Relative error prediction via kernel regression smoothers

Jones, M. C.; Park, Heungsun; Shin, Key-Il; Vines, S. K.; Jeong, Seok-Oh

doi:10.1016/j.jspi.2007.11.001

Cited by 26 publications

(15 citation statements)

References 18 publications

(15 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that the asymptotic bias expression does not depend on the error distribution and is exactly the same as in the error‐free case (Jones et al, ), and the errors in variables only affect the variance of the estimator.…”

Section: Assumptions and Main Resultsmentioning

confidence: 94%

“…In nonparametric analysis, there exist few papers in the literature that paid attention to this subject. By considering the kernel method combined with local linear approach, Jones, Park, Shin, Vines, and Jeong () investigated the nonparametric prediction via relative error regression and studied the asymptotic properties of an estimator minimizing the sum of the squared relative errors. Recently, a version of the kernel regression estimator proposed by these authors is studied asymptotically and numerically by Attouch, Laksaci, and Messabihi () in the spatial framework context, whereas Demongeot, Hamie, Laksaci, and Rachdi () proposed a functional version of the relative kernel regression estimator.…”

Section: Introductionmentioning

confidence: 99%

“…For an arbitrary function

sans-serifg

, let ϕ

sans-serifg

denotes its Fourier transform, that is,

ϕ_{sans-serifg} (t) = \int_{double-struckR} e^{i t x} g (x) d x, t \in R, with i^{2} = - 1,

and for a real random variable Z , we denote by ϕ Z its characteristic function. To estimate the regression function m , Fan and Truong () proposed the following kernel estimator:

\overset{m}{true} false(x false) = \frac{\sum_{j = 1}^{n} Y_{j} K_{n} ((), \frac{x - W_{j}}{b})}{\sum_{j = 1}^{n} K_{n} ((), \frac{x - W_{j}}{b})},

where

K_{n} false(x false) = \frac{1}{2 π} \int_{R} e^{- i t x} \frac{ϕ_{K} false(t false)}{ϕ_{U} false(t false/ b false)} d t .

First, notice that in the error‐free case (i.e., when X is observed) and when we dispose a sample ( X 1 , Y 1 ),…,( X n , Y n ) distributed as the pair ( X , Y ), the estimator of proposed by Jones et al () is given by

\overset{m}{true} false(x false) = \frac{\sum_{j = 1}^{n} Y_{j}^{- 1} K ((), \frac{x - X_{j}}{b})}{\sum_{j = 1}^{n} Y_{j}^{- 2} K ((), \frac{x - X_{j}}{b})}

…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Relative error prediction in nonparametric deconvolution regression model

Thiam

2018

Statistica Neerlandica

View full text Add to dashboard Cite

JEL Classification: 62G05; 62G08; 62G20In this paper, we studied an alternative estimator of the regression function when the covariates are observed with error. It is based on the minimization of the relative mean squared error. We obtain expressions for its asymptotic bias and variance together with an asymptotic normality result.Our technique is illustrated on simulation studies. Numerical results suggest that the studied estimator can lead to tangible improvements in prediction over the usual kernel deconvolution regression estimator, particularly in the presence of several outliers in the dataset. KEYWORDSalmost-sure convergence, asymptotic normality, deconvolution problem, mean square relative error, nonparametric estimation

show abstract

Section: Assumptions and Main Resultsmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

“…For an arbitrary function

sans-serifg

, let ϕ

sans-serifg

denotes its Fourier transform, that is,

ϕ_{sans-serifg} (t) = \int_{double-struckR} e^{i t x} g (x) d x, t \in R, with i^{2} = - 1,

and for a real random variable Z , we denote by ϕ Z its characteristic function. To estimate the regression function m , Fan and Truong () proposed the following kernel estimator:

\overset{m}{true} false(x false) = \frac{\sum_{j = 1}^{n} Y_{j} K_{n} ((), \frac{x - W_{j}}{b})}{\sum_{j = 1}^{n} K_{n} ((), \frac{x - W_{j}}{b})},

where

K_{n} false(x false) = \frac{1}{2 π} \int_{R} e^{- i t x} \frac{ϕ_{K} false(t false)}{ϕ_{U} false(t false/ b false)} d t .

