A Note on Regression When There is Extraneous Information About One of the Coefficients
Abstract
(1953). A Note on Regression When There is Extraneous Information About One of the Coefficients. Journal of the American Statistical Association: Vol. 48, No. 264, pp. 799-808.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Eq. (2) can be fitted subject to linear equality restrictions, which would reduce the number of parameters to be estimated.
“First, Eq. (2) can be fitted subject to linear equality restrictions, which would reduce the number of parameters to be estimated [56,57].”
From Syndemics and Health Disparities: A Methodological Note (2016) · cites this paper as [56]
Cites
THE GENERALIZATION OF ‘STUDENT'S’ PROBLEM WHEN SEVERAL DIFFERENT POPULATION VARLANCES ARE INVOLVED
WELCH, B. L. (1947) · Biometrika · doi:10.1093/biomet/34.1-2.28 · Cited by 4,135 · see citing works
IV.—On Least Squares and Linear Combination of Observations
Aitken, A. C. (1936) · Proceedings of the Royal Society of Edinburgh · doi:10.1017/s0370164600014346 · Cited by 954 · see citing works
THE DEMAND FOR FOOD IN THE UNITED KINGDOM BEFORE THE WAR
Stone, R. (1951) · Metroeconomica · doi:10.1111/j.1467-999x.1951.tb00074.x · Cited by 9 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Empirical Strategies in Labor Economics
Angrist, J. D., & Krueger, A. B. (1999) · Handbook of Labor Economics · doi:10.1016/s1573-4463(99)03004-7 · Cited by 1,628 · see citing works
Angrist, J. D., & Krueger, A. B. (1992) · Journal of the American Statistical Association · doi:10.1080/01621459.1992.10475212 · Cited by 463 · see citing works
Angrist, J. D., & Krueger, A. B. (1990) · National Bureau of Economic Research · doi:10.3386/w3571 · Cited by 445 · see citing works
On Pure and Mixed Statistical Estimation in Economics
Theil, H., & Goldberger, A. S. (1992) · Advanced studies in theoretical and applied econometrics · doi:10.1007/978-94-011-2546-8_18 · Cited by 404 · see citing works
Surveys in Applied Economics: Models of Consumer Behaviour
Brown, A. J., & Deaton, A. (1972) · The Economic Journal · doi:10.2307/2231303 · Cited by 347 · see citing works
Inequality Restrictions in Regression Analysis
Judge, G. G., & Takayama, T. (1966) · Journal of the American Statistical Association · doi:10.1080/01621459.1966.10502016 · Cited by 195 · see citing works
Syndemics and Health Disparities: A Methodological Note
Tsai, A. C., & Venkataramani, A. S. (2016) · AIDS and Behavior · doi:10.1007/s10461-015-1260-2 · Cited by 176 · see citing works
On Least Squares with Insufficient Observations
Chipman, J. S. (1964) · Journal of the American Statistical Association · doi:10.1080/01621459.1964.10480751 · Cited by 183 · see citing works
Technology and Scale in Electricity Generation
Dhrymes, P. J., & Kurz, M. (1964) · Econometrica · doi:10.2307/1913038 · Cited by 105 · see citing works
The Market Demand for Durable Goods
Stone, R., & Rowe, D. A. (1957) · Econometrica · doi:10.2307/1907959 · Cited by 92 · see citing works
Maximum Likelihood and Bayesian Estimation of Transition Probabilities
Lee, T. C., Judge, G. G., & Zellner, A. (1968) · Journal of the American Statistical Association · doi:10.1080/01621459.1968.10480918 · Cited by 67 · see citing works
The Likelihood Approach to Pooling Cross-Section and Time-Series Data
Maddala, G. S. (1971) · Econometrica · doi:10.2307/1909668 · Cited by 60 · see citing works
An alternative stochastic restricted Liu estimator in linear regression
Yang, H., & Xu, J. (2007) · Statistical Papers · doi:10.1007/s00362-007-0102-3 · Cited by 56 · see citing works
A new stochastic mixed ridge estimator in linear regression model
Li, Y., & Yang, H. (2008) · Statistical Papers · doi:10.1007/s00362-008-0169-5 · Cited by 54 · see citing works
A stochastic restricted ridge regression estimator
Özkale, M. R. (2009) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2009.02.005 · Cited by 50 · see citing works
