169
Views
123
CrossRef citations to date
0
Altmetric
Original Articles

Unbiased estimation of a nonlinear function a normal mean with application to measurement err oorf models

Pages 4335-4358 | Received 01 Oct 1988, Published online: 27 Jun 2007

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (18)

Jia-Ren Tsai & Pen-Hwang Liau. (2023) Effect of measurement error size in linear heteroscedastic measurement error models. Communications in Statistics - Simulation and Computation 52:10, pages 5052-5081.
Read now
Wenhui Liu, Zhonghua Li & Zhaojun Wang. (2023) Remedial approaches to decrease the effect of measurement errors on polynomial profile monitoring. Communications in Statistics - Simulation and Computation 0:0, pages 1-15.
Read now
Yunfeng Zhao & Jing Guan. (2023) A new robust parameter estimation approach for multinomial categorical response data with outliers and mismeasured covariates. Communications in Statistics - Theory and Methods 52:17, pages 6179-6206.
Read now
Huijuan Ma, Limin Peng & Haoda Fu. (2019) Quantile regression modeling of latent trajectory features with longitudinal data. Journal of Applied Statistics 46:16, pages 2884-2904.
Read now
Nur Aainaa Rozliman, Adriana Irawati Nur Ibrahim & Rossita Muhamad Yunus. (2018) Bayesian approach to errors-in-variables in count data regression models with departures from normality and overdispersion. Journal of Statistical Computation and Simulation 88:2, pages 203-220.
Read now
Yuanshan Wu, Yanyuan Ma & Guosheng Yin. (2015) Smoothed and Corrected Score Approach to Censored Quantile Regression With Measurement Errors. Journal of the American Statistical Association 110:512, pages 1670-1683.
Read now
Jian Chen, John J. Hanfelt & Yijian Huang. (2015) A Simple Corrected Score for Logistic Regression with Errors-in-Covariates. Communications in Statistics - Theory and Methods 44:10, pages 2024-2036.
Read now
Yu-Jen Cheng & Ciprian M. Crainiceanu. (2009) Cox Models With Smooth Functional Effect of Covariates Measured With Error. Journal of the American Statistical Association 104:487, pages 1144-1154.
Read now
Magne Thoresen & Petter Laake. (2007) A simulation study of statistical tests in logistic measurement error models. Journal of Statistical Computation and Simulation 77:8, pages 683-694.
Read now
David M Zucker. (2005) A Pseudo–Partial Likelihood Method for Semiparametric Survival Regression With Covariate Errors. Journal of the American Statistical Association 100:472, pages 1264-1277.
Read now
S. Baran. (2005) A Consistent Estimator for Linear Models with Dependent Observations. Communications in Statistics - Theory and Methods 33:10, pages 2469-2486.
Read now
Steven J Novick & Leonard A Stefanski. (2002) Corrected Score Estimation via Complex Variable Simulation Extrapolation. Journal of the American Statistical Association 97:458, pages 472-481.
Read now
Yijian Huang & C Y Wang. (2001) Consistent Functional Methods for Logistic Regression With Errors in Covariates. Journal of the American Statistical Association 96:456, pages 1469-1482.
Read now
Yijian Huang & C.Y. Wang. (2000) Cox Regression with Accurate Covariates Unascertainable: A Nonparametric-Correction Approach. Journal of the American Statistical Association 95:452, pages 1209-1219.
Read now
Michal Kulich & D.Y. Lin. (2000) Additive Hazards Regression with Covariate Measurement Error. Journal of the American Statistical Association 95:449, pages 238-248.
Read now
Patricia Gimenez, Heleno Bolfarine & Enrico A. Colosimo. (1999) Estimation in weibull regression model with measurement error. Communications in Statistics - Theory and Methods 28:2, pages 495-510.
Read now
L.A. Stefanski & J.R. Cook. (1995) Simulation-Extrapolation: The Measurement Error Jackknife. Journal of the American Statistical Association 90:432, pages 1247-1256.
