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  1. The efficiency of bias-corrected estimators for nonparametric kernel estimation based on local estimating equations
    Autor*in: Kauermann, Göran; Müller, Marlene; Carroll, Raymond J.
    Erschienen: 1997
    Verlag:  Humboldt-Universität, Berlin

    Stuetzle and Mittal (1979) for ordinary nonparametric kernel regression and Kauermann and Tutz (1996) for nonparametric generalized linear model kernel regression constructed estimators with lower order bias than the usual estimators, without the... mehr

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    Stuetzle and Mittal (1979) for ordinary nonparametric kernel regression and Kauermann and Tutz (1996) for nonparametric generalized linear model kernel regression constructed estimators with lower order bias than the usual estimators, without the need for devices such as second derivative estimation and multiple bandwidths of different order. We derive a similar estimator in the context of local (multivariate) estimation based on estimating functions. As expected, this lower order bias is bought at a cost of increased variance. Surprisingly, when compared to ordinary kernel and local linear kernel estimators, the bias-corrected estimators increase variance by a factor independent of the problem, depending only on the kernel used. The variance increase is approximately 40% and more for kernels in standard use. However, the variance increase is still less than that incurred when undersmoothing a local quadratic regression estimator. -- Bootstrap ; Nonparametric Regression ; Estimating Equations ; Generalized Linear Models ; Local Linear Regression ; Bias Reduction

     
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    hdl: 10419/66263
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 1997,70
    Umfang: Online-Ressource (PDF-Datei: 7 S., 180,48 KB)
  2. Estimation in an additive model when the components are linked parametrically
    Autor*in: Carroll, Raymond J.; Härdle, Wolfgang; Mammen, Enno
    Erschienen: 1999
    Verlag:  Humboldt-Universität, Berlin

    Motivated by a nonparametric GARCH model we consider nonparametric additive regression and autoregression models in the special case that the additive components are linked parametrically. We show that the parameter can be estimated with parametric... mehr

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    Motivated by a nonparametric GARCH model we consider nonparametric additive regression and autoregression models in the special case that the additive components are linked parametrically. We show that the parameter can be estimated with parametric rate and give the normal limit. Our procedure is based on two steps. In the first step nonparametric smoothers are used for the estimation of each additive component without taking into account the parametric link of the functions. In a second step the parameter is estimated by using the parametric restriction between the additive components. Interestingly, our method needs no undersmoothing in the first step. -- Finance ; Nonparametric Regression ; Additive Models ; Asymptotics ; Autoregression ; GARCH Models ; Measurement Error ; Time Series

     
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    hdl: 10419/61777
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 1999,1
    Umfang: Online-Ressource (PDF-Datei: 23 S., 315,68 KB)
  3. Nonparametric function estimation of the relationship between two repeatedly measured variables
    Autor*in: Ruckstuhl, A.; Welsh, A. H.; Carroll, Raymond J.
    Erschienen: 1997
    Verlag:  Humboldt-Universität, Berlin

    We describe methods for estimating the regression function nonparametrically and for estimating the variance components in a simple variance component model which is sometimes used for repeated measures data or data with a simple clustered structure.... mehr

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    We describe methods for estimating the regression function nonparametrically and for estimating the variance components in a simple variance component model which is sometimes used for repeated measures data or data with a simple clustered structure. We consider a number of different ways of estimating the regression function. The main results are that the simple pooled estimator which treats the data as independent performs very well asymptotically but that we can construct estimators which perform better asymptotically in some circumstances. -- semiparametric estimation ; Local linear regression ; local quasi-likelihood estimator ; smoothing ; variance components

     
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    hdl: 10419/66234
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 1997,7
    Umfang: Online-Ressource (PDF-Datei: 22 S., 277,28 KB)
  4. Measurement error, biases, and the validation of complex models
    Autor*in: Carroll, Raymond J.; Galindo, Christian D.
    Erschienen: 1997
    Verlag:  Humboldt-Universität, Berlin

    There are three major points to this article: 1. Measurement error causes biases in regression fits. The line one would obtain if one could accurately measure exposure to environmental lead media will differ in important ways when one measures... mehr

