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Nonparametric regression

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Articles 1 - 19 of 19

Full-Text Articles in Physical Sciences and Mathematics

Research Of State Vector In Short-Term Passengers Flow Forecasting Based On Nonparametric Regression, Guo Han, Pengpeng Jiao Jun 2020

Research Of State Vector In Short-Term Passengers Flow Forecasting Based On Nonparametric Regression, Guo Han, Pengpeng Jiao

Journal of System Simulation

Abstract: KNNR (K Nearest Neighbor Based Nonparametric Regression) Method was used for short-term traffic forecast and the choice of state vector was studied. The result shows that taking the data of some historical periods as the state vector has a good prediction. Although the correlation of the historical passenger flow between different Rail transit sites is significant, it neglects the fact that the passengers enter each station is independent. So taking the historical passenger flow of adjacent sites as the state vector is not appropriate.

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Spatially Adaptive Estimation Of Spectrum, Yi None Xie Jan 2020

Spatially Adaptive Estimation Of Spectrum, Yi None Xie

Open Access Theses & Dissertations

When analyzing a stationary time series, one of the questions we are often interested in is how to estimate its spectrum. Many approaches have been proposed to this end. Most are focused on smoothing the periodogram using a single smoothing parameter across all Fourier frequencies. In this paper, we smooth the log periodogram by placing a spatially adaptive prior called the dynamic shrinkage prior, so that varying degrees of smoothing may be applied to different intervals of Fourier frequencies, resulting in less biased estimates of the spectrum. Further research will extend this approach to spectral estimation for nonstationary time series.

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One And Two-Step Estimation Of Time Variant Parameters And Nonparametric Quantiles, Bogdan Gadidov Jul 2019

One And Two-Step Estimation Of Time Variant Parameters And Nonparametric Quantiles, Bogdan Gadidov

Doctor of Data Science and Analytics Dissertations

This dissertation develops and discusses several one-step and two-step smoothing methods of time variant nonparametric quantiles and time variant parameters from probability models. First, we investigate and develop nonparametric techniques for measuring extreme quantiles. The method involves aggregating data by an explanatory variable such as time and smoothing the resulting data with a nonparametric method like kernel, local polynomial or spline smoothing. We demonstrate both in application and simulation that this two-step procedure of quantile estimation is superior to the parametric quantile regression. We then develop a one-step method which combines the strength of maximum likelihood estimation with a local …

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A Bayesian Model For Spectral Density Estimation, Yi Xie Jan 2018

A Bayesian Model For Spectral Density Estimation, Yi Xie

Open Access Theses & Dissertations

When we analyze a stationary time series, one of the questions we often meet is how to estimate its spectral density. Many approaches have been proposed to this end. In this paper we estimate the spectral density of a stationary time series nonparametrically. We fit a nonparametric regression model to the log periodogram and use third-degree B-spline functions as basis functions. Since the the number of basis functions is relatively large, we place priors such as random-walk and regularized horseshoe on the coefficients of the basis functions to avoid over-fitting and smooth the log periodogram.

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The Regression Smoother Lowess: A Confidence Band That Allows Heteroscedasticity And Has Some Specified Simultaneous Probability Coverage, Rand Wilcox Dec 2017

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 …

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Nonparametric Compound Estimation, Derivative Estimation, And Change Point Detection, Sisheng Liu Jan 2017

Nonparametric Compound Estimation, Derivative Estimation, And Change Point Detection, Sisheng Liu

Theses and Dissertations--Statistics

Firstly, we reviewed some popular nonparameteric regression methods during the past several decades. Then we extended the compound estimation (Charnigo and Srinivasan [2011]) to adapt random design points and heteroskedasticity and proposed a modified Cp criteria for tuning parameter selection. Moreover, we developed a DCp criteria for tuning paramter selection problem in general nonparametric derivative estimation. This extends GCp criteria in Charnigo, Hall and Srinivasan [2011] with random design points and heteroskedasticity. Next, we proposed a change point detection method via compound estimation for both fixed design and random design case, the adaptation of heteroskedasticity was considered for the method. …

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Image Denoising By A Local Clustering Framework, Partha Sarathi Mukherjee, Peihua Qiu Jan 2015

Image Denoising By A Local Clustering Framework, Partha Sarathi Mukherjee, Peihua Qiu

