A computational approach to nonparametric regression: bootstrapping cmars method

Download

index.pdf

Date

2011

Author

Yazıcı, Ceyda

Metadata

Show full item record

Item Usage Stats

253
views

131
downloads

Bootstrapping is a resampling technique which treats the original data set as a population and draws samples from it with replacement. This technique is widely used, especially, in mathematically intractable problems. In this study, it is used to obtain the empirical distributions of the parameters to determine whether they are statistically significant or not in a special case of nonparametric regression, Conic Multivariate Adaptive Regression Splines (CMARS). Here, the CMARS method, which uses conic quadratic optimization, is a modified version of a well-known nonparametric regression model, Multivariate Adaptive Regression Splines (MARS). Although performing better with respect to several criteria, the CMARS model is more complex than that of MARS. To overcome this problem, and to improve the CMARS performance further, three different bootstrapping regression methods, namely, Random-X, Fixed-X and Wild Bootstrap are applied on four data sets with different size and scale. Then, the performances of the models are compared using various criteria including accuracy, precision, complexity, stability, robustness and efficiency. Random-X yields more precise, accurate and less complex models particularly for medium size and medium scale data even though it is the least efficient method.

Subject Keywords

Statistics.

URI

http://etd.lib.metu.edu.tr/upload/12613708/index.pdf
https://hdl.handle.net/11511/21010

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Robust estimation and hypothesis testing under short-tailedness and inliers Akkaya, Ayşen (Springer Science and Business Media LLC, 2005-06-01) Estimation and hypothesis testing based on normal samples censored in the middle are developed and shown to be remarkably efficient and robust to symmetric short-tailed distributions and to inliers in a sample. This negates the perception that sample mean and variance are the best robust estimators in such situations (Tiku, 1980; Dunnett, 1982).
A computational approach to nonparametric regression: bootstrapping CMARS method Yazici, Ceyda; Yerlikaya-Ozkurt, Fatma; Batmaz, İnci (2015-10-01) Bootstrapping is a computer-intensive statistical method which treats the data set as a population and draws samples from it with replacement. This resampling method has wide application areas especially in mathematically intractable problems. In this study, it is used to obtain the empirical distributions of the parameters to determine whether they are statistically significant or not in a special case of nonparametric regression, conic multivariate adaptive regression splines (CMARS), a statistical machin...
Robust control charts Çetinyürek, Aysun; Sürücü, Barış; Department of Statistics (2006) Control charts are one of the most commonly used tools in statistical process control. A prominent feature of the statistical process control is the Shewhart control chart that depends on the assumption of normality. However, violations of underlying normality assumption are common in practice. For this reason, control charts for symmetric distributions for both long- and short-tailed distributions are constructed by using least squares estimators and the robust estimators -modified maximum likelihood, trim...
A marginalized multilevel model for bivariate longitudinal binary data Inan, Gul; İlk Dağ, Özlem (Springer Science and Business Media LLC, 2019-06-01) This study considers analysis of bivariate longitudinal binary data. We propose a model based on marginalized multilevel model framework. The proposed model consists of two levels such that the first level associates the marginal mean of responses with covariates through a logistic regression model and the second level includes subject/time specific random intercepts within a probit regression model. The covariance matrix of multiple correlated time-specific random intercepts for each subject is assumed to ...
Adaptive estimation and hypothesis testing methods Dönmez, Ayça; Tiku, Moti Lal; Department of Statistics (2010) For statistical estimation of population parameters, Fisher’s maximum likelihood estimators (MLEs) are commonly used. They are consistent, unbiased and efficient, at any rate for large n. In most situations, however, MLEs are elusive because of computational difficulties. To alleviate these difficulties, Tiku’s modified maximum likelihood estimators (MMLEs) are used. They are explicit functions of sample observations and easy to compute. They are asymptotically equivalent to MLEs and, for small n, are equal...

Citation Formats

C. Yazıcı, “A computational approach to nonparametric regression: bootstrapping cmars method,” M.S. - Master of Science, Middle East Technical University, 2011.