Brown, A. J., & Deaton, A. (1973) · Palgrave Macmillan UK eBooks · doi:10.1007/978-1-349-01860-4_4 · Cited by 49 · see citing works
A mean square error test when stochastic restrictions are used in regression
Yancey, T. A., Judge, G. G., & Bock, M. E. (1974) · Communications in Statistics · doi:10.1080/03610927408827175 · Cited by 38 · see citing works
Chapter 5 Model choice and specification analysis
Leamer, E. E. (1983) · Handbook of econometrics · doi:10.1016/s1573-4412(83)01009-0 · Cited by 37 · see citing works
Frontiers: The Identity Fragmentation Bias
Lin, T., & Misra, S. (2022) · Marketing Science · doi:10.1287/mksc.2022.1360 · Cited by 33 · see citing works
A Further Study of Predictions in Linear Mixed Models
Yang, H., Ye, H., & Xue, K. (2014) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2012.725497 · Cited by 32 · see citing works
An Application of Econometric Models to International Marketing
Armstrong, J. S. (1970) · Journal of Marketing Research · doi:10.1177/002224377000700206 · Cited by 32 · see citing works
A new ridge-type estimator in stochastic restricted linear regression
Li, Y., & Yang, H. (2010) · Statistics · doi:10.1080/02331880903573153 · Cited by 31 · see citing works
Qin, D. (1997) · doi:10.1093/0198292872.001.0001 · Cited by 29 · see citing works
Time series forecasts and extra‐model information
Pankratz, A. (1989) · Journal of Forecasting · doi:10.1002/for.3980080202 · Cited by 28 · see citing works
The Early Use of Matrix Diagonal Increments in Statistical Problems
Piegorsch, W. W., & Casella, G. (1989) · SIAM Review · doi:10.1137/1031089 · Cited by 27 · see citing works
The ET Interview: Professor James Durbin
Phillips, P. C. B. (1988) · Econometric Theory · doi:10.1017/s0266466600011907 · Cited by 27 · see citing works
Hou, Z., Domke, G. M., Russell, M. B., Coulston, J. W., Nelson, M. D., Xu, Q., & McRoberts, R. E. (2020) · Forest Ecology and Management · doi:10.1016/j.foreco.2020.118777 · Cited by 26 · see citing works
An Application of Econometric Models to International Marketing
Armstrong, J. S. (1970) · Journal of Marketing Research · doi:10.2307/3150108 · Cited by 24 · see citing works
Experimental Evidence on Combining Cross-Section and Time Series Information
Johnson, K. H., & Lyon, H. L. (1973) · The Review of Economics and Statistics · doi:10.2307/1925669 · Cited by 24 · see citing works
The weighted ridge estimator in stochastic restricted linear measurement error models
Ghapani, F., Rasekh, A., & Babadi, B. (2016) · Statistical Papers · doi:10.1007/s00362-016-0786-3 · Cited by 22 · see citing works
Determinacy in the Linear Model: Gauss to Bose and Koopmans
Aldrich, J. (1999) · International Statistical Review · doi:10.1111/j.1751-5823.1999.tb00427.x · Cited by 21 · see citing works
Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics
Leiva, V., Liu, S., Ши, Л., & Cysneiros, F. J. A. (2015) · Journal of Applied Statistics · doi:10.1080/02664763.2015.1072140 · Cited by 18 · see citing works
Stone, R. (2014) · Elsevier eBooks · doi:10.1016/b978-1-4832-0058-3.50020-0 · Cited by 18 · see citing works
Mixed Liu estimator in linear measurement error models
Ghapani, F., & Babadi, B. (2017) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2017.1321768 · Cited by 16 · see citing works
Two kinds of restricted modified estimators in linear regression model
Li, Y., & Yang, H. (2010) · Journal of Applied Statistics · doi:10.1080/02664763.2010.505951 · Cited by 14 · see citing works
Linear restrictions, rank reduction, and biased estimation in linear regression
Chipman, J. S. (1999) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(98)10138-6 · Cited by 12 · see citing works
Prior information in econometric real estate appraisal: a mixed estimation procedure
Doszyń, M. (2021) · Journal of European real estate research · doi:10.1108/jerer-11-2020-0057 · Cited by 11 · see citing works
A stochastic restrictedk–dclass estimator
Yang, H., & Wu, J. (2011) · Statistics · doi:10.1080/02331888.2011.555547 · Cited by 11 · see citing works