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    There are three major points to this article: 1. Measurement error causes biases in regression fits. The line one would obtain if one could accurately measure exposure to environmental lead media will differ in important ways when one measures exposure with error. 2. The effects of measurement error vary from study-to-study. It is dangerous to take measurement error corrections derived from one study and apply them to data from entirely different studies or populations. 3. Measurement error can falsely invalidate a correct (complex mechanistic) model. If one builds a model such as the IEUBK carefully using essentially error-free lead exposure data, and applies this model in a different data set with error-prone exposures, the complex mechanistic model will almost certainly do a poor job of prediction, especially of extremes. While mean blood lead levels from such a process may be accurately predicted, in most cases one would expect serious under- or over-estimates of the proportion of the population whose blood lead level exceeds certain standards.

     
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    hdl: 10419/66262
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 1997,9
    Umfang: Online-Ressource (PDF-Datei: 13 S., 166,11 KB), graph. Darst.
  5. Polynomial regression and estimation function in the presence of multiplication measurement error, with application to nutrition
    Autor*in: Iturria, Stephen J.; Carroll, Raymond J.; Firth, David
    Erschienen: 1997
    Verlag:  Humboldt-Universität, Berlin

    In this paper we consider the polynomial regression model in the presence of multiplicative measurement error in the predictor. Consistent parameter estimates and their associated standard errors are derived. Two general methods are considered, with... mehr

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    In this paper we consider the polynomial regression model in the presence of multiplicative measurement error in the predictor. Consistent parameter estimates and their associated standard errors are derived. Two general methods are considered, with the methods differing in their assumptions about the distributions of the predictor and the measurement errors. Data from a nutrition study are analyzed using the methods. Finally, the results from a simulation study are presented and the performances of the methods compared. -- Bootstrap ; Measurement Error ; Errors-in-Variables ; Asymptotic theory ; Estimating Equations ; Nonlinear Regression ; Nutrition

     
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    hdl: 10419/66311
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 1997,10
    Umfang: Online-Ressource (PDF-Datei: 16 S., 278,83 KB), graph. Darst.
  6. Nonparametric kernel and regression spline estimation in the presence of measurement error
    Autor*in: Maca, J. D.; Carroll, Raymond J.; Ruppert, David
    Erschienen: 1997
    Verlag:  Humboldt-Universität, Berlin

    In many regression applications both the independent and dependent variables are measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two different nonparametric... mehr

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    In many regression applications both the independent and dependent variables are measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two different nonparametric techniques, regression splines and kernel estimation, of which both can be used in the presence of measurement error. Within the kernel regression context, we derive the limit distribution of the SIMEX estimate. With the regression spline technique, two different methods of estimations are used. The first method is the SIMEX algorithm which attempts to estimate the bias, and remove it. The second method is a structural approach, where one hypothesizes a distribution for the independent variable which depends on estimable parameters. A series of examples and simulations illustrate the methods. -- Bootstrap ; Measurement Error ; Local Polynomial Regression ; SIMEX ; Asymptotic theory ; Estimating Equations ; Nonlinear Regression ; Bandwidth Selection ; Regression Splines ; Sandwich Estimation

     
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    hdl: 10419/66297
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 1997,11
    Umfang: Online-Ressource (PDF-Datei: 16 S., 280,63 KB), graph. Darst.
  7. Design aspects of calibration studies in nutrition, with analysis of missing data in linear measurement error models
    Autor*in: Carroll, Raymond J.; Freedman, Laurence; Pee, David
    Erschienen: 1997
    Verlag:  Humboldt-Universität, Berlin

    Motivated by an example in nutritional epidemiology, we investigate some design and analysis aspects of linear measurement error models with missing surrogate data. The specific problem investigated consists of an initial large sample in which the... mehr