Read now

Articles from other publishers (105)

Ching‐Yun Wang, Wen‐Han Hwang & Xiao Song. (2024) Biomarker data with measurement error in medical research: A literature review. WIREs Computational Statistics 16:1.
Crossref
Qingyang Liu & Xianzheng Huang. (2024) Parametric modal regression with error in covariates. Biometrical Journal 66:1.
Crossref
Xiao Song. (2023) A corrected smoothed score approach for semiparametric accelerated failure time model with error‐contaminated covariates. Statistics in Medicine 42:22, pages 4043-4055.
Crossref
Yuan Ye, Zhongchun Liu, Deng Pan & Yuanshan Wu. (2023) Regression analysis of logistic model with latent variables. Statistics in Medicine 42:6, pages 860-877.
Crossref
Xiaomeng Zhang, Xinyu Zhang & Yanyuan Ma. (2021) A model‐averaging treatment of multiple instruments in Poisson models with errors. Canadian Journal of Statistics 51:1, pages 173-198.
Crossref
Fei Jiang, Yeqing Zhou, Jianxuan Liu & Yanyuan Ma. (2023) On high-dimensional Poisson models with measurement error: Hypothesis testing for nonlinear nonconvex optimization. The Annals of Statistics 51:1.
Crossref
Xiaobo Wang, Jiayu Huang, Guosheng Yin, Jian Huang & Yuanshan Wu. (2022) Double bias correction for high-dimensional sparse additive hazards regression with covariate measurement errors. Lifetime Data Analysis 29:1, pages 115-141.
Crossref
Timo B. Brakenhoff, Maarten van Smeden & Daniel L. Oberski. 2023. Clinical Applications of Artificial Intelligence in Real-World Data. Clinical Applications of Artificial Intelligence in Real-World Data 97 108 .
Yuen Tsz Abby Lau & Jun Yan. (2022) Bias analysis of generalized estimating equations under measurement error and practical bias correction. Stat 11:1.
Crossref
Wen-Han Hwang, Jakub Stoklosa & Ching-Yun Wang. (2022) Population Size Estimation Using Zero-Truncated Poisson Regression with Measurement Error. Journal of Agricultural, Biological and Environmental Statistics 27:2, pages 303-320.
Crossref
Eni Musta & Ingrid Van Keilegom. (2021) A simulation-extrapolation approach for the mixture cure model with mismeasured covariates. Electronic Journal of Statistics 15:2.
Crossref
Fevi Novkaniza, Khairil Anwar Notodiputro, I Wayan Mangku & Kusman Sadik. (2021) Density Estimation of Neonatal Mortality Rate Using Empirical Bayes Deconvolution in Central Java Province, Indonesia. Procedia Computer Science 179, pages 361-367.
Crossref
Dylan Spicker & Michael P. Wallace. (2020) Measurement error and precision medicine: Error‐prone tailoring covariates in dynamic treatment regimes. Statistics in Medicine 39:26, pages 3732-3755.
Crossref
Firouzeh Noghrehchi, Jakub Stoklosa & Spiridon Penev. (2020) Multiple imputation and functional methods in the presence of measurement error and missingness in explanatory variables. Computational Statistics 35:3, pages 1291-1317.
Crossref
Min-Jue Zhang & Rong-Xian Yue. (2019) Locally D-optimal designs for heteroscedastic polynomial measurement error models. Metrika 83:6, pages 643-656.
Crossref
Maarten van Smeden, Timothy L Lash & Rolf H H Groenwold. (2020) Reflection on modern methods: five myths about measurement error in epidemiological research. International Journal of Epidemiology 49:1, pages 338-347.
Crossref
Heleno Bolfarine, Mário de Castro & Manuel GaleaHeleno Bolfarine, Mário de Castro & Manuel Galea. 2020. Regression Models for the Comparison of Measurement Methods. Regression Models for the Comparison of Measurement Methods 5 15 .
