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library orrh € i}ePf\rtTfli1nt of St~i':F(>; North Carolma State UnwersltyMEASUREMENT ERROR AND CORRECTIONS FOR ATTENUATION IN

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MacMahon, et al. (1990) present a meta-analysis of the effect of blood pressure on coronary heart disease, as well as new methods for estimation in measurement error models for the case when a replicate or second measurement is made of the fallible predictor. The correction for attenuation used by these authors is compared to others already exis...

MacMahon, et al. (1990) present a meta-analysis of the effect of blood pressure on coronary heart disease, as well as new methods for estimation in measurement error models for the case when a replicate or second measurement is made of the fallible predictor. The correction for attenuation used by these authors is compared to others already existing in the literature, as well as to a new instrumental variable method. The assumptions justifying the various methods are examined and their efficiencies are studied via simulation. Compared to the methods we discuss, that of MacMahon, et al. (1990) may have substantial bias in some circumstances because it does not take into account: (i) possible correlations among the predictors within a study; (ii) possible bias in the second measurement; or (iii) possibly differing marginal distributions of the predictors and/or measurement errors across studies Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-02-27

Source:

http://www.stat.ncsu.edu/library/mimeo.archive/ISMS_1992_2222.pdf

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text

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en

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310 Collections of general statistics *(computed)*

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In regre~sion.~1¥_~.~-",.:te~.!~rS.2~sl!_1. §. often transformed to remove heteroscedasti-Glty-~:o'''''''~n'a model already exists I. for the untransformed re-spB-iise;"'thei\""'lt"!cari ~ ~ preserved by applying the i. ~- ·'-~c~'<~·",:,:::.';"••~,~:,~.:. same transform to both the model and the response. This methodology, _.',,_ _ '~'~_"""~_~I"...

In regre~sion.~1¥_~.~-",.:te~.!~rS.2~sl!_1. §. often transformed to remove heteroscedasti-Glty-~:o'''''''~n'a model already exists I. for the untransformed re-spB-iise;"'thei\""'lt"!cari ~ ~ preserved by applying the i. ~- ·'-~c~'<~·",:,:::.';"••~,~:,~.:. same transform to both the model and the response. This methodology, _.',,_ _ '~'~_"""~_~I"'''''''" '.".,::: ":" '.::.-:._ _ c Iwhich we call "transforJl.brth.s,.ides~.QiUt been- applied in several recent papers, and appears highly useful in practice. When a parametric transformation family such as the power transformations is used, then the transformation can be estimated by maximum likelihood. The MLE, however, is very sensitive to outliers. In this article, we propose diagnostics to indicate cases influential for the transformation orPage 2 regression parameters. We also propose a robust bounded-influence estimator similar to the Krasker-Welsch regression estimator. Acknowledge.ent Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-02-27

Source:

http://www.stat.ncsu.edu/library/mimeo.archive/ISMS_1986_1706.pdf

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text

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en

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Diagnostics and Robust Estimation When Transforming the Regression Model and the Response

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In regression analysis, the response is often transformed to remove heteroscedasticity and/or skewness. When a model already exists for the untransformedresponse, then it can be preserved by transforming both the model and the response with the same transformation. This methodology, which we call II transform both sides II has been appl ied in s...

In regression analysis, the response is often transformed to remove heteroscedasticity and/or skewness. When a model already exists for the untransformedresponse, then it can be preserved by transforming both the model and the response with the same transformation. This methodology, which we call II transform both sides II has been appl ied in several recent papers, and appears highly useful in practice. When a • parametric transformation family such as power transformations is used, ~en the transformation can be estimated by maximum likelihood. The MLE however is very sensitive to outliers. In this article, we propose 2 diagnostics which indicate cases influential for the transformation or e regression parameters. We also propose a robust bounded-influence estimator similar to the Krasker-Welsch regression estimate. Both the diagnostics and the robust estimator can be implemented on standard software. 4 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-02-27

Source:

http://www.stat.ncsu.edu/library/mimeo.archive/ISMS__1592.pdf

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text

Language:

en

DDC:

519 Probabilities & applied mathematics *(computed)* ; 310 Collections of general statistics *(computed)*

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A comparison between maximum likelihood and generalized least squares in a heteroscedastic model

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by

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-02-27

Source:

http://www.stat.ncsu.edu/library/mimeo.archive/ISMS__1334.pdf

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Robust estimation in heteroscedastic linear models when there are many parameters

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We study estiuultion of regression parameters in heteroscedastic linear models when the number of parameters is large. The results

We study estiuultion of regression parameters in heteroscedastic linear models when the number of parameters is large. The results Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-09-20

Source:

http://www.stat.ncsu.edu/library/mimeo.archive/ISMS__1321.pdf

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text

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en

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Key Words and Phrases ; Iieteroscedasticity ; Linear MOdels ; Regression ; Weighted Least Squares ; Robustness

Key Words and Phrases ; Iieteroscedasticity ; Linear MOdels ; Regression ; Weighted Least Squares ; Robustness Minimize

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Title:

Transformations in Regression: A Robust Analysis

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-09-20

Source:

http://www.stat.ncsu.edu/library/mimeo.archive/ISMS__1544.pdf

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text

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en

Subjects:

Power transfonnations ; Box-Cox model ; robust estimation ; influence functions ; bounded influence ; likelihood-raLio-type tests

Power transfonnations ; Box-Cox model ; robust estimation ; influence functions ; bounded influence ; likelihood-raLio-type tests Minimize

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Title:

ON PREDICTION AND THE POWER TRANSPORMATION FAMILY

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The power transformation family studied by Box and Cox (1964) for transforming to a normal linear model has recently been further studied by Bickel and Doksum (1978), who show that "the cost of not knowing Aand estimating it. is generally severe"; some of the variances for regression parameters can be extremely large. We consider prediction of f...