\overset{m}{true} false(x false) = \frac{\sum_{j = 1}^{n} Y_{j}^{- 1} K ((), \frac{x - X_{j}}{b})}{\sum_{j = 1}^{n} Y_{j}^{- 2} K ((), \frac{x - X_{j}}{b})}

…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Relative error prediction in nonparametric deconvolution regression model

Thiam

2018

Statistica Neerlandica

View full text Add to dashboard Cite

show abstract

“…Step (1) Detection of the Incipient Slew Bearing Defect Using MSET and SPRT Twelve features were extracted from four different methods [31]. Not all features were sensitive to the change of the bearing condition.…”

Section: 1mentioning

confidence: 99%

Integrated Condition Monitoring and Prognosis Method for Incipient Defect Detection and Remaining Life Prediction of Low Speed Slew Bearings

2017

View full text Add to dashboard Cite

This paper presents an application of multivariate state estimation technique (MSET), sequential probability ratio test (SPRT) and kernel regression for low speed slew bearing condition monitoring and prognosis. The method is applied in two steps.Step (1) is the detection of the incipient slew bearing defect. In this step, combined MSET and SPRT is used with circular-domain kurtosis, time-domain kurtosis, wavelet decomposition (WD) kurtosis, empirical mode decomposition (EMD) kurtosis and the largest Lyapunov exponent (LLE) feature.Step (2) is the prediction of the selected features' trends and the estimation of the remaining useful life (RUL) of the slew bearing. In this step, kernel regression is used with time-domain kurtosis, WD kurtosis and the LLE feature. The application of the method is demonstrated with laboratory slew bearing acceleration data.

show abstract

“…For S220: (3) Figure 9 shows the relative error [27] of temperature of both oils between test data and fitted data, and the calculation equation is as Formula (4). As shown in Figure 9, the relative error is less than 0.5% at almost all times except at a few moments such as at the beginning of operation.…”

Section: Prediction Of Operating Temperaturementioning

confidence: 99%

Experimental Evaluation of Lubrication Characteristics of a New Type Oil-Film Bearing Oil Using Multi-Sensor System

et al. 2016

View full text Add to dashboard Cite

Abstract:In order to evaluate the operating performance of a new type oil-film bearing oil S220, a new test bearing was designed based on oil-film bearing test rig. The operating temperature of S220 was tested through the thermocouples installed on a test bearing; the operating oil-film pressure was tested through pressure transducers; and the operating oil-film thickness was tested through displacement transducers. Meanwhile, M220 was also tested as a comparison, and both oils are based on mineral oil. The results showed that all property indexes of the test rig can meet the specified requirements and can guarantee the performance test of oil-film bearing oil; the operating temperature of S220 is generally equal to that of M220, and both have the same operating stability. The temperature property conforms to Formula (1) and the operating temperature under different load cases can be predicted. Although oil-film pressure of M220 is a little more stable, the oil-film pressure of S220 is similar to that of M220. Moreover, both have the similar oil-film thickness, and the oil-film thickness of S220 is slightly smaller than that of M220, especially at the beginning of operation. Ultimately, oil S220 is evaluated to be suitable for actual engineering application.

show abstract

Relative error prediction via kernel regression smoothers

Cited by 26 publications

References 18 publications

Relative error prediction in nonparametric deconvolution regression model

Relative error prediction in nonparametric deconvolution regression model

Integrated Condition Monitoring and Prognosis Method for Incipient Defect Detection and Remaining Life Prediction of Low Speed Slew Bearings

Experimental Evaluation of Lubrication Characteristics of a New Type Oil-Film Bearing Oil Using Multi-Sensor System

Contact Info

Product

Resources

About