The Treatment of Linear Restrictions in Regression Analysis

Chipman, John S.; Rao, M.M.M.

doi:10.2307/1913745

Cited by 60 publications

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“…The most closely related paper of which we are aware of is that of Rao [1962] ; our work was done independe ntly of his. (The relevance of the very rece nt paper of Chipman and Rao [1964], whic h contains other refe re nces of interest, is detailed at the end of section 5.2.) Valuable summaries of various aspects of th e theory of least squares can be found in Deming [1943J, Plac kett [1949[1943J, Plac kett [ , 1960, Rao [1946], and Scheffe [1959].…”

Section: Introductionmentioning

confidence: 99%

Weak generalized inverses and minimum variance linear unbiased estimation

Goldman¹,

Zelen²

1964

J. RES. NATL. BUR. STAN. SECT. B. MATH. MATH. PHYS.

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This paper prese nts a unifi ed account of the theory of least square s and its adaptations to statis· tic al mode ls mo re compli cated than th e classical one. Firs t co mes a d e velopme nt of the prop e rties of weak ge ne ral ized matrix inve rses, a useful variant of th e more familiar pseudo·inverse. These properties are e mpl oyed in a proof of th e usual Gauss theorem, a nd in analyzin g th e case in whic h known linea r res traints are obeye d by the para me te rs. Anothe r situ ation treated is that of a s ingular varia nce-co variance matrix for the observati ons . Appli cations in clude the case of equi-co rrelated variabl es (i ncludin g es timation d es pite igno rance of th e co rre lation), lin ea r " res tra ints" s ubj ect to random error, and step wi se linear es timatio n.

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Section: Introductionmentioning

confidence: 99%

Weak generalized inverses and minimum variance linear unbiased estimation

Goldman¹,

Zelen²

1964

J. RES. NATL. BUR. STAN. SECT. B. MATH. MATH. PHYS.

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“…where X' is the appropriate (Jk x 1) vector of Lagrange multipliers (see Chipman andRao, 1964, or Theil, 1966). Thus,…”

Section: A Restricted Least Squares Estimatormentioning

confidence: 99%

A Search Algorithm for the Estimation of Interregional Migration in Local Areas

Meier¹

1973

Environ Plan A

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A discrete step steepest descent search algorithm is developed for the estimation of interregional migration rates in local areas from historical time series. Objective function values are obtained from a constrained least-squares optimization, and it is found that the dimensions of the search space correspond to the number of smoothing operations in the columns of the data input matrix. The iterative algorithm requires the use of symptomatic indicators of intercensal population and is shown to yield improved results over a simple least squares approach. IntroductionIn a recent study focused on population projection for local areas in New England, a technique was necessary for estimating local migration rates from past population series (Meier, 1970(Meier, , 1972. The method developed by Rogers (1967aRogers ( , 1967bRogers ( , 1968, tested on regions and populations much larger than the communities in the Springfield metropolitan area of Massachusetts, which constituted one of the study areas, fitted this requirement conceptually. Preliminary results, however, directed attention to a number of difficulties when the method was applied to small regions. This study seeks to develop an improved estimation technique, based in part on Rogers' original work (Rogers, 1968), but incorporating a number of refinements necessary for a successful application to local areas.

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“…Basic distributional properties of the RLS estimator, efficiency comparisons, hypothesis tests and realworld applications can be found in Chipman and Rao (1964), Trenkler (1987), Ramanathan (1993), Greene (2007) and Wooldridge (2013). It is well known that the RLS estimator can be expressed in terms of the ordinary least squares (OLS) estimator.…”

Section: Introductionmentioning

confidence: 99%

Influence diagnostic analysis in the possibly heteroskedastic linear model with exact restrictions

Liu

Leiva

et al. 2015

Stat Methods Appl

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The local influence method has proven to be a useful and powerful tool for detecting influential observations on the estimation of model parameters. This method has been widely applied in different studies related to econometric and statistical modelling. We propose a methodology based on the Lagrange multiplier method with a linear penalty function to assess local influence in the possibly heteroskedastic linear regression model with exact restrictions. The restricted maximum likelihood estimators and information matrices are presented for the postulated model. Several perturbation schemes for the local influence method are investigated to identify potentially influential observations. Three real-world examples are included to illustrate and validate our methodology.

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The Treatment of Linear Restrictions in Regression Analysis

Cited by 60 publications

References 0 publications

Weak generalized inverses and minimum variance linear unbiased estimation

Weak generalized inverses and minimum variance linear unbiased estimation

A Search Algorithm for the Estimation of Interregional Migration in Local Areas

Influence diagnostic analysis in the possibly heteroskedastic linear model with exact restrictions

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