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Ponnet J, Segaert P, Van Aelst S, Verdonck T. Robust Inference and Modeling of Mean and Dispersion for Generalized Linear Models. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2022.2140054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/31/2022]
Affiliation(s)
- Jolien Ponnet
- KU Leuven, Department of Mathematics, Celestijnenlaan 200B, 3001 Leuven, Belgium
| | - Pieter Segaert
- KU Leuven, Department of Mathematics, Celestijnenlaan 200B, 3001 Leuven, Belgium
| | - Stefan Van Aelst
- KU Leuven, Department of Mathematics, Celestijnenlaan 200B, 3001 Leuven, Belgium
| | - Tim Verdonck
- KU Leuven, Department of Mathematics, Celestijnenlaan 200B, 3001 Leuven, Belgium
- UAntwerp, Department of Mathematics, Middelheimlaan 1, 2020 Antwerp, Belgium
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2
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Robust MAVE for single-index varying-coefficient models. J Korean Stat Soc 2022. [DOI: 10.1007/s42952-022-00187-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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3
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Gai Y, Zhu X, Zhang J. Testing symmetry of model errors for nonparametric regression models by using correlation coefficient 1. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2019.1670844] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Yujie Gai
- School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China
| | - Xuehu Zhu
- School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China
| | - Jun Zhang
- College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen-Hong Kong Joint Research Center for Applied Statistical Sciences, Shenzhen University, Shenzhen, China
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4
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Mo W, Liu Y. Efficient learning of optimal individualized treatment rules for heteroscedastic or misspecified treatment‐free effect models. J R Stat Soc Series B Stat Methodol 2021. [DOI: 10.1111/rssb.12474] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Weibin Mo
- Department of Statistics and Operations Research University of North Carolina at Chapel Hill Chapel Hill North Carolina USA
| | - Yufeng Liu
- Department of Statistics and Operations Research Department of Genetics Department of Biostatistics Carolina Center for Genome Sciences Lineberger Comprehensive Cancer Center University of North Carolina at Chapel Hill Chapel Hill North Carolina USA
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5
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du Roy de Chaumaray M, Marbac M, Patilea V. Wilks’ theorem for semiparametric regressions with weakly dependent data. Ann Stat 2021. [DOI: 10.1214/21-aos2081] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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6
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Jiang J, Lin H, Zhong Q, Li Y. Analysis of multivariate non-gaussian functional data: A semiparametric latent process approach. J MULTIVARIATE ANAL 2021. [DOI: 10.1016/j.jmva.2021.104888] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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7
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Gai Y, Zhang J. Single-index relative error regression models. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2021.1982972] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Yujie Gai
- School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China
| | - Jun Zhang
- College of Mathematics and Statistics, Shenzhen University, Shenzhen, China
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Affiliation(s)
- Sen Na
- Department of Statistics, University of Chicago, Chicago, U.S.A
| | - Mladen Kolar
- Booth School of Business, University of Chicago, Chicago, U.S.A
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9
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Zhang J. Model checking for multiplicative linear regression models with mixed estimators. STAT NEERL 2021. [DOI: 10.1111/stan.12239] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jun Zhang
- College of Mathematics and Statistics Shenzhen University Shenzhen China
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Zhang J, Feng S, Gai Y. Partial index additive models with additive distortion measurement errors. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2020.1757712] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Jun Zhang
- College of Mathematics and Statistics, Shenzhen University, Shenzhen, China
| | - Sanying Feng
- School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
| | - Yujie Gai
- School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China
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Gai Y, Zhang J. Detection of the symmetry of model errors for partial linear single-index models. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2020.1752381] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Yujie Gai
- School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China
| | - Jun Zhang
- College of Mathematics and Statistics, Shenzhen University, Shenzhen, China
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12
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Estimation and variable selection for partial linear single-index distortion measurement errors models. Stat Pap (Berl) 2019. [DOI: 10.1007/s00362-019-01119-6] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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13
