinite non-homogeneous Poisson process is model which reflects the possibility of introducing new faults when correcting or modifying the software. In this paper, polynomial hazard function have been proposed, which can efficiency application for software reliability. Algorithm for estimating the parameters used to maximum likelihood estimator and bisection method. Model selection based on mean square error and the coefficient of determination for the sake of efficient model were employed. In numerical example, log power time model of the existing model in this area and the polynomial hazard function model were compared using failure interval time. Because polynomial hazard function model is more efficient in terms of reliability, polynomial hazard function model as an alternative to the existing model also were able to confirm that can use in this area.

• Journal of the Korean Statistical Society
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• 제9권1호
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• pp.61-77
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• 1980

In response surface experiments, a polynomial model is often used to fit the response surface by the method of least squares. However, if the vectors of predictor variables are multicollinear, least squares estimates of the regression parameters have a high probability of being unsatisfactory. Hoerland Kennard have demonstrated that these undesirable effects of multicollinearity can be reduced by using "ridge" estimates in place of the least squares estimates. Ridge regrssion theory in literature has been mainly concerned with selection of k for the first order polynomial regression model and the precision of $\hat{\beta}(k)$, the ridge estimator of regression parameters. The problem considered in this paper is that of selecting k of ridge regression for a given polynomial regression model with an arbitrary order. A criterion is proposed for selection of k in the context of integrated mean square error of fitted responses, and illustrated with an example. Also, a type of admissibility condition is established and proved for the propose criterion.criterion.

• Asian-Australasian Journal of Animal Sciences
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• 제24권1호
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• pp.17-27
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• 2011

A selection experiment for reduced residual feed intake (RFI) in Yorkshire pigs consisted of a line selected for lower RFI (LRFI) and a random control line (CTRL). Longitudinal measurements of daily feed intake (DFI) and body weight (BW) from generation 5 of this experiment were used. The objectives of this study were to evaluate the use of random regression (RR) and nonlinear mixed models to predict DFI and BW for individual pigs, accounting for the substantial missing information that characterizes these data, and to evaluate the effect of selection for RFI on BW and DFI curves. Forty RR models with different-order polynomials of age as fixed and random effects, and with homogeneous or heterogeneous residual variance by month of age, were fitted for both DFI and BW. Based on predicted residual sum of squares (PRESS) and residual diagnostics, the quadratic polynomial RR model was identified to be best, but with heterogeneous residual variance for DFI and homogeneous residual variance for BW. Compared to the simple quadratic and linear regression models for individual pigs, these RR models decreased PRESS by 1% and 2% for DFI and by 42% and 36% for BW on boars and gilts, respectively. Given the same number of random effects as the polynomial RR models, i.e., two for BW and one for DFI, the non-linear Gompertz model predicted better than the polynomial RR models but not as good as higher order polynomial RR models. After five generations of selection for reduced RFI, the LRFI line had a lower population curve for DFI and BW than the CTRL line, especially towards the end of the growth period.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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• pp.337-339
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• 2004

In this paper, we discuss optimal design of Fuzzy Polynomial Neural Networks by means of Genetic Algorithms(GAs). Proceeding the layer, this model creates the optimal network architecture through the selection and the elimination of nodes by itself. So, there is characteristic of flexibility. We use a triangle and a Gaussian-like membership function in premise part of rules and design the consequent structure by constant and regression polynomial (linear, quadratic and modified quadratic) function between input and output variables. GAs is applied to improve the performance with optimal input variables and number of input variables and order. To evaluate the performance of the GAs-based FPNNs, the models are experimented with the use of Medical Imaging System(MIS) data.