Chi-Lun Cheng, Jia-Ren Tsai & Hans Schneeweiss. (2018) Polynomial regression with heteroscedastic measurement errors in both axes: Estimation and hypothesis testing. Statistical Methods in Medical Research 28:9, pages 2681-2696.
Crossref
Wen‐Han Hwang, Dean Heinze & Jakub Stoklosa. (2019) A weighted partial likelihood approach for zero‐truncated models. Biometrical Journal 61:4, pages 1073-1087.
Crossref
Di Shu & Grace Y. Yi. (2019) Weighted causal inference methods with mismeasured covariates and misclassified outcomes. Statistics in Medicine 38:10, pages 1835-1854.
Crossref
Oksana Chernova & Alexander Kukush. (2018) Confidence regions in Cox proportional hazards model with measurement errors and unbounded parameter set. Modern Stochastics: Theory and Applications 5:1, pages 37-52.
Crossref
Stefanie Muff, Manuela Ott, Julia Braun & Leonhard Held. (2017) Bayesian two-component measurement error modelling for survival analysis using INLA—A case study on cardiovascular disease mortality in Switzerland. Computational Statistics & Data Analysis 113, pages 177-193.
Crossref
Jun Zhang, Zhenghui Feng, Peirong Xu & Hua Liang. (2015) Generalized varying coefficient partially linear measurement errors models. Annals of the Institute of Statistical Mathematics 69:1, pages 97-120.
Crossref
Nur Aainaa Rozliman, Adriana Irawati Nur Ibrahim & Rossita Mohammad Yunus. Bayesian approach to errors-in-variables in regression models. Bayesian approach to errors-in-variables in regression models.
Grace Y. YiGrace Y. Yi. 2017. Statistical Analysis with Measurement Error or Misclassification. Statistical Analysis with Measurement Error or Misclassification 193 256 .
Grace Y. YiGrace Y. Yi. 2017. Statistical Analysis with Measurement Error or Misclassification. Statistical Analysis with Measurement Error or Misclassification 87 150 .
Jakub Stoklosa, Yih-Huei Huang, Elise Furlan & Wen-Han Hwang. (2016) On quadratic logistic regression models when predictor variables are subject to measurement error. Computational Statistics & Data Analysis 95, pages 109-121.
Crossref
Yingsi Yang & Man Yu Wong. (2015) Tests for detecting overdispersion in models with measurement error in covariates. Statistics in Medicine 34:27, pages 3563-3576.
Crossref
Stefanie Muff & Lukas F. Keller. (2015) Reverse attenuation in interaction terms due to covariate measurement error. Biometrical Journal 57:6, pages 1068-1083.
Crossref
Chung-Wei Shen & Yi-Hau Chen. (2015) Model selection for marginal regression analysis of longitudinal data with missing observations and covariate measurement error. Biostatistics 16:4, pages 740-753.
Crossref
Ming Zhu & Yijian Huang. (2015) Trend-constrained corrected score for proportional hazards model with covariate measurement error. Contemporary Clinical Trials Communications 1, pages 5-16.
Crossref
YiPing Yang, GaoRong Li & TieJun Tong. (2015) Corrected empirical likelihood for a class of generalized linear measurement error models. Science China Mathematics 58:7, pages 1523-1536.
Crossref
Alicia L. Carriquiry. 2015. International Encyclopedia of the Social & Behavioral Sciences. International Encyclopedia of the Social & Behavioral Sciences 850 855 .
Raymond J. Carroll. 2014. Wiley StatsRef: Statistics Reference Online. Wiley StatsRef: Statistics Reference Online.
Aurore Delaigle. (2014) Nonparametric Kernel Methods with Errors‐in‐Variables: Constructing Estimators, Computing them, and Avoiding Common Mistakes. Australian & New Zealand Journal of Statistics 56:2, pages 105-124.
Crossref
Patricia Giménez & María Laura Patat. (2012) Local influence for functional comparative calibration models with replicated data. Statistical Papers 55:2, pages 431-454.
