estimation of distribution functions in measurement error models Borden Indiana

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estimation of distribution functions in measurement error models Borden, Indiana

Section 2 gives a summary of the DKM that are used in our package. Please try the request again. Carroll, Delaigle, and Hall (2009) discussed the nonparametric prediction in measurement error models when the covariate is measured with heteroscedastic errors. Using SIMEX for Smoothing-Parameter Choice in Errors-in-Variables Problems.

Please enable JavaScript to use all the features on this page. For example, additional “negative control” data are available in Lumina Bead microarray studies. Heteroscedastic contaminationIn many real applications, the distributions of measurement errors could vary with each subject or even with each observation, so the errors are heteroscedastic. Estimation using the fast Fourier transformDeconvolution estimation involves n numerical integrations for each grid where the density is to be estimated, thus directly programming in R is quite slow.

Wang, Fan, and Wang (2010) explored smooth distribution estimators with heteroscedastic error. Kernel Density-Estimation Using the Fast Fourier-Transform. In errors-in-variables problems, we only implement the deconvolution kernel regression estimator, which is a special case of the local polynomial regression estimator with errors-in-variables, proposed by Delaigle, Fan, and Carroll (2009) Applica- tion of the estimator to estimating hypertension prevalence based on real data is also examined.

To verify the galaxy formation theories, one is to estimate the density function from contaminated data that are effective in unveiling the numbers of bumps or components.In econometrics: The stochastic volatility We see that the deconvolution estimators work quite well to recover the functions in both simulated cases. Hence, consideration of heteroscedastic errors is very important. There are two typical choices of the kernel functions for normal errors.

One could think of several examples in which measurement error can be a concern:In medicine: The NHANES-I epidemiological study is a cohort study consisting of thousands of women who were investigated Our method is data-driven in the sense that we use only known information, namely, the error distribution and the data. We also notice that the effect of measurement errors on the distribution function F(x) is relatively small with the pre-specified levels of error variances. The Annals of Statistics. 1990;18:806–830.

View full text Journal of Statistical Planning and InferenceVolume 143, Issue 3, March 2013, Pages 479–493 Estimation of distribution functions in measurement error modelsI. Citing articles (0) This article has not been cited. Click the View full text link to bypass dynamically loaded article content. Your cache administrator is webmaster.

The primary variable of interest in the study is the “long-term” saturated fat intake which was known to be imprecisely measured. The bandwidth is chosen by eye to be as small as possible while retaining smoothness. Please try the request again. Optimal Rates of Convergence for Deconvolving a Density.

Journal of Time Series Analysis. 2004;25(4):563–582.De Blok WJG, McGaugh SS, Rubin VC. Our R functions allow both homoscedastic errors and heteroscedastic errors. The system returned: (22) Invalid argument The remote host or network may be down. Your cache administrator is webmaster.

The difference in the precision of the “FFT” and “Direct” methods is very subtle and negligible. It is reasonable to assume that Velocity is the covariate measured with heteroscedastic normal error, hence we consider the deconvolution method using the estimator in (12). The true regression function is set to m(x) = x2 − 2x. Hence, the resulting deconvoluting kernel with normal error isL1(x)=1π∫01cos(tx)(1−t2)3eσ2t22h2dl.The requirement for this support kernel can be relaxed when the error variance is small in Gaussian deconvolution.

Screen reader users, click here to load entire articleThis page uses JavaScript to progressively load the article content as a user scrolls. One tries to estimate the conditional mean curve m(x)=E(Y∣X=x)=∫yf(x,y)dyfX(x)=r(x)fX(x),(10) where f(x, y) and fX(x) denote the joint density of (X, Y) and the marginal density of X, respectively. Please try the request again. We consider the following kernels in the package.Kernels for normal errors The normal distribution N(0, σ2) is the most commonly-used error distribution in practice.

Journal of the Royal Statistical Society C. 1982;31(1):93–99.Staudenmayer J, Ruppert D, Buonaccorsi J. The spots then become fluorescent, and a microarray scanner is used to “read” the intensities in the microarray. We consider the standard normal kernel function, so the resulting deconvoluting kernel for the case of Laplacian errors isL3(x)=12πe−x22(1+(σh)2(1−x2)).The R functions DeconPdf and DeconCdf in the decon package perform the deconvolution The research of Xiao-Feng Wang is supported in part by the NIH grant UL1 RR024989.Contributor InformationXiao-Feng Wang, Department of Quantitative Health Science/Biostatistics Section, Cleveland Clinic Foundation, 9500 Euclid Ave, Cleveland OH

Canadian Journal of Statistics. 1992;20:155–169.Fan J, Truong YK. Please enable JavaScript to use all the features on this page. Our package numerically evaluates MISE^(h) on a fine grid of h-values, then selects the optimal h that minimizes MISE^(h) on the grid. The framingham data in the package contain four variables, “SBP11”, “SBP12”,“SBP21”, “SBP22”.

The function DeconCPdf allows us to estimate the conditional density function with homoscedastic errors.2.4. A MAC system with a 2.8 GHz Intel Core 2 Duo and 4GB memory was used for the simulation study.Table 1Timings in seconds for calculations of deconvolution density estimators by the