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    Motivated by an example in nutritional epidemiology, we investigate some design and analysis aspects of linear measurement error models with missing surrogate data. The specific problem investigated consists of an initial large sample in which the response (a food frequency questionnaire, FFQ) is observed, and then a smaller calibration study in which replicates of the error prone predictor are observed (food records or recalls, FR). The difference between our analysis and most of the measurement error model literature is that in our study, the selection into the calibration study can depend upon the value of the response. Rationale for this type of design is given. Two major problems are investigated. In the design of a calibration study, one has the option of larger sample sizes and fewer replicates, or smaller sample sizes and more replicates. Somewhat surprisingly, neither strategy is uniformly preferable in cases of practical interest. The answers depend on the instrument used (recalls or records) and the parameters of interest. The second problem investigated is one of analysis. In the usual linear model with no missing data, method of moments estimates and normal-theory maximum likelihood estimates are approximately equivalent, with the former method in most use because it can be calculated easily and explicitly. Both estimates are valid without any distributional assumptions. In contrast, in the missing data problem under consideration, only the moments estimate is distribution-free, but the maximum likelihood estimate has at least 50% greater precision in practical situations when normality obtains. Implications for the design of nutritional calibration studies are discussed. -- Measurement Error ; Errors-in-Variables ; Estimating Equations ; Nutrition ; Sampling Designs ; Linear regression ; Maximum Likelihood ; Method of Moments ; Missing Data ; Model Robustness ; Semiparametrics ; Stratified Sampling ; Weighting

     
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    hdl: 10419/66235
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 1997,12
    Umfang: Online-Ressource (PDF-Datei: 26, [2] S., 253,24 KB), graph. Darst.
  8. Estimating covariance matrices using estimating functions in nonparametric and semiparametric regression
    Autor*in: Carroll, Raymond J.; Iturria, Stephen J.; Gutierrez, Roberto G.
    Erschienen: 1997
    Verlag:  Humboldt-Universität, Berlin

    We use ideas from estimating function theory to derive new, simply computed consistent covariance matrix estimates in nonparametric regression and in a class of semiparametric problems. Unlike other estimates in the literature, ours do not require... mehr

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    We use ideas from estimating function theory to derive new, simply computed consistent covariance matrix estimates in nonparametric regression and in a class of semiparametric problems. Unlike other estimates in the literature, ours do not require auxiliary or additional nonparametric regressions. -- Nonparametric regression ; Estimating Equations ; Kernel regression ; Plug-in Semiparametrics ; Smoothing

     
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    hdl: 10419/66254
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 1997,14
    Umfang: Online-Ressource (PDF-Datei: 6 S., 104,69 KB)
  9. Nonparametric estimation via local estimating equations, with applications to nutrition calibration
    Autor*in: Carroll, Raymond J.; Ruppert, David; Welsh, A. H.
    Erschienen: 1997
    Verlag:  Humboldt-Universität, Berlin

    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... mehr

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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 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 application to nutrition is called "nonparametric calibration" after the term used for studies in that field. Other applications include local polynomial regression for generalized linear models, robust local regression, and local transformations in a latent variable model. Extensions to partially parametric models are discussed. -- Measurement Error ; Local Polynomial Regression ; Nonlinear Regression ; Bandwidth Selection ; Sandwich Estimation ; Missing Data ; Logistic Regression ; Asymptotic Theory ; Partial Linear Models

     
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    hdl: 10419/66273
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 1997,17
    Umfang: Online-Ressource (PDF-Datei: 29, [4] S., 312,54 KB), graph. Darst.
  10. Large sample theory in a semiparametric partially linear errors-in-variables models
    Autor*in: Liang, Hua; Härdle, Wolfgang; Carroll, Raymond J.
    Erschienen: 1997
    Verlag:  Humboldt-Universität, Berlin

    We consider the partially linear model relating a response Y to predictors (X,T) with mean function XT ß + g (T) when the X's are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswalis (1994) leads to biased... mehr

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    We consider the partially linear model relating a response Y to predictors (X,T) with mean function XT ß + g (T) when the X's are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswalis (1994) leads to biased estimates of both the parameter ß and the function g(·) when measurement error is ignored. We derive a simple modification of their estimator which is a semiparametric version of the usual parametric correction for attenuation. The resulting estimator of ß is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich-type ideas are also developed. -- Measurement Error ; Errors-in-Variables ; Functional Relations ; Non-parametric Likelihood ; Orthogonal Regression ; Partially Linear Model ; Semiparametric Models ; Structural Relations

     
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    hdl: 10419/66252
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 1997,27
    Umfang: Online-Ressource (PDF-Datei: 16 S., 227,05 KB), graph. Darst.