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Zhang J, Gai Y, Lin B, Zhu X. Nonlinear regression models with single‐index heteroscedasticity. STAT NEERL 2019. [DOI: 10.1111/stan.12170] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jun Zhang
- College of Mathematics and Statistics, Institute of Statistical SciencesShenzhen University Shenzhen China
| | - Yujie Gai
- School of Statistics and MathematicsCentral University of Finance and Economics Beijing China
| | - Bingqing Lin
- College of Mathematics and Statistics, Institute of Statistical SciencesShenzhen University Shenzhen China
| | - Xuehu Zhu
- School of Mathematics and StatisticsXi'an Jiaotong University Xi'an China
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14
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Zhang J, Gai Y, Lin B. Detection of marginal heteroscedasticity for partial linear single-index models. COMMUN STAT-SIMUL C 2019. [DOI: 10.1080/03610918.2019.1565585] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Jun Zhang
- College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen University, Shenzhen, China
| | - Yujie Gai
- School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China
- Department of Biostatistics School of Public Health, University of Texas at Houston, Houston, TX, USA
| | - Bingqing Lin
- College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen University, Shenzhen, China
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Zhang J, Niu C, Lu T, Wei Z. Estimation of the error distribution function for partial linear single-index models. COMMUN STAT-SIMUL C 2018. [DOI: 10.1080/03610918.2018.1468461] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Jun Zhang
- College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen University, Shenzhen, China
| | - Cuizhen Niu
- School of Statistics, Beijing Normal University, Beijing, China
| | - Tao Lu
- Department of Mathematics and Statistics, University of Nevada, Reno, NV, USA
| | - Zhenghong Wei
- College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen University, Shenzhen, China
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Liang L, Carroll R, Ma Y. Dimension reduction and estimation in the secondary analysis of case-control studies. Electron J Stat 2018; 12:1782-1821. [PMID: 30100949 PMCID: PMC6086603 DOI: 10.1214/18-ejs1446] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
Studying the relationship between covariates based on retrospective data is the main purpose of secondary analysis, an area of increasing interest. We examine the secondary analysis problem when multiple covariates are available, while only a regression mean model is specified. Despite the completely parametric modeling of the regression mean function, the case-control nature of the data requires special treatment and semi-parametric efficient estimation generates various nonparametric estimation problems with multivariate covariates. We devise a dimension reduction approach that fits with the specified primary and secondary models in the original problem setting, and use reweighting to adjust for the case-control nature of the data, even when the disease rate in the source population is unknown. The resulting estimator is both locally efficient and robust against the misspecification of the regression error distribution, which can be heteroscedastic as well as non-Gaussian. We demonstrate the advantage of our method over several existing methods, both analytically and numerically.
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Affiliation(s)
- Liang Liang
- Department of Biostatistics, Harvard University, Boston, MA 02115, USA,
| | - Raymond Carroll
- Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843, USA, and School of Mathematical and, Physical Sciences, University of Technology Sydney, PO Box 123 Broadway NSW 2007, Australia,
| | - Yanyuan Ma
- Department of Statistics, Penn State University, University Park, PA 16802, USA,
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19
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Hu Q, Lin L. Conditional feature screening for mean and variance functions in models with multiple-index structure. METRIKA 2018. [DOI: 10.1007/s00184-018-0646-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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20
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Gijbels I, Ibrahim MA, Verhasselt A. Testing the heteroscedastic error structure in quantile varying coefficient models. CAN J STAT 2017. [DOI: 10.1002/cjs.11346] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Irène Gijbels
- Department of Mathematics and Leuven Statistics Research Center (LStat); KU Leuven Belgium
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22
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Fang Y, Lian H, Liang H. A generalized partially linear framework for variance functions. ANN I STAT MATH 2017. [DOI: 10.1007/s10463-017-0619-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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23
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Fang Y, Lian H, Liang H, Ruppert D. Variance function additive partial linear models. Electron J Stat 2015. [DOI: 10.1214/15-ejs1080] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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