Crossref
Babak Babadi, Abdolrahman Rasekh, Ali Akbar Rasekhi, Karim Zare & Mohammad Reza Zadkarami. (2014) A Variance Shift Model for Detection of Outliers in the Linear Measurement Error Model. Abstract and Applied Analysis 2014, pages 1-9.
Crossref
Sergiy Shklyar. 2014. Modern Stochastics and Applications. Modern Stochastics and Applications 337 349 .
Jeffrey S. Buzas, Leonard A. Stefanski & Tor D. Tosteson. 2014. Handbook of Epidemiology. Handbook of Epidemiology 1241 1282 .
Laine Thomas, Leonard A. Stefanski & Marie Davidian. (2013) Moment adjusted imputation for multivariate measurement error data with applications to logistic regression. Computational Statistics & Data Analysis 67, pages 15-24.
Crossref
Jia‐Ren Tsai & Chen‐Tuo Liao. (2013) Method comparison on estimation for an unknown specimen in a heteroscedastic controlled calibration model. Journal of Chemometrics 27:7-8, pages 207-216.
Crossref
David M. Zucker, Malka Gorfine, Yi Li, Mahlet G. Tadesse & Donna Spiegelman. (2013) A Regularization Corrected Score Method for Nonlinear Regression Models with Covariate Error. Biometrics 69:1, pages 80-90.
Crossref
Patricia Giménez & Manuel Galea. (2013) Influence measures on corrected score estimators in functional heteroscedastic measurement error models. Journal of Multivariate Analysis 114, pages 1-15.
Crossref
Grace Y. Yi & Jerald F. Lawless. (2012) Likelihood‐based and marginal inference methods for recurrent event data with covariate measurement error. Canadian Journal of Statistics 40:3, pages 530-549.
Crossref
H. J. Wang, L. A. Stefanski & Z. Zhu. (2012) Corrected-loss estimation for quantile regression with covariate measurement errors. Biometrika 99:2, pages 405-421.
Crossref
Xiao-bing Zhao & Xian Zhou. (2012) Measurement error in proportional hazards models for survival data with long-term survivors. Acta Mathematicae Applicatae Sinica, English Series 28:2, pages 275-288.
Crossref
Grace Y. Yi, Yanyuan Ma & Raymond J. Carroll. (2012) A functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error. Biometrika 99:1, pages 151-165.
Crossref
Yueqin Wu & Minggao Gu. (2012) Bias corrected estimation for generalized probit regression with covariate measurement error and censored responses. Journal of Statistical Planning and Inference 142:1, pages 221-231.
Crossref
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 411 417 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 383 410 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 305 360 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 263 304 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 183 261 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 89 182 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 81 88 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 527 569 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 493 525 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 477 491 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 461 475 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 419 441 .
Erik Grafarend & Joseph AwangeErik W. Grafarend & Joseph L. Awange. 2012. Linear and Nonlinear Models. Linear and Nonlinear Models 1 80 .
Yih-Huei Huang, Wen-Han Hwang & Fei-Yin Chen. (2011) Differential Measurement Errors in Zero-Truncated Regression Models for Count Data. Biometrics 67:4, pages 1471-1480.
Crossref
Laine Thomas, Leonard Stefanski & Marie Davidian. (2011) A Moment-Adjusted Imputation Method for Measurement Error Models. Biometrics 67:4, pages 1461-1470.
Crossref
Julie McIntyre & Leonard A. Stefanski. (2009) Density Estimation with Replicate Heteroscedastic Measurements. Annals of the Institute of Statistical Mathematics 63:1, pages 81-99.
Crossref
Qi Long, W. Dana Flanders, Veronika Fedirko & Roberd M. Bostick. (2009) Robust statistical methods for analysis of biomarkers measured with batch/experiment‐specific errors. Statistics in Medicine 29:3, pages 361-370.
