Smoothing Spline ANOVA Models

Gu, Chong

doi:10.1007/978-1-4614-5369-7

Cited by 552 publications

(693 citation statements)

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“…In this subsection, we compare the "best" additive multivariate kernel model, selected in the preceding subsection, with four different methods: the binning method (BIN), popular in the wind industry and arguably the most widely used method in practice, BVK (Jeon and Taylor 2012), BART (Chipman et al 2010), and SSANOVA (Gu 2013 Tables 3 and 4 because we split the training and test datasets randomly, so that the training/test datasets used in this subsection are not exactly the same as those in the previous section.…”

Section: Comparison Of the Estimation Accuracy Of Different Modelsmentioning

confidence: 99%

Power Curve Estimation With Multivariate Environmental Factors for Inland and Offshore Wind Farms

Lee¹,

Ding²,

Genton³

et al. 2015

Journal of the American Statistical Association

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In the wind industry, a power curve refers to the functional relationship between the power output generated by a wind turbine and the wind speed at the time of power generation.Power curves are used in practice for a number of important tasks including predicting wind power production and assessing a turbine's energy production efficiency. Nevertheless, actual wind power data indicate that the power output is affected by more than just wind speed.Several other environmental factors, such as wind direction, air density, humidity, turbulence intensity, and wind shears, have potential impact. Yet, in industry practice, as well as in the literature, current power curve models primarily consider wind speed and, sometimes, wind speed and direction. We propose an additive multivariate kernel method that can include the aforementioned environmental factors as a new power curve model. Our model provides, conditional on a given environmental condition, both the point estimation and density estimation of power output. It is able to capture the nonlinear relationships between environmental factors and the wind power output, as well as the high-order interaction effects among some of the environmental factors. Using operational data associated with four turbines in an inland wind farm and two turbines in an offshore wind farm, we demonstrate the improvement achieved by our kernel method.

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Section: Comparison Of the Estimation Accuracy Of Different Modelsmentioning

confidence: 99%

Power Curve Estimation With Multivariate Environmental Factors for Inland and Offshore Wind Farms

Lee¹,

Ding²,

Genton³

et al. 2015

Journal of the American Statistical Association

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show abstract

“…, X p is assumed to take some predetermined form that depends on the unknown parameters in θ. In contrast, a smoothing spline model is a form of nonparametric regression (see Craven & Wahba, 1979;Gu, 2013;Hastie et al, 2009;Ramsay & Silverman, 2005;Ruppert, Wand, & Carroll, 2003;Silverman, 1985;Wahba, 1990;Wang, 2011;Wood, 2006). Unlike a parametric regression model, a nonparametric regression model does not assume that the relationship between Y and X 1 , .…”

Section: Smoothing Spline Modelsmentioning

confidence: 99%

Adding bias to reduce variance in psychological results: A tutorial on penalized regression

Helwig

2017

TQMP

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Regression models are commonly used in psychological research. In most studies, regression coefficients are estimated via maximum likelihood (ML) estimation. It is well-known that ML estimates have desirable large sample properties, but are prone to overfitting in small to moderate sized samples. In this paper, we discuss the benefits of using penalized regression, which is a form of penalized likelihood (PL) estimation. Informally, PL estimation can be understood as introducing bias to estimators for the purpose of reducing their variance, with the ultimate goal of providing better solutions. We focus on the Gaussian regression model, where ML and PL estimation reduce to ordinary least squares (OLS) and penalized least squares (PLS) estimation, respectively. We cover classic OLS and stepwise regression, as well as three popular penalized regression approaches: ridge regression, the lasso, and the elastic net. We compare the different penalties (or biases) imposed by each method, and discuss the resulting features each penalty encourages in the solution. To demonstrate the methods, we use an example where the goal is to predict a student's math exam performance from 30 potential predictors. Using a step-by-step tutorial with R code, we demonstrate how to (i) load and prepare the data for analysis, (ii) fit the OLS, stepwise, ridge, lasso, and elastic net models, (iii) extract and compare the model fitting results, and (iv) evaluate the performance of each method. Our example reveals that penalized regression methods can produce more accurate and more interpretable results than the classic OLS and stepwise regression solutions.

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“…By giving constraint with limits [0,1], it will make the end of the curve becomes linear, it is so-called a natural cubic spline. Natural cubic splines basis function, B, described by Gu (2002) …”

Section: Smoothing Splines Regressionmentioning

confidence: 99%

Modeling the human development index and the percentage of poor people using quantile smoothing splines

Mulyani¹,

Andriyana²,

Sudartianto³

2017

AIP Conference Proceedings

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Smoothing Spline ANOVA Models

Cited by 552 publications

References 0 publications

Power Curve Estimation With Multivariate Environmental Factors for Inland and Offshore Wind Farms

Power Curve Estimation With Multivariate Environmental Factors for Inland and Offshore Wind Farms

Adding bias to reduce variance in psychological results: A tutorial on penalized regression

Modeling the human development index and the percentage of poor people using quantile smoothing splines

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