The Effect of Errors in the Independent Variables in Linear Regression

Davies, R. B.; Hutton, B.

doi:10.2307/2335377

Cited by 61 publications

(27 citation statements)

References 3 publications

(6 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this circumstance the problem is known as an errors-in-variables (EIV) problem and it is well known the that traditional least square method provides inconsistent estimators [18]. If all measurement errors are iid then the total least squares (TLS) method (see [19]–[21]) is the correct procedure and [22] provides distributional results for the parameter estimators in the Gaussian case.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy

Cohen

Ober

2013

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data.

show abstract

Section: Introductionmentioning

confidence: 99%

Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy

Cohen

Ober

2013

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

show abstract

“…One noise source that is especially important to model is the error in the reference spectra and associated response matrix ( ) ij R ρ so that techniques from the errors in predictors literature [40] could be applied. For example, the MCMC approach to implement the Bayesian variable selection can easily accommodate errors in predictors, particularly if combined with a MIMBS-type approach that reduces the number of possible absorbers to a representative basis set.…”

Section: Comprehensive Assessment Of All Noise Sourcesmentioning

confidence: 99%

“…Many of these sensors rely on Radio-Isotope Identification (RIID) algorithms using γ spectroscopy to distinguish innocent nuisance alarms arising from naturally occurring radioactive material (NORM) from alarms arising from threat isotopes. NORM examples include 40 K from cat litter and 232 Th in soil. Threat isotopes include special nuclear material (SNM) isotopes such as isotopes of U and Pu.…”

Section: Introductionmentioning

confidence: 99%

Radio-Isotope Identification Algorithms for NaI γ Spectra

Burr

Hamada

2009

Algorithms

View full text Add to dashboard Cite

The performance of Radio-Isotope Identification (RIID) algorithms using NaI-based γ spectroscopy is increasingly important. For example, sensors at locations that screen for illicit nuclear material rely on isotope identification using NaI detectors to distinguish innocent nuisance alarms, arising from naturally occurring radioactive material, from alarms arising from threat isotopes. Recent data collections for RIID testing consist of repeat measurements for each of several measurement scenarios to test RIID algorithms. It is anticipated that vendors can modify their algorithms on the basis of performance on chosen measurement scenarios and then test modified algorithms on data for other measurement scenarios. It is therefore timely to review the current status of RIID algorithms on NaI detectors. This review describes γ spectra from NaI detectors, measurement issues and challenges, current RIID algorithms, data preprocessing steps, the role and current quality of synthetic spectra, and opportunities for improvements

show abstract

“…Behnken and Draper (1972) study the pattern of variation in the vii and note that wide variation reflects nonhomogeneous spacing of the rows of X. Huber (1975) and Davies and Hutton (1975) point out that if max(vii) is not considerably smaller than 1, it is probable that an outlier will go undetected when the residuals are examined. The average of the vii is p'/n and thus max(vii) 2 pl/n.…”

Section: T H E Role Of V I N Data a N A L Y S E Smentioning

confidence: 99%