Asymptotics of Multivariate Regression with Consecutively Added Dependent Varibles

V.M. Raats, B.B. van der Genugten, J.J.A. Moors

Research output: Working paper › Discussion paper › Other research output

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Abstract

We consider multivariate regression where new dependent variables are consecutively added during the experiment (or in time).So, viewed at the end of the experiment, the number of observations decreases with each added variable. The explanatory variables are observed throughout.In a previous paper we determined the least squares and maximum likelihood estimators for the parameters in this model.In this paper we discuss the estimation technique of iterative least squares to calculate the maximum likelihood estimates and we prove the consistency of the estimators in each iteration.Moreover, we introduce a general class of estimators for the regression parameters based on arbitrary starting estimators for the covariance matrix.We prove the consistency of these new estimators and - for sake of completeness - of the previously obtained least squares and maximum likelihood estimators as well.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages20
Volume2004-77
Publication statusPublished - 2004

Publication series

NameCentER Discussion Paper
Volume2004-77

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Multivariate Regression
Estimator
Least Squares
Dependent
Maximum Likelihood Estimator
Maximum Likelihood Estimate
Covariance matrix
Experiment
Completeness
Regression
Iteration
Calculate
Decrease
Arbitrary
Model

Keywords

  • added dependent variables
  • consistency
  • iterative weighted least squares
  • maximum likelihood
  • monotone missing data

Cite this

Raats, V. M., van der Genugten, B. B., & Moors, J. J. A. (2004). Asymptotics of Multivariate Regression with Consecutively Added Dependent Varibles. (CentER Discussion Paper; Vol. 2004-77). Tilburg: Econometrics.
Raats, V.M. ; van der Genugten, B.B. ; Moors, J.J.A. / Asymptotics of Multivariate Regression with Consecutively Added Dependent Varibles. Tilburg : Econometrics, 2004. (CentER Discussion Paper).
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Raats, VM, van der Genugten, BB & Moors, JJA 2004 'Asymptotics of Multivariate Regression with Consecutively Added Dependent Varibles' CentER Discussion Paper, vol. 2004-77, Econometrics, Tilburg.

Asymptotics of Multivariate Regression with Consecutively Added Dependent Varibles. / Raats, V.M.; van der Genugten, B.B.; Moors, J.J.A.

Tilburg : Econometrics, 2004. (CentER Discussion Paper; Vol. 2004-77).

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Asymptotics of Multivariate Regression with Consecutively Added Dependent Varibles

AU - Raats, V.M.

AU - van der Genugten, B.B.

AU - Moors, J.J.A.

N1 - Pagination: 20

PY - 2004

Y1 - 2004

N2 - We consider multivariate regression where new dependent variables are consecutively added during the experiment (or in time).So, viewed at the end of the experiment, the number of observations decreases with each added variable. The explanatory variables are observed throughout.In a previous paper we determined the least squares and maximum likelihood estimators for the parameters in this model.In this paper we discuss the estimation technique of iterative least squares to calculate the maximum likelihood estimates and we prove the consistency of the estimators in each iteration.Moreover, we introduce a general class of estimators for the regression parameters based on arbitrary starting estimators for the covariance matrix.We prove the consistency of these new estimators and - for sake of completeness - of the previously obtained least squares and maximum likelihood estimators as well.

AB - We consider multivariate regression where new dependent variables are consecutively added during the experiment (or in time).So, viewed at the end of the experiment, the number of observations decreases with each added variable. The explanatory variables are observed throughout.In a previous paper we determined the least squares and maximum likelihood estimators for the parameters in this model.In this paper we discuss the estimation technique of iterative least squares to calculate the maximum likelihood estimates and we prove the consistency of the estimators in each iteration.Moreover, we introduce a general class of estimators for the regression parameters based on arbitrary starting estimators for the covariance matrix.We prove the consistency of these new estimators and - for sake of completeness - of the previously obtained least squares and maximum likelihood estimators as well.

KW - added dependent variables

KW - consistency

KW - iterative weighted least squares

KW - maximum likelihood

KW - monotone missing data

M3 - Discussion paper

VL - 2004-77

T3 - CentER Discussion Paper

BT - Asymptotics of Multivariate Regression with Consecutively Added Dependent Varibles

PB - Econometrics

CY - Tilburg

ER -

Raats VM, van der Genugten BB, Moors JJA. Asymptotics of Multivariate Regression with Consecutively Added Dependent Varibles. Tilburg: Econometrics. 2004. (CentER Discussion Paper).

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