Denote the **estimated variance** function by g̃. L. L., Speed T. This is equivalent to fitting a locally constant regression model to the reduced data {(Ȳi,·, Si)} (Huang & Pan, 2002). http://edvinfo.com/measurement-error/measurement-bias-example.html

J., Dudoit S., Gong E. The bias decreases quickly as m increases and is relatively small even when m = 9. National Library of Medicine 8600 Rockville Pike, Bethesda MD, 20894 USA Policies and Guidelines | Contact We use cookies to enhance your experience on our website. Available at http://www.pstat.ucsb.edu/faculty/yuedong.Weng L, Dai H, Zhan Y, He Y, Stepaniants SB, Bassett DE. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2670068/

Consider a kernel estimator for Step 2 in the permutation SIMEX method. Statist. A Bayesian framework for the analysis of microarray expression data: regularized t-test and statistical inferences of gene changes. The performance of both the SIMEX methods depends on approximations to the exact extrapolants.

Based on our experience, a linear function was used as the extrapolant.Define the integrated mean squared error as IMSE = ∫ E{ĝ (x)−g(x)}2fX(x)dx, where fX is the density function of X. Assoc. **1995;89:1314-28. **We note that, rather than offering formal conclusions, the fits here serve the purpose of illustration only.Fig. 3Tumour study. J., Churchill G.

Local estimating equations; p. 214-27. IntroductionMicroarray experiments quantify expression levels on a global scale by measuring transcript abundance of thousands of genes simultaneously (Nguyen et al., 2002; Leung & Cavalieri, 2003). Acad. http://biomet.oxfordjournals.org/content/95/2/437.refs Biostatistics. 2005;6:59–75. [PubMed]Devanarayan V, Stefanski LA.

Search this journal: Advanced » Current Issue September 2016 103 (3) Alert me to new issues The Journal About this journal Rights & Permissions Dispatch date of the next issue We Genet. Statist. Improved statistical tests for differential gene expression by shrinking variance components estimates.

Lin Y., Nadler S. Your cache administrator is webmaster. CrossRefMedlineGoogle Scholar Jain N., Thatte J., Braciale T., Ley K., O'Connell M., Lee J. L., editors.

pp. 291–312.Lönnstedt I, Speed T. http://edvinfo.com/measurement-error/classical-measurement-error.html J. New York: Cambridge University Press; 2003. Figure 1 shows the true function, observations and the naive estimator ĝN.

Statist. Nonparametric regression in the presence of measurement error. Obviously the measurement error makes observations more widely spread and thus causes attenuation in the naive estimator ĝN. http://edvinfo.com/measurement-error/measurement-error-definition.html Local estimating equation.

Some key wordsKey words Heteroscedasticity Local polynomial regression Measurement error Microarray Nonparametric regression Permutation simex Simulation-extrapolation Variance function estimation References Alon U., Barkai N., Notterman D., Gish K., Ybarra S., Mack Biometrika. 1999;86:541–54.Carroll RJ, Ruppert D, Welsh AH. When both n and m are large, the values of MSE for the permutation SIMEX method is dominated by bias caused by the approximate extrapolant function.

The system returned: (22) Invalid argument The remote host or network may be down. Denote the resulting estimator by ĝS(·, ζ).Step 3 Extrapolate ĝS(·, ζ) back to ζ = −1.We call the above method ‘direct SIMEX’. Google Scholar Smyth G. In fact, the following result shows that ĝN is usually not consistent.Fig. 1Plots of (a) sample variances vs true Xi, (b) sample variances vs sample means Ȳi,., (c) true variance function,

Broad patterns of gene expression revealed by clustering of tumour and normal colon tissues probed by oligonucleotide arrays. R., Bittner M. For all simulations, we set B = 50 and repeated the simulations 500 times.We used the estimating function (5) with λ = 1/2. check my blog The dpill function for selecting a data-driven bandwidth sometimes failed, and we therefore fixed the bandwidth at 0.25.

Abstract/FREE Full Text Baldi P., Long A. We now describe permutation SIMEX for nonparametric estimation of the variance function.Step 1 For j = 1, ···, m,generate Zb,i,k ~ N(0, 1) independently, i = 1, ···, n, k = TRENDS Genet. 2003;11:649–59. [PubMed]Lin Y, Nadler ST, Attie AD, Yandell BS. Biostatistics 2005;6:59-75.

Biometrics 2002;58:701-17. Since it is based on a relatively large number of replications, the fit with the full data can be treated as a benchmark. Empirical simulation extrapolation for measurement error models with replicate measurements. When measurement error is ignoredFor ease of exposition, in this section we consider locally constant regression estimation only.

Email: [email protected] U, Barkai N, Notterman D, Gish K, Ybarra S, Mack D, Levine AJ. The direct SIMEX method reduces both bias and variance in the naive estimator for all situations. Empirical simulation extrapolation for measurement error models with replicate measurements. We used a locally linear regression estimator with estimating function (5), λ = 1/2, and bandwidth h = 0.8.

The system returned: (22) Invalid argument The remote host or network may be down. Replicated microarray data. Appl. BMC Biotechnol. 2001;1:1–8. [PMC free article] [PubMed]Leung Y, Cavalieri D.