Mathematics Faculty Publications and Presentations

Images often contain noise due to imperfections in various image acquisition techniques. Noise should be removed from images so that the details of image objects (e.g., blood vessels, inner foldings, or tumors in the human brain) can be clearly seen, and the subsequent image analyses are reliable. With broad usage of images in many disciplines—for example, medical science—image denoising has become an important research area. In the literature, there are many different types of image denoising techniques, most of which aim to preserve image features, such as edges and edge structures, by estimating them explicitly or implicitly. Techniques based on …

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Developments In Nonparametric Regression Methods With Application To Raman Spectroscopy Analysis, Jing Guo Jan 2015

Developments In Nonparametric Regression Methods With Application To Raman Spectroscopy Analysis, Jing Guo

Theses and Dissertations--Epidemiology and Biostatistics

Raman spectroscopy has been successfully employed in the classification of breast pathologies involving basis spectra for chemical constituents of breast tissue and resulted in high sensitivity (94%) and specificity (96%) (Haka et al, 2005). Motivated by recent developments in nonparametric regression, in this work, we adapt stacking, boosting, and dynamic ensemble learning into a nonparametric regression framework with application to Raman spectroscopy analysis for breast cancer diagnosis. In Chapter 2, we apply compound estimation (Charnigo and Srinivasan, 2011) in Raman spectra analysis to classify normal, benign, and malignant breast tissue. We explore both the spectra profiles and their derivatives to …

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Functionals Of Gasser--Muller Estimators, Petre Babilua, Elizbar Nadaraya, Grigol Sokhadze Jan 2014

Functionals Of Gasser--Muller Estimators, Petre Babilua, Elizbar Nadaraya, Grigol Sokhadze

Turkish Journal of Mathematics

The asymptotic properties of a general functional of the Gasser--Muller estimator are investigated in the Sobolev space. The convergence rate, consistency, and central limit theorem are established.

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Variable Selection In Nonparametric And Semiparametric Regression Models, Liangjun Su, Yonghui Zhang Jan 2013

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.

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Improved Cardiovascular Risk Prediction Using Nonparametric Regression And Electronic Health Record Data, Edward Kennedy, Wyndy Wiitala, Rodney Hayward, Jeremy Sussman Dec 2012

Improved Cardiovascular Risk Prediction Using Nonparametric Regression And Electronic Health Record Data, Edward Kennedy, Wyndy Wiitala, Rodney Hayward, Jeremy Sussman

Edward H. Kennedy

Use of the electronic health record (EHR) is expected to increase rapidly in the near future, yet little research exists on whether analyzing internal EHR data using flexible, adaptive statistical methods could improve clinical risk prediction. Extensive implementation of EHR in the Veterans Health Administration provides an opportunity for exploration. Our objective was to compare the performance of various approaches for predicting risk of cerebrovascular and cardiovascular (CCV) death, using traditional risk predictors versus more comprehensive EHR data. Regression methods outperformed the Framingham risk score, even with the same predictors (AUC increased from 71% to 73% and calibration also improved). …

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Comparing The Strength Of Association Of Two Predictors Via Smoothers Or Robust Regression Estimators, Rand R. Wilcox May 2011

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 …

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Kernel Regression In The Presence Of Correlated Errors, Kris De Brabanter, Jos De Brabanter, Johan A.K. Suykens, Bart De Moor Jan 2011

Kernel Regression In The Presence Of Correlated Errors, Kris De Brabanter, Jos De Brabanter, Johan A.K. Suykens, Bart De Moor

Kris De Brabanter

It is a well-known problem that obtaining a correct bandwidth and/or smoothing parameter in nonparametric regression is difficult in the presence of correlated errors. There exist a wide variety of methods coping with this problem, but they all critically depend on a tuning procedure which requires accurate information about the correlation structure. We propose a bandwidth selection procedure based on bimodal kernels which successfully removes the correlation without requiring any prior knowledge about its structure and its parameters. Further, we show that the form of the kernel is very important when errors are correlated which is in contrast to the …

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Statistical Topology Via Morse Theory, Persistence And Nonparametric Estimation, Peter Bubenik, Gunnar Carlsson, Peter T. Kim, Zhiming Luo Jan 2010

Statistical Topology Via Morse Theory, Persistence And Nonparametric Estimation, Peter Bubenik, Gunnar Carlsson, Peter T. Kim, Zhiming Luo

