Total least squares (original) (raw)
In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account. It is a generalization of Deming regression and also of orthogonal regression, and can be applied to both linear and non-linear models. The total least squares approximation of the data is generically equivalent to the best, in the Frobenius norm, low-rank approximation of the data matrix.
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| dbo:abstract | In der Statistik dient die orthogonale Regression (genauer: orthogonale lineare Regression) zur Berechnung einer Ausgleichsgeraden für eine endliche Menge metrisch skalierter Datenpaare nach der Methode der kleinsten Quadrate. Wie in anderen Regressionsmodellen wird dabei die Summe der quadrierten Abstände der von der Geraden minimiert. Im Unterschied zu anderen Formen der linearen Regression werden bei der orthogonalen Regression nicht die Abstände in - bzw. -Richtung verwendet, sondern die orthogonalen Abstände. Dieses Verfahren unterscheidet nicht zwischen einer unabhängigen und einer abhängigen Variablen. Damit können – anders als bei der linearen Regression – Anwendungen behandelt werden, bei denen beide Variablen und messfehlerbehaftet sind. Die orthogonale Regression ist ein wichtiger Spezialfall der Deming-Regression. Sie wurde erstmals 1840 im Zusammenhang mit einem geodätischen Problem von Julius Weisbach angewendet, 1878 von in die Statistik eingeführt und in allgemeinerem Rahmen 1943 von W. E. Deming für technische und ökonomische Anwendungen bekannt gemacht. (de) In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account. It is a generalization of Deming regression and also of orthogonal regression, and can be applied to both linear and non-linear models. The total least squares approximation of the data is generically equivalent to the best, in the Frobenius norm, low-rank approximation of the data matrix. (en) В прикладной статистике метод наименьших полных квадратов (МНПК, TLS — англ. Total Least Squares) — это вид , техника моделирования данных с помощью метода наименьших квадратов, в которой принимаются во внимание ошибки как в зависимых, так и в независимых переменных. Метод является обобщением регрессии Деминга и ортогональной регрессии и может быть применён как к линейным, так и нелинейным моделям. Аппроксимация данных методом наименьших полных квадратов в общем виде эквивалентна лучшей по норме Фробениуса матрицы данных. (ru) |
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| rdfs:comment | In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account. It is a generalization of Deming regression and also of orthogonal regression, and can be applied to both linear and non-linear models. The total least squares approximation of the data is generically equivalent to the best, in the Frobenius norm, low-rank approximation of the data matrix. (en) В прикладной статистике метод наименьших полных квадратов (МНПК, TLS — англ. Total Least Squares) — это вид , техника моделирования данных с помощью метода наименьших квадратов, в которой принимаются во внимание ошибки как в зависимых, так и в независимых переменных. Метод является обобщением регрессии Деминга и ортогональной регрессии и может быть применён как к линейным, так и нелинейным моделям. Аппроксимация данных методом наименьших полных квадратов в общем виде эквивалентна лучшей по норме Фробениуса матрицы данных. (ru) In der Statistik dient die orthogonale Regression (genauer: orthogonale lineare Regression) zur Berechnung einer Ausgleichsgeraden für eine endliche Menge metrisch skalierter Datenpaare nach der Methode der kleinsten Quadrate. Wie in anderen Regressionsmodellen wird dabei die Summe der quadrierten Abstände der von der Geraden minimiert. Im Unterschied zu anderen Formen der linearen Regression werden bei der orthogonalen Regression nicht die Abstände in - bzw. -Richtung verwendet, sondern die orthogonalen Abstände. Dieses Verfahren unterscheidet nicht zwischen einer unabhängigen und einer abhängigen