An Effective Bandwidth Selector for Local Least Squares Regression

Ruppert, David; Sheather, Simon J.; Wand, M. P.

doi:10.2307/2291516

Cited by 302 publications

(311 citation statements)

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“…by Härdle & Marron (1985), Härdle et al (1988), Park & Marron (1990), Ruppert et al (1995), Wand & Jones (1995) and Xia (1998), among others. Herrmann et al (1992) and Wu & Zhao (2007) dealt with models with stationary errors.…”

Section: ·5 Bandwidth Selectionmentioning

confidence: 96%

Testing parametric assumptions of trends of a nonstationary time series

Zhang

2011

Biometrika

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SUMMARYThe paper considers testing whether the mean trend of a nonstationary time series is of certain parametric forms. A central limit theorem for the integrated squared error is derived, and with that a hypothesis-testing procedure is proposed. The method is illustrated in a simulation study, and is applied to assess the mean pattern of lifetime-maximum wind speeds of global tropical cyclones from 1981 to 2006. We also revisit the trend pattern in the central England temperature series.

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Section: ·5 Bandwidth Selectionmentioning

confidence: 96%

Testing parametric assumptions of trends of a nonstationary time series

Zhang

2011

Biometrika

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“…We used the function dpill (Ruppert et al, (1995)) in the pack-age KernSmooth for choosing the bandwidth and the function locpoly for performing the local linear regression. Table 1 used.…”

Section: Numerical Studiesmentioning

confidence: 99%

Simultaneous Confidence Bands in Nonlinear Regression Models with Nonstationarity

Li¹,

Liu²,

Wang³

et al. 2017

STAT SINICA

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We consider nonparametric estimation of the regression function g(·)in a nonlinear regression model Yt = g(Xt) + σ(Xt)et, where the regressor (Xt) is a nonstationary unit root process and the error (et) is a sequence of independent and identically distributed (i.i.d.) random variables. With proper centering and scaling, the maximum deviation of the local linear estimator of the regression function g is shown to be asymptotically Gumbel. Based on the latter result, we construct simultaneous confidence bands for g, which can be used to test patterns of the regression function. Our results extend existing ones that typically require independent or stationary weakly dependent regressors. We examine the finite sample behavior of the proposed approach via simulated and empirical data examples.

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“…A drawback of the cross-validation method is its inherent variability. 7,17 We use the C p criterion since it provides an unbiased estimate of the sum of the squared error over the time samples, and it is a unitless characterization (the fitted degree of freedom) which allows comparison between methods. The C p statistic for a local regression estimateμ(x) is…”

Section: Model Assessmentmentioning

confidence: 99%

“…4 The advantages of this approach include simplicity, ease of fast computation, and superior boundary behavior. 6,17 A detailed summary of the advantages of local regression compared to kernel fitting may be found in. 8 Despite its popularity in statistics, local regression is far less well-known in biology and medicine.…”

Section: Introductionmentioning

confidence: 99%

“…9,13 Polynomial fitting as a robust smoothing technique has demonstrated its potential in diverse areas for many years, and now the theory and computation of local least-squares approaches can be found in some major recent contributions. 4,6,17 In this technique, no assumption is made about the form of the regression function: the complexity of the model will be determined completely by the data. Local regression has the necessary ability to provide an excellent tradeoff between the two desirable but conflicting properties of regression: smoothing the noise versus preserving signal information.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Assessment of the Esophageal Pressure in Gastroesophageal Reflux Disease by the Local Regression

Liang

Chen

2005

Ann Biomed Eng

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Abstract-Gastroesophageal reflux disease (GERD) is one of the most prevalent gastrointestinal diseases. It is characterized by excessive reflux of gastric content (acid, pepsin, etc.) into the esophagus causing symptoms (heartburn, acid regurgitation, etc.) and mucosal inflammation and injuries. GERD occurs when the lower esophageal sphincter (LES) has a low resting pressure and stomach contents leak back, or reflux, into the esophagus. Therefore, the accurate measurement of the LES pressure is of great importance for the diagnosis of GERD. The LES pressure signal, involving severe respiratory contamination and motion artifacts, demands specific capabilities not provided by conventional data analysis methods. Recently, local regression has proved to be a very attractive technique to the nonparametric regression in statistics. In this contribution we apply the ideas of local regression to develop strategies for selecting smoothing parameters of local linear squares estimators, and present its application on the extraction of the LES pressure in GERD. The results from both extensive simulations and real data demonstrate the ability of local regression to characterize the LES pressure, which is consistent with the clinical observation.

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An Effective Bandwidth Selector for Local Least Squares Regression

Cited by 302 publications

References 0 publications

Testing parametric assumptions of trends of a nonstationary time series

Testing parametric assumptions of trends of a nonstationary time series

Simultaneous Confidence Bands in Nonlinear Regression Models with Nonstationarity

Assessment of the Esophageal Pressure in Gastroesophageal Reflux Disease by the Local Regression

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