DOI: https://doi.org/10.31493/tit1811.0302

Analysis of the multicollinear econometric model parameters with a rank deficient observation matrix

Viktor Kutovyi, Olga Katunina, Oleg Shutovskyi

Abstract


The topic of determining informative predictors, forming rational exogenous variables, substantiating the dimension and structure of predictor spaces is considered. The purpose of design and selection of characteristics is to prevent the effect of retraining, reduce the dimension in studying the processes apart from a master, build classifiers, reflect the process of dividing data into classes and determine the boundaries of solutions in limited space, as well as reasonable interpretation, provide in-depth understanding of the model and data for studying, visualization in spaces, the dimension of which is perceived by the researcher. The design predictor spaces and develop effective procedures problems for estimating the parameters of econometric models with multicollinear variables are developed. The study was made under alternative approaches to form the interdependencies models features. A mathematical toolkit is proposed for calculating the parameters of a linear econometric model in case of rank deficient observation matrix, based on the study of singular expansions. Using a singular toolkit for decomposing and analyzing the data matrix makes it possible to increase the operational efficiency and predictive quality of the procedures for estimating econometric models parameters. The mathematical approach to the construction of models of the interdependence of factors is intended to select characteristics and construct predictor spaces in the study of systems with multicollinear variables and rank deficient observation matrix.

Keywords


design features; econometric model; multicollinearity; matrix of observations of incomplete rank; singular schedule; eigenvalues

References


Johnston J., 1971. Econometric Metods. MeGraw-Hill, 437.

Lawson C.L., Hanson R.J., 1974. Solving Least Squares Problems. Prentice – Hall, Inc., Englewood Cliffs N.J., 340.

Voevodin V.V., 1977. Vychislitel`nye osnovy lineinoi algebry. [numerical foundations of linear algebra]. Nauka, Moscow, 303(in Russian).

Kutovyi V.O., 2001. Pro teoremu HaussaMarkova u vypadku vyrodzhenoi matrytsi sposterezhen. Dopov. Dokl. Akad. Nauk Ukraine, No.5, 19-22 (in Ukrainian).

Kutovyi V.O., 2000. Pro zastosuvania instrumentalnyh zminnyh dlia vyznachenia parametriv zagalnoi liniynoi modeli Modeliuvayia ta informaciyni systey v economici.Kyiv.KNEU, No.64 (in Ukrainian) 168-173.

Kutovyi V.O., Roskach O.S., 1997. Matematyko-statystychne uzagalnenia pokrokovyh metodiv pobudovy predyktornyh prostoriv. Mashynna obrobka informacii, No.59, 140-149 (in Ukrainian).

Kutovyi V.O., Roskach O.S., 1997. Pro zastosyvania na EOM algorytmu FarraraGlaubera.Mashyna obrobka informacii. Kyiv, KNEU, No.61, 142-149 (in Ukrainian).

Kutovyi V.O., 1999. Pro umovy zastosuvania teoremy Gaussa-Markova. Vcheni zapysky Kyiv, KNEU, No.2C, 206-208 (in Ukrainian).

Kutovyi V.O., 2001. Pro efektyvnist zmishenyh ocinok parametriv economichnyh modelei. Kyiv, KNEU, No.3, 324-326 (in Ukrainian).

Aitken A.C., 1993. One Least-squares and Linear Combinetion of Observations. Proc., RoyalSoc., Edinburgh, No.55, 42-46.

Pavies O., 1993. Statistical momentpods in research and production, New York, 1957.

Plackett R., 1960. Principles of regression analysis. Oxfopd.

Weatherburn C.E., 1961. A first course in mathematical statistics. University Press, Cambridge, brosch, 18 s, 6 d, 278.

Hamilton W., 1964. Statistucs in physical science. New York, 1964.

Jürgen Grob., 2004. The general GaussMarkov model with hjssibl singular dispersion matrix. Statistical Paper, No.45, 311-336.

Farrar D.E., Glauber, R.R., 1967. Multicollinearity in Regression Analysis: The Problem Revisited. Review of Economics and Statistics, 49(1), 92-107.

Yangge Fian, Beisiegel M., Dagenais E., Haines C., 2008. On the natural restrietions in the singular Grauss-Markov model. Statistical Papers, Vol.49, 553-564.

Silvey S.D., 1969. Multicallinearity and Imprecise Estimation. Jornal of the Real Statical Society, Series B, No.31, 539-552.

Makhinko А., Makhinko N., 2017. Osoblyvosti imovirnisnoho rozrakhunku vysotnykh sporud pry vrakhuvanni vypadkovosti obokh skladovykh vitrovoho vplyvu Probabilistic design of high-rise buildings with two stochastic components of wind velocity. Underwater Technologies, Iss.6, 16-27 (in Ukrainian).

Bogdanov V., 2017. Impact of a hard cylinder with flat surface on the elastic layer. Underwater Technologies, Iss.5, 8-15 (in Ukrainian).

Skochko V., 2017. Shaping of the frameworks of technical forms, which defined by implicit functions on a plane. Underwater Technologies, Iss.7, 3-17 (in Ukrainian)


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.