Estimation Analogies in Control
Havenner, A., & Craine, R. (1981) · Journal of the American Statistical Association · doi:10.1080/01621459.1981.10477733 · Cited by 11 · see citing works
New Stochastic Restricted Biased Regression Estimators
Dawoud, İ., & Eledum, H. Y. (2024) · Mathematics · doi:10.3390/math13010015 · Cited by 10 · see citing works
Estimation in Singular Linear Models with Stochastic Linear Restrictions
Xu, J., & Yang, H. (2007) · Communication in Statistics- Theory and Methods · doi:10.1080/03610920601126530 · Cited by 10 · see citing works
Ghapani, F., Rasekh, A., Akhoond, M. R., & Babadi, B. (2015) · DOAJ (DOAJ: Directory of Open Access Journals) · Cited by 10 · see citing works
QML Estimators in Linear Regression Models with Functional Coefficient Autoregressive Processes
Hu, H. (2010) · Mathematical Problems in Engineering · doi:10.1155/2010/956907 · Cited by 9 · see citing works
Roozbeh, M., Maanavi, M., & Mohamed, N. A. (2023) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2023.2243361 · Cited by 9 · see citing works
A Stochastic Restricted Principal Components Regression Estimator in the Linear Model
He, D., & Wu, Y. (2014) · The Scientific World JOURNAL · doi:10.1155/2014/231506 · Cited by 9 · see citing works
ON ECONOMISTS' BELIEF IN THE LAW OF SMALL NUMBERS
Busche, K., & Kennedy, P. (1984) · Economic Inquiry · doi:10.1111/j.1465-7295.1984.tb00708.x · Cited by 9 · see citing works
Altukhaes, W. B., Roozbeh, M., & Mohamed, N. A. (2024) · AIMS Mathematics · doi:10.3934/math.20241519 · Cited by 8 · see citing works
Might expert knowledge improve econometric real estate mass appraisal?
Doszyń, M. (2022) · The Journal of Real Estate Finance and Economics · doi:10.1007/s11146-022-09891-3 · Cited by 8 · see citing works
Stochastic response restrictions
Haupt, H., & Oberhofer, W. (2004) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2004.08.006 · Cited by 8 · see citing works
Stochastic Restricted LASSO-Type Estimator in the Linear Regression Model
Kayanan, M., & Wijekoon, P. (2020) · Journal of Probability and Statistics · doi:10.1155/2020/7352097 · Cited by 8 · see citing works
A SPECIFICATION BIAS INTERPRETATION OF CROSS‐SECTION VS. TIME SERIES PARAMETER ESTIMATES
Aigner, D. J., & Simon, J. L. (1970) · Economic Inquiry · doi:10.1111/j.1465-7295.1970.tb01084.x · Cited by 8 · see citing works
A test of the rational expectations hypothesis using data from a natural experiment
Conte, A., Moffatt, P. G., Botti, F., Cagno, D. T. D., & D’Ippoliti, C. (2011) · Applied Economics · doi:10.1080/00036846.2011.597734 · Cited by 8 · see citing works
Long-Range Forecasting for a Consumer Durable in an International MarketPreprint
Armstrong, J. S. (2011) · SSRN Electronic Journal · doi:10.2139/ssrn.1969710 · Cited by 8 · see citing works
A comparison of mixed and minimax estimators of linear models
Timo Teräsvirta, Y. (1981) · Communication in Statistics- Theory and Methods · doi:10.1080/03610928108828148 · Cited by 8 · see citing works
On the Performance of Principal Component Liu-Type Estimator under the Mean Square Error Criterion
Wu, J. (2013) · Journal of Applied Mathematics · doi:10.1155/2013/858794 · Cited by 7 · see citing works
On the Stochastic Restricted Almost Unbiased Estimators in Linear Regression Model
Wu, J., & Yang, H. (2013) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2012.704540 · Cited by 7 · see citing works
On the Weighted Mixed Almost Unbiased Ridge Estimator in Stochastic Restricted Linear Regression
Liu, C., Yang, H., & Wu, J. (2013) · Journal of Applied Mathematics · doi:10.1155/2013/902715 · Cited by 7 · see citing works
Ghapani, F., Rasekh, A., & Babadi, B. (2015) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2015.1122047 · Cited by 7 · see citing works
A new stochastic restricted Liu-type estimator in linear regression model
Yıldız, N. (2017) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2017.1373813 · Cited by 7 · see citing works