• Elastomers and Composites
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• 제51권4호
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• pp.308-316
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• 2016

The rubber materials are widely used in automobile industry due to their capability of a large amount of elastic deformation under a force. Current trend of design process requires prediction of functional properties of parts at early stage. The behavior of rubber material can be modeled using strain energy density function. In this study, five different strain energy density functions - Neo-Hookean model, Reduced Polynomial $2^{nd}$ model, Ogden $3^{rd}$ model, Arruda Boyce model and Van der Waals model - were used to estimate the behavior of carbon black added natural rubber under uniaxial load. Two kinds of tests - uniaxial tension test and biaxial tension test - were performed and used to correlate the coefficients of the strain energy density function. Numerical simulations were carried out using finite element analysis and compared with experimental results. Simulation revealed that Ogden $3^{rd}$ model predicted the behavior of carbon added natural rubber under uniaxial load regardless of experimental data selection for coefficient correlation. However, Reduced Polynomial $2^{nd}$, Ogden $3^{rd}$, and Van der Waals with uniaxial tension test and biaxial tension test data selected for coefficient correlation showed close estimation of behavior of biaxial tension test. Reduced Polynomial $2^{nd}$ model predicted the behavior of biaxial tension test most closely.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.1505-1509
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• 2005

This paper introduces a new architecture of genetically optimized self-organizing fuzzy polynomial neural networks by means of information granulation. The conventional SOFPNNs developed so far are based on mechanisms of self-organization and evolutionary optimization. The augmented genetically optimized SOFPNN using Information Granulation (namely IG_gSOFPNN) results in a structurally and parametrically optimized model and comes with a higher level of flexibility in comparison to the one we encounter in the conventional FPNN. With the aid of the information granulation, we determine the initial location (apexes) of membership functions and initial values of polynomial function being used in the premised and consequence part of the fuzzy rules respectively. The GA-based design procedure being applied at each layer of genetically optimized self-organizing fuzzy polynomial neural networks leads to the selection of preferred nodes with specific local characteristics (such as the number of input variables, the order of the polynomial, a collection of the specific subset of input variables, and the number of membership function) available within the network. To evaluate the performance of the IG_gSOFPNN, the model is experimented with using gas furnace process data. A comparative analysis shows that the proposed IG_gSOFPNN is model with higher accuracy as well as more superb predictive capability than intelligent models presented previously.

• 한국항공우주학회지
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• 제41권1호
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• pp.48-53
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• 2013

다항식 반응면 모델은 실제의 물리적, 수치적 실험을 대체하는 근사모델로 여러 공학분야에서 사용되고 있다. 일반적으로 반응면 구성에 필요한 실험점 수를 줄이기 위하여 낮은 차수의 다항식을 사용하므로, 심한 비선형성이 동반되는 현상에 대한 모델링에는 한계가 있다. 본 연구에서는 다항식의 차수를 증가시키는 방법 및 다항식을 구성하는 최적의 기저함수를 선정하는 방법을 통해 다항식 반응면의 모델링 능력을 확장할 수 있는 방법을 개발하였다. 최적 기저함수의 선정에는 유전 알고리즘을 적용하였으며, 1 변수 및 2변수 함수와 풍동시험 데이터에 대한 모델링 사례를 통해 개발된 방법이 비선형성이 심한 현상을 모델링하는데 적용될 수 있음을 확인하였다.

• 품질경영학회지
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• 제6권1호
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• pp.14-17
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• 1978

반응표본 실험에 있어서 반응변수와 여러개의 독립변수와의 함수관계를 규명하기 위하여 다항회귀모형이 많이 사용되고 있으며 또한 이 다항회귀모형은 최적반응조건을 결정하고 제품의 질을 조절하기 위하여서도 쓰여진다. 이 논문에서 연구하는 문제는 다항회귀모형을 구성하고 있는 많은 항(項) 중에서 어떤 항들을 선택하여 주는 것이 정도(精度)있게 추정하기 위하여 적절한가 하는 문제이다. 정도(精度)가 향상되는 반응표면을 발견한다는 것은 최적반응조건을 결정하고 변수간의 함수관계를 정확하게 구하는데 도움을 준다. 다항회귀모형에서 적절한 항(項)들은 선택하기 위하여 이 논문에서는 하나의 기준을 제시할 것이며, 실제로 공장에서 응용될 수 있는 예제를 들어 설명하고 있다.