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Full-Text Articles in Physical Sciences and Mathematics
The Regression Smoother Lowess: A Confidence Band That Allows Heteroscedasticity And Has Some Specified Simultaneous Probability Coverage, Rand Wilcox
Journal of Modern Applied Statistical Methods
Many nonparametric regression estimators (smoothers) have been proposed that provide a more flexible method for estimating the true regression line compared to using some of the more obvious parametric models. A basic goal when using any smoother is computing a confidence band for the true regression line. Let M(Y|X) be some conditional measure of location associated with the random variable Y, given X and let x be some specific value of the covariate. When using the LOWESS estimator, an extant method that assumes homoscedasticity can be used to compute a confidence interval for M(Y|X = x). A trivial way of …
Variable Selection In Nonparametric And Semiparametric Regression Models, Liangjun Su, Yonghui Zhang
Variable Selection In Nonparametric And Semiparametric Regression Models, Liangjun Su, Yonghui Zhang
Research Collection School Of Economics
This chapter reviews the literature on variable selection in nonparametric and semiparametric regression models via shrinkage. We highlight recent developments on simultaneous variable selection and estimation through the methods of least absolute shrinkage and selection operator (Lasso), smoothly clipped absolute deviation (SCAD) or their variants, but restrict our attention to nonparametric and semiparametric regression models. In particular, we consider variable selection in additive models, partially linear models, functional/varying coefficient models, single index models, general nonparametric regression models, and semiparametric/nonparametric quantile regression models.
Comparing The Strength Of Association Of Two Predictors Via Smoothers Or Robust Regression Estimators, Rand R. Wilcox
Comparing The Strength Of Association Of Two Predictors Via Smoothers Or Robust Regression Estimators, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
Consider three random variables, Y , X1 and X2, having some unknown trivariate distribution and let n2j (j = 1, 2) be some measure of the strength of association between Y and Xj. When n2j is taken to be Pearson’s correlation numerous methods for testing Ho : n21 = n22 have been proposed. However, Pearson’s correlation is not robust and the methods for testing H0 are not level robust in general. This article examines methods for testing H0 based on a robust fit. The …
Inferences About The Components Of A Generalized Additive Model, Rand R. Wilcox
Inferences About The Components Of A Generalized Additive Model, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
A method for making inferences about the components of a generalized additive model is described. It is found that a variation of the method, based on means, performs well in simulations. Unlike many other inferential methods, switching from a mean to a 20% trimmed mean was found to offer little or no advantage in terms of both power and controlling the probability of a Type I error.