Econometric Models of Real Estate Prices with Prior Information. Mixed Estimation
Doszyń, M. (2022) · Real Estate Management and Valuation · doi:10.2478/remav-2022-0021 · Cited by 6 · see citing works
THE RELATIONSHIP BETWEEN RIDGE REGRESSION AND THE MINIMUM MEAN SQUARE ERROR ESTIMATOR OF CHIPMAN
Bacon, R. W., & Hausman, J. A. (1974) · Oxford Bulletin of Economics and Statistics · doi:10.1111/j.1468-0084.1974.mp36002004.x · Cited by 6 · see citing works
Wu, J. (2014) · Journal of Applied Mathematics · doi:10.1155/2014/173836 · Cited by 5 · see citing works
Two Stochastic Restricted Principal Components Regression Estimator in Linear Regression
Wu, J., & Yang, H. (2013) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2011.639004 · Cited by 5 · see citing works
Casetti, E. (1997) · Advances in spatial science · doi:10.1007/978-3-662-03499-6_2 · Cited by 5 · see citing works
The Bayesian Approach to Research in Economic Education
Kennedy, P. (1986) · The Journal of Economic Education · doi:10.1080/00220485.1986.10845142 · Cited by 5 · see citing works
THE THEORY OF MIXED ESTIMATION IN ECONOMETRIC MODELING
CONWAY, R. N., & Mittelhammer, R. C. (1986) · Studies in Economics and Finance · doi:10.1108/eb028665 · Cited by 5 · see citing works
THE USE OF PRIOR INFORMATION IN ESTIMATING THE PARAMETERS OF ECONOMIC RELATIONSHIPS
Judge, G. G., & Yancey, T. A. (1969) · Metroeconomica · doi:10.1111/j.1467-999x.1969.tb00776.x · Cited by 5 · see citing works
Agriculture and dairy in Eastern Europe after transition focused on Poland and Hungary
Tonini, A. (2007) · doi:10.18174/44380 · Cited by 5 · see citing works
Small area estimation using nested-error models and auxiliary data
Harter, R. (1983) · doi:10.31274/rtd-180813-8573 · Cited by 5 · see citing works
Roozbeh, M. (2025) · Journal of Applied Statistics · doi:10.1080/02664763.2025.2541252 · Cited by 4 · see citing works
Likelihood-based estimation and prediction for a measles outbreak in Samoa
Wu, D. H., Petousis‐Harris, H., Paynter, J., Suresh, V., & Maclaren, O. J. (2023) · Infectious Disease Modelling · doi:10.1016/j.idm.2023.01.007 · Cited by 4 · see citing works
Performance of Some Stochastic Restricted Ridge Estimator in Linear Regression Model
Wu, J., & Liu, C. (2014) · Journal of Applied Mathematics · doi:10.1155/2014/508793 · Cited by 4 · see citing works
POOLING TIME SERIES AND CROSS SECTION DATA: A MINIMUM CHI‐SQUARED APPROACH*
Buse, A. (1981) · Manchester School · doi:10.1111/j.1467-9957.1981.tb00949.x · Cited by 4 · see citing works
Singh, S., Jain, K., & Sharma, S. (2012) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2012.04.013 · Cited by 4 · see citing works
Yang, H., & Wu, J. (2011) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2010.510256 · Cited by 4 · see citing works
Modelling dairy supply for Hungary and Poland by generalised maximum entropy using prior information
Tonini, A., & Jongeneel, R. A. (2008) · European Review of Agricultural Economics · doi:10.1093/erae/jbn018 · Cited by 4 · see citing works
An extension of mixed estimation, with an application to forecasting new product growth
Kennedy, P. (1991) · Empirical Economics · doi:10.1007/bf01206036 · Cited by 4 · see citing works
The Existence of a World Demand for Money Function: Preliminary Results
Frowen, S. F., & Kouris, G. (1977) · Credit and Capital Markets – Kredit und Kapital · doi:10.3790/ccm.10.1.1 · Cited by 4 · see citing works
Unmodeled Error Analysis on Trajectory and Orbital Estimation
Bush, N. (1971) · Technometrics · doi:10.1080/00401706.1971.10488785 · Cited by 3 · see citing works
Altukhaes, W. B., Roozbeh, M., & Mohamed, N. A. (2024) · Mathematics · doi:10.3390/math12172787 · Cited by 3 · see citing works
A new stochastic mixed Liu estimator in linear regression model
Li, Y. (2018) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2018.1549250 · Cited by 3 · see citing works
On the equivalence of pooled and mixed estimation
Buse, A. (1997) · Statistical Papers · doi:10.1007/bf02925225 · Cited by 3 · see citing works