Crossref
Jeffrey S. Buzas. (2009) A note on corrected scores for logistic regression. Statistics & Probability Letters 79:22, pages 2351-2358.
Crossref
Alexander Kukush, Andrii Malenko & Hans Schneeweiss. (2009) Optimality of the quasi-score estimator in a mean–variance model with applications to measurement error models. Journal of Statistical Planning and Inference 139:10, pages 3461-3472.
Crossref
Marie-Laure Martin-Magniette & Marie-Luce Taupin. (2009) Estimation of the hazard function in a semiparametric model with covariate measurement error. ESAIM: Probability and Statistics 13, pages 87-114.
Crossref
Annamaria Guolo. (2008) Robust techniques for measurement error correction: a review. Statistical Methods in Medical Research 17:6, pages 555-580.
Crossref
Xiao Song & C. Y. Wang. (2008) Semiparametric Approaches for Joint Modeling of Longitudinal and Survival Data with Time‐Varying Coefficients. Biometrics 64:2, pages 557-566.
Crossref
David M. Zucker & Donna Spiegelman. (2008) Corrected score estimation in the proportional hazards model with misclassified discrete covariates. Statistics in Medicine 27:11, pages 1911-1933.
Crossref
Shalabh & Christian HeumannHans Schneeweiss. 2008. Recent Advances in Linear Models and Related Areas. Recent Advances in Linear Models and Related Areas 45 58 .
Shalabh & Christian HeumannThomas Augustin, Angela Döring & David Rummel. 2008. Recent Advances in Linear Models and Related Areas. Recent Advances in Linear Models and Related Areas 253 278 .
Arturo A. Z. Zavala, Heleno Bolfarine & Mário de Castro. (2006) Consistent estimation and testing in heteroscedastic polynomial errors-in-variables models. Annals of the Institute of Statistical Mathematics 59:3, pages 515-530.
Crossref
Sergiy Shklyar, Hans Schneeweiss & Alexander Kukush. (2006) Quasi Score is more Efficient than Corrected Score in a Polynomial Measurement Error Model. Metrika 65:3, pages 275-295.
Crossref
Hans Schneeweiss & Thomas Augustin. (2006) Some recent advances in measurement error models and methods. Allgemeines Statistisches Archiv 90:1, pages 183-197.
Crossref
Hans Schneeweiß & Thomas Augustin. 2006. Modern Econometric Analysis. Modern Econometric Analysis 183 198 .
Xiao Song & Yijian Huang. (2005) On Corrected Score Approach for Proportional Hazards Model with Covariate Measurement Error. Biometrics 61:3, pages 702-714.
Crossref
S. Shklyar & H. Schneeweiss. (2005) A comparison of asymptotic covariance matrices of three consistent estimators in the Poisson regression model with measurement errors. Journal of Multivariate Analysis 94:2, pages 250-270.
Crossref
Raymond J. Carroll. 2005. Encyclopedia of Biostatistics. Encyclopedia of Biostatistics.
Patricia Giménez & María Laura Patat. (2005) Estimation in comparative calibration models with replicate measurement. Statistics & Probability Letters 71:2, pages 155-164.
Crossref
Alexander Kukush, Hans Schneeweiss & Roland Wolf. (2005) Relative efficiency of three estimators in a polynomial regression with measurement errors. Journal of Statistical Planning and Inference 127:1-2, pages 179-203.
Crossref
Jeffrey S. Buzas, Leonard A. Stefanski & Tor D. Tosteson. 2005. Handbook of Epidemiology. Handbook of Epidemiology 729 765 .
Alexander Kukush, Hans Schneeweis & Roland Wolf. (2004) Three estimators for the poisson regression model with measurement errors. Statistical Papers 45:3, pages 351-368.
Crossref
Thomas Augustin. (2004) An Exact Corrected Log‐Likelihood Function for Cox's Proportional Hazards Model under Measurement Error and Some Extensions. Scandinavian Journal of Statistics 31:1, pages 43-50.
