The effects of error magnitude and bandwidth selection for deconvolution with unknown error distribution

References

• Carroll , R. J. and Hall , P. 1988 . Optimal Rates of Convergence for Deconvolving a Density . Journal of the American Statistical Associations , 83 : 1184 – 1186 .
   Web of Science ®Google Scholar
• Comte , F. 2004 . Kernel Deconvolution of Stochastic Volatility Models . Journal of Time Series Analysis , 25 : 563 – 582 .
   Web of Science ®Google Scholar
• Comte , F. and Lacour , C. 2011 . Data-driven Density Estimation in the Presence of Additive Noise with Unknown Distribution . Journal of the Royal Statistical Society Series B-Statistical Methodology , 73 : 601 – 627 .
   Web of Science ®Google Scholar
• Delaigle , A. 2008 . An Alternative View of the Deconvolution Problem . Statistica Sinica , 18 : 1025 – 1045 .
   Web of Science ®Google Scholar
• Delaigle , A. and Gijbels , I. 2004 . Practical Bandwidth Selection in Deconvolution Kernel Density Estimation . Computational Statistics and Data Analysis , 45 : 249 – 267 .
   Web of Science ®Google Scholar
• Delaigle , A. and Hall , P. 2008 . Using SIMEX for Smoothing-parameter Choice in Errors-in-variables Problems . Journal of the American Statistical Association , 103 : 280 – 287 .
   Web of Science ®Google Scholar
• Delaigle , A. and Meister , A. 2008 . Density Estimation with Heteroscedastic Error . Bernoulli , 14 : 562 – 579 .
   Web of Science ®Google Scholar
• Delaigle , A. , Hall , P. and Meister , A. 2008 . On Deconvolution with Repeated Measurements . Annals of Statistics , 36 : 665 – 685 .
   Web of Science ®Google Scholar
• Dunning , M. J. , Barbosa-Morais , N. L. , Lynch , A. G. , Tavare , S. and Ritchie , M. E. 2008 . Statistical Issues in the Analysis of Illumina Data . BMC Bioinformatics , 9, 85 : 1 – 15 . http://www.biomedcentral.com/content/pdf/1471-2105-9-85.pdf
   Google Scholar
• Fan , J. 1991a . Global Behavior of Deconvolution Kernel Estimates . Statistica Sinica , 1 : 541 – 551 .
   Web of Science ®Google Scholar
• Fan , J. 1991b . On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems . Annals of Statistics , 19 : 1257 – 1272 .
   Web of Science ®Google Scholar
• Fan , J. 1992 . Deconvolution with Supersmooth Distributions . The Canadian Journal of Statistics , 20 : 155 – 169 .
   Web of Science ®Google Scholar
• Hall , P. and Lahiri , S. N. 2008 . Estimation of Distributions, Moments and Quantiles in Deconvolution Problems . Annals of Statistics , 36 : 2110 – 2134 .
   Web of Science ®Google Scholar
• Hall , P. and Qiu , P. 2007a . Nonparametric Estimation of a Point-Spread Function in multivariate Problems . Annals of Statistics , 35 : 1512 – 1534 .
   Web of Science ®Google Scholar
• Hall , P. and Qiu , P. 2007b . Blind Deconvolution and Deblurring in Image Analysis . Statistica Sinica , 17 : 1483 – 1509 .
   Web of Science ®Google Scholar
• Hesse , C. 1999 . Data-Driven Deconvolution . Journal of Nonparametric Statistics , 10 : 343 – 373 .
   Web of Science ®Google Scholar
• Irizarry , R. , Hobbs , B. , Collin , F. , Beazer-Barclay , Y. , Antonellis , K. , Scherf , U. and Speed , T. 2003 . Exploration, Normalization, and Summaries of High Density Oligonucleotide Array Probe Level Data . Biostatistics , 4 : 249 – 264 .
   PubMed Web of Science ®Google Scholar
• Johannes , J. 2009 . Deconvolution with Unknown Error Distribution . Annals of Statistics , 37 : 2301 – 2323 .
   Web of Science ®Google Scholar
• Meister , A. 2009 . Deconvolution Problems in Nonparametric Statistics , Lecture Notes in Statistics New York : Springer .
   Google Scholar
• Neumann , M. H. 1997 . On the Effect of Estimating the Error Density in Nonparametric Deconvolution . Journal of Nonparametric Statistics , 7 : 307 – 330 .
   Google Scholar
• Port , S. C. 1994 . Theoretical Probability for Applications , Lecture Notes in Statistics New York : Wiley .
   Google Scholar
• Qiu , P. 2008 . A Nonparametric Procedure for Blind Image Deblurring . Computational Statistics & Data Analysis , 52 : 4828 – 4841 .
   Web of Science ®Google Scholar
• Qiu , P. and Sun , J. 2007 . Local Smoothing Image Segmentation for Spotted Microarray Images . Journal of the American Statistical Association , 102 : 1129 – 1144 .
   Web of Science ®Google Scholar
• Silver , J. D. , Ritchie , M. E. and Smyth , G. K. 2009 . Microarray Background Correction: Maximum Likelihood Estimation for the Normal–exponential Convolution . Biostatistics , 10 : 352 – 363 .
   PubMed Web of Science ®Google Scholar
• Stefanski , L. A. and Carroll , R. J. 1990 . Deconvoluting Kernel Density Estimators . Statistics , 21 : 169 – 184 .
   Google Scholar
• Stefanski , L. A. and Cook , J. R. 1995 . Simulation Extrapolation: The Measurement Error Jackknife . Journal of the American Statistical Association , 90 : 1247 – 1256 .
   Web of Science ®Google Scholar
• Stone , C. J. 1982 . Optimal Global Rates of Convergence for Nonparametric Regression . Annals of Statistics , 10 : 1040 – 1053 .
   Web of Science ®Google Scholar
• Van Es , B. , Spreij , P. and Van Zanten , H. 2003 . Nonparametric Volatility Density Estimation . Bernoulli , 9 : 451 – 465 .
   Web of Science ®Google Scholar
• Wang , X. F. and Wang , B. 2011 . Deconvolution Estimation in Measurement Error Models: The R Package decon . Journal of Statistical Software , 39 ( 10 ) : 1 – 24 .
   PubMed Web of Science ®Google Scholar
• Wang , X. F. and Ye , D. 2010 . On Nonparametric Comparison of Images and Regression Surfaces . Journal of Statistical Planning and Inference , 140 : 2875 – 2884 .
   PubMed Web of Science ®Google Scholar
• Wang , X. F. , Fan , Z. and Wang , B. 2010 . Estimating Smooth Distribution Function in the Presence of Heteroscedastic Measurement Errors . Computational Statistics and Data Analysis , 54 : 25 – 36 .
   PubMed Web of Science ®Google Scholar
• Wang , B. , Wang , X. F. and Xi , Y. 2011 . Normalizing Bead-based MicroRNA Expression Data: A Measurement Error Model-Based Approach . Bioinformatics , 27 : 1506 – 1512 .
   PubMed Web of Science ®Google Scholar
• Xie , Y. , Wang , X. and Story , M. 2009 . Statistical Methods of Background Correction for Illumina BeadArray Data . Bioinformatics , 25 : 751 – 757 .
   PubMed Web of Science ®Google Scholar
• Zhang , C. H. 1990 . Fourier Methods for Estimating Mixing Densities and Distributions . Annals of Statistics , 18 : 806 – 831 .
   Web of Science ®Google Scholar