Generalized approach to the problem of regression
Partyka, D., & Zaja̧c, J. (2015) · Analysis and Mathematical Physics · doi:10.1007/s13324-014-0096-7 · Cited by 3 · see citing works
Passi, R. M. (1979) · Technometrics · doi:10.1080/00401706.1979.10489821 · Cited by 3 · see citing works
Alvárez, L. J., Delrieu, J. C., & Jareño, J. (1997) · Journal of Policy Modeling · doi:10.1016/s0161-8938(96)00056-7 · Cited by 3 · see citing works
On a pooled estimator and its finite-sample moments
Mikhail, W. M., & Ghazal, G. A. (1991) · Journal of Econometrics · doi:10.1016/0304-4076(91)90038-f · Cited by 3 · see citing works
Consistent Projections in Multi-Sector Models
Stone, R. (1967) · Palgrave Macmillan UK eBooks · doi:10.1007/978-1-349-08461-6_9 · Cited by 3 · see citing works
Hood, W. C. (1955) · The Canadian Journal of Economics and Political Science · doi:10.2307/138202 · Cited by 3 · see citing works
The Identity Fragmentation BiasPreprint
Lin, T., & Misra, S. (2019) · SSRN Electronic Journal · doi:10.2139/ssrn.3507185 · Cited by 3 · see citing works
On the weighted mixed Liu-type estimator under unbiased stochastic restrictions
Yıldız, N. (2016) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2016.1235189 · Cited by 2 · see citing works
Stochastic restricted estimation in partially linear additive errors-in-variables models
Wei, C., & Yang, J. (2018) · Statistical Papers · doi:10.1007/s00362-018-0978-0 · Cited by 2 · see citing works
An application of econometric models to international marketing
Armstrong, A. S. P. J. (1970) · The International Executive · doi:10.1002/tie.5060120411 · Cited by 2 · see citing works
On the estimation of generalized linear probability model involving discrete random variables
Roy, A. R., & Srivastava, V. K. (1968) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf02911657 · Cited by 2 · see citing works
Missing agricultural price data: an application of mixed estimation
Castillo, M. J., Useche, P., & Moss, C. B. (2008) · Applied Economics Letters · doi:10.1080/13504850802167207 · Cited by 2 · see citing works
The Identity Fragmentation BiasPreprint
Lin, T., & Misra, S. (n.d.) · RePEc: Research Papers in Economics · Cited by 2 · see citing works
Al-Dulaimi, R. J. H., & Alheety, M. I. (2022) · International Conference on Contemporary Information Technology and Mathematics (ICCITM) · doi:10.1109/iccitm56309.2022.10031912 · Cited by 1 · see citing works
On Diagnostics in Stochastic Restricted Linear Regression Models
Wang, S., Liu, M., & Deng, X. (2014) · Open Journal of Statistics · doi:10.4236/ojs.2014.49071 · Cited by 1 · see citing works
Deriving Restricted Least Squares without a Lagrangean
Vahid, F., Alvárez, L. J., Dolado, J. J., Paruolo, P., & Zheng, J. X. (1994) · Econometric Theory · doi:10.1017/s0266466600008574 · Cited by 1 · see citing works
Li, Y. (2016) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2015.1137598 · Cited by 1 · see citing works
Ridge stochastic restricted estimators in semiparametric linear measurement error models
Emami, H. (2018) · Journal of the Iranian Statistical Society · doi:10.29252/jirss.17.2.9 · Cited by 1 · see citing works
- Authors
- Durbin, J.
- Affiliations
- London School of Economics and Political Science (GB)
- Corresponding author
- Durbin, J.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1953-12
- Volume
- 48
- Issue
- 264
- Pages
- 799-808
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W1983547829
- Cited by
- 143
- References
- 3
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 5 · 2023: 3 · 2022: 6 · 2021: 1 · 2020: 4 · 2019: 1 · 2018: 3 · 2017: 2 · 2016: 3 · 2015: 5 · 2014: 7 · 2013: 5 · 2012: 2
- FWCI
- 1.56
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- UCL Discovery (University College London) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- regression analysis, extraneous information, Bayesian regression, prior distributions, parameter estimation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review