Crossref
Tong Li & Cheng Hsiao. (2004) Robust estimation of generalized linear models with measurement errors. Journal of Econometrics 118:1-2, pages 51-65.
Crossref
Jouni Kuha & Jonathan Temple. (2007) Covariate Measurement Error in Quadratic Regression. International Statistical Review 71:1, pages 131-150.
Crossref
Huai-Zhen Qin & Shi-Yong Feng. (2003) Deconvolution kernel estimator for mean transformation with ordinary smooth error. Statistics & Probability Letters 61:4, pages 337-346.
Crossref
CHENGCHENG HU & D. Y. LIN. (2002) Cox Regression with Covariate Measurement Error. Scandinavian Journal of Statistics 29:4, pages 637-655.
Crossref
Jie Q. Guo & Tong Li. (2002) Poisson regression models with errors-in-variables: implication and treatment. Journal of Statistical Planning and Inference 104:2, pages 391-401.
Crossref
Chi-Lun Cheng & Hans Schneeweiss. 2002. Total Least Squares and Errors-in-Variables Modeling. Total Least Squares and Errors-in-Variables Modeling 131 143 .
Y. H. Steve Huang & Longcheen Huwang. (2008) On the polynomial structural relationship. Canadian Journal of Statistics 29:3, pages 495-512.
Crossref
S. Baran. (2001) A new consistent estimator for linear errors-in-variables models. Computers & Mathematics with Applications 41:7-8, pages 821-833.
Crossref
A.L. Carriquiry. 2001. International Encyclopedia of the Social & Behavioral Sciences. International Encyclopedia of the Social & Behavioral Sciences 9435 9442 .
Patricia Gimenez & Heleno Bolfarine. (2000) Comparing consistent estimators in comparative calibration models. Journal of Statistical Planning and Inference 86:1, pages 143-155.
Crossref
W R Gould, L A Stefanski & K H Pollock. (1999) Use of simulation–extrapolation estimation in catch–effort analyses. Canadian Journal of Fisheries and Aquatic Sciences 56:7, pages 1234-1240.
Crossref
I. Fazekas & A. G. Kukush. (1998) Asymptotic properties of estimators in nonlinear functional errors-in-variables with dependent error terms. Journal of Mathematical Sciences 92:3, pages 3890-3895.
Crossref
Jeffrey S. Buzas. (1998) Unbiased scores in proportional hazards regression with covariate measurement error. Journal of Statistical Planning and Inference 67:2, pages 247-257.
Crossref
Kouhei Akazawa, Naoko Kinukawa & Tsuyoshi Nakamura. (1998) A NOTE ON THE CORRECTED SCORE FUNCTION ADJUSTING FOR MISCLASSIFICATION. JOURNAL OF THE JAPAN STATISTICAL SOCIETY 28:1, pages 115-123.
Crossref
I. Fazekas & A.G. Kukush. (1997) Asymptotic properties of an estimator in nonlinear functional errors-in-variables models with dependent error terms. Computers & Mathematics with Applications 34:10, pages 23-39.
Crossref
R.B. Arellano‐Valle, H. Bolfarine & F. Vilca‐Labra. (2008) Ultrastructural elliptical models. Canadian Journal of Statistics 24:2, pages 207-216.
Crossref
J.S. Buzas & L.A. Stefanski. (1996) A note on corrected-score estimation. Statistics & Probability Letters 28:1, pages 1-8.
Crossref
Myung-Sang Moon & Richard F. Gunst. (1995) Polynomial measurement error modeling. Computational Statistics & Data Analysis 19:1, pages 1-21.
Crossref
Tsuyoshi Nakamura & Kouhei Akazawa. (1994) Computer program for the proportional hazards measurement error model. Computer Methods and Programs in Biomedicine 45:3, pages 203-212.
Crossref
Tsuyoshi Nakamura & Kouhei Akazawa. (1992) Covariate Measurement Errors in Censored Survival Data.. Japanese Journal of Biometrics 13:2, pages 47-63.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.