Mathematics and Statistics Faculty Publications

In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation procedure can then be evaluated using the bottleneck distance between the estimated persistent homology and the true persistent homology. The connection to statistics comes from the fact that when viewed as a nonparametric regression problem, the bottleneck distance is bounded by the sup-norm loss. Consequently, a sharp asymptotic minimax bound is determined under the sup–norm risk over H¨older classes of functions for the nonparametric regression problem on …

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Generalized Monotonic Functional Mixed Models With Application To Modeling Normal Tissue Complications , Matthew Schipper, Jeremy Taylor, Xihong Lin Aug 2006

Generalized Monotonic Functional Mixed Models With Application To Modeling Normal Tissue Complications , Matthew Schipper, Jeremy Taylor, Xihong Lin

The University of Michigan Department of Biostatistics Working Paper Series

Normal tissue complications are a common side effect of radiation therapy. They are the consequence of the dose of radiation received by the normal tissue surrounding the tumor site. It is not known what function of the dose distribution to the normal tissue drives the presence and severity of the complications. Regarding the density of the dose distribution as a curve, a summary measure is obtained by integrating a weighting function of dose (w(d)) over the dose density. For biological reasons the weight function should be monotonic. We propose to study the dose effect on a clinical outcome using a …

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Inferences About The Components Of A Generalized Additive Model, Rand R. Wilcox Nov 2005

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.

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Equivalent Kernels Of Smoothing Splines In Nonparametric Regression For Clustered/Longitudinal Data, Xihong Lin, Naisyin Wang, Alan H. Welsh, Raymond J. Carroll Sep 2003

Equivalent Kernels Of Smoothing Splines In Nonparametric Regression For Clustered/Longitudinal Data, Xihong Lin, Naisyin Wang, Alan H. Welsh, Raymond J. Carroll

The University of Michigan Department of Biostatistics Working Paper Series

We compare spline and kernel methods for clustered/longitudinal data. For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, the recent work of Welsh, et al. (2002) shows that the same is not true for clustered/longitudinal data. First, conventional kernel methods fail to account for the within- cluster correlation, while spline methods are able to account for this correlation. Second, kernel methods and spline methods were found to have different local behavior, with conventional kernels being local and splines being non-local. To resolve these differences, we show that a smoothing …

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Efficient Semiparametric Marginal Estimation For Longitudinal/Clustered Data, Naisyin Wang, Raymond J. Carroll, Xihong Lin Sep 2003

Efficient Semiparametric Marginal Estimation For Longitudinal/Clustered Data, Naisyin Wang, Raymond J. Carroll, Xihong Lin

The University of Michigan Department of Biostatistics Working Paper Series

We consider marginal generalized semiparametric partially linear models for clustered data. Lin and Carroll (2001a) derived the semiparametric efficinet score funtion for this problem in the mulitvariate Gaussian case, but they were unable to contruct a semiparametric efficient estimator that actually achieved the semiparametric information bound. We propose such an estimator here and generalize the work to marginal generalized partially liner models. Asymptotic relative efficincies of the estimation or throughout are investigated. The finite sample performance of these estimators is evaluated through simulations and illustrated using a longtiudinal CD4 count data set. Both theoretical and numerical results indicate that properly …

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Wavelet-Based Nonparametric Modeling Of Hierarchical Functions In Colon Carcinogenesis., Jeffrey S. Morris, Marina Vannucci, Philip J. Brown, Raymond J. Carroll Sep 2003

Wavelet-Based Nonparametric Modeling Of Hierarchical Functions In Colon Carcinogenesis., Jeffrey S. Morris, Marina Vannucci, Philip J. Brown, Raymond J. Carroll

Jeffrey S. Morris

In this article we develop new methods for analyzing the data from an experiment using rodent models to investigate the effect of type of dietary fat on O6-methylguanine-DNA-methyltransferase (MGMT), an important biomarker in early colon carcinogenesis. The data consist of observed profiles over a spatial variable contained within a two-stage hierarchy, a structure that we dub hierarchical functional data. We present a new method providing a unified framework for modeling these data, simultaneously yielding estimates and posterior samples for mean, individual, and subsample-level profiles, as well as covariance parameters at the various hierarchical levels. Our method is nonparametric in that …

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