Preponderantly increasing/decreasing data in regression analysis
For the given data (wI, xI, yI ), i = 1, . . . , n, and the given model function f (x; θ), where θ is a vector of unknown parameters, the goal of regression analysis is to obtain estimator θ∗ of the unknown parameters θ such that the vector of residuals is minimized in some sense. The common approac...
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| Format: | Article |
| Language: | English |
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Croatian Operational Research Society
2016-12-01
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| Series: | Croatian Operational Research Review |
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| Online Access: | http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=257102&lang=en |
| _version_ | 1818537344235470848 |
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| author | Darija Marković |
| author_facet | Darija Marković |
| author_sort | Darija Marković |
| collection | DOAJ |
| description | For the given data (wI, xI, yI ), i = 1, . . . , n, and the given model function f (x; θ), where θ is a vector of unknown parameters, the goal of regression analysis is to obtain estimator θ∗ of the unknown parameters θ such that the vector of residuals is minimized in some sense. The common approach to this problem of minimization is the least-squares method, that is minimizing the L2 norm of the vector of residuals. For nonlinear model functions, what is necessary is finding at least the sufficient conditions on the data that will guarantee the existence of the best least-squares estimator. In this paper we will describe and examine in detail the property of preponderant increase/decrease of the data, which ensures the existence of the best estimator for certain important nonlinear model functions. |
| first_indexed | 2024-12-11T18:49:34Z |
| format | Article |
| id | doaj.art-767c3949facd4f0187abcc2bd6b3ee2f |
| institution | Directory Open Access Journal |
| issn | 1848-0225 1848-9931 |
| language | English |
| last_indexed | 2024-12-11T18:49:34Z |
| publishDate | 2016-12-01 |
| publisher | Croatian Operational Research Society |
| record_format | Article |
| series | Croatian Operational Research Review |
| spelling | doaj.art-767c3949facd4f0187abcc2bd6b3ee2f2022-12-22T00:54:21ZengCroatian Operational Research SocietyCroatian Operational Research Review1848-02251848-99312016-12-017226927610.17535/crorr.2016.0018Preponderantly increasing/decreasing data in regression analysisDarija Marković0Department of Mathematics, J. J. Strossmayer University of Osijek, Trg Ljudevita Gaja 6, 31000 Osijek, CroatiaFor the given data (wI, xI, yI ), i = 1, . . . , n, and the given model function f (x; θ), where θ is a vector of unknown parameters, the goal of regression analysis is to obtain estimator θ∗ of the unknown parameters θ such that the vector of residuals is minimized in some sense. The common approach to this problem of minimization is the least-squares method, that is minimizing the L2 norm of the vector of residuals. For nonlinear model functions, what is necessary is finding at least the sufficient conditions on the data that will guarantee the existence of the best least-squares estimator. In this paper we will describe and examine in detail the property of preponderant increase/decrease of the data, which ensures the existence of the best estimator for certain important nonlinear model functions.http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=257102&lang=enregression analysisnonlinear least squaresexistence problempreponderant increase/decrease propertyChebyshev inequality |
| spellingShingle | Darija Marković Preponderantly increasing/decreasing data in regression analysis Croatian Operational Research Review regression analysis nonlinear least squares existence problem preponderant increase/decrease property Chebyshev inequality |
| title | Preponderantly increasing/decreasing data in regression analysis |
| title_full | Preponderantly increasing/decreasing data in regression analysis |
| title_fullStr | Preponderantly increasing/decreasing data in regression analysis |
| title_full_unstemmed | Preponderantly increasing/decreasing data in regression analysis |
| title_short | Preponderantly increasing/decreasing data in regression analysis |
| title_sort | preponderantly increasing decreasing data in regression analysis |
| topic | regression analysis nonlinear least squares existence problem preponderant increase/decrease property Chebyshev inequality |
| url | http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=257102&lang=en |
| work_keys_str_mv | AT darijamarkovic preponderantlyincreasingdecreasingdatainregressionanalysis |