The power transformation family studied by Box and Cox (1964) for transforming to a normal linear model has recently been further studied by Bickel and Doksum (1978), who show that "the cost of not knowing Aand estimating it. is generally severe"; some of the variances for regression parameters can be extremely large. We consider prediction of future observations (untransformed) when the data can be transfo~ed to a linear model and show that while there is a cost due to estimating A it is generally not severe. Similar results emerge for the two sample problems. Monte-Carlo results lend credence to the asymptotic calculations. Key Words and Phrases: Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-02-24

Source:

http://www.stat.ncsu.edu/library/mimeo.archive/ISMS__1264.pdf

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Document Type:

text

Language:

en

Subjects:

Power transformations ; Prediction ; Robustness ; Box-Cox family ; Asymptotic theory

Power transformations ; Prediction ; Robustness ; Box-Cox family ; Asymptotic theory Minimize

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NAME DATE • META-ANALYSIS, MEASUREMENT ERROR AND CORRECTIONS FOR ATTENUATION

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MacMahon, et al. (1990) present a meta-analysis of the effect of blood pressure on coronary heart disease, as well as new methods for estimation in measurement error models for the case when a replicate or second measurement is made of the fallible predictor. The correction for attenuation used by these authors is compared to others already exis...

MacMahon, et al. (1990) present a meta-analysis of the effect of blood pressure on coronary heart disease, as well as new methods for estimation in measurement error models for the case when a replicate or second measurement is made of the fallible predictor. The correction for attenuation used by these authors is compared to others already existing in the literature, as well as to a new instrumental variable method. The assumptions justifying the various methods are examined and their efficiencies are studied via simulation. Compared to the methods we discuss, that of MacMahon, et al. (1990) may have substantial bias in some circumstances because it does not take into account: (i) possible correlations among the predictors within a study; (ii) possible bias in the second measurement; or (iii) possibly differing marginal distributions of the predictors across studies Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-02-27

Source:

http://www.stat.ncsu.edu/library/mimeo.archive/ISMS_1991_2201.pdf

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Title:

Nonparametric Estimation Via Local Estimating Equations, With Applications To Nutrition Calibration

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Estimating equations have found wide popularity recently in parametric problems, yielding consistent estimators with asymptotically valid inferences obtained via the sandwich formula. Motivated by a problem in nutritional epidemiology, we use estimating equations to derive nonparametric estimators of a "parameter" depending on a predictor. The n...

Estimating equations have found wide popularity recently in parametric problems, yielding consistent estimators with asymptotically valid inferences obtained via the sandwich formula. Motivated by a problem in nutritional epidemiology, we use estimating equations to derive nonparametric estimators of a "parameter" depending on a predictor. The nonparametric component is estimated via local polynomials with loess or kernel weighting; asymptotic theory is derived for the latter. In keeping with the estimating equation paradigm, variances of the nonparametric function estimate are estimated using the sandwich method, in an automatic fashion, without the need typical in the literature to derive asymptotic formulae and plug-in an estimate of a density function. The same philosophy is used in estimating the bias of the nonparametric function, i.e., we use an empirical method without deriving asymptotic theory on a case-by-case basis. The methods are applied to a series of examples. The appli. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

ftp://ftp.orie.cornell.edu/pub/techreps/TR1168.ps

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text

Language:

en

DDC:

310 Collections of general statistics *(computed)*

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STATISTICS IN MEDICINE Statist. Med. 2004; 00:1–24 Simple fitting of subject-specific curves for longitudinal data

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We present a simple semiparametric model for fitting subject-specific curves for longitudinal data. Individual curves are modeled as penalized splines with random coefficients. This model has a mixed model representation, and it is easily implemented in standard statistical software. We conduct an analysis of the long-term effect of radiation th...

We present a simple semiparametric model for fitting subject-specific curves for longitudinal data. Individual curves are modeled as penalized splines with random coefficients. This model has a mixed model representation, and it is easily implemented in standard statistical software. We conduct an analysis of the long-term effect of radiation therapy on the height of children suffering from acute lymphoblastic leukemia using penalized splines in the framework of semiparametric mixed effects models. The analysis revealed significant differences between therapies and showed that the growth rate of girls in the study cannot be fully explained by the group-average curve and that individual curves are necessary to reflect the individual response to treatment. We also showhowto implement these models in S-PLUS and R in the appendix. Copyright c ○ 2004 John Wiley & Sons, Ltd. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-17

Source:

http://www.stat.tamu.edu/~carroll/ftp/2004.papers.directory/durban_final.pdf

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Document Type:

text

Language:

en

Subjects:

key words ; Linear mixed models ; Restricted likelihood ratio tests ; Penalized splines ; Acute

key words ; Linear mixed models ; Restricted likelihood ratio tests ; Penalized splines ; Acute Minimize

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310 Collections of general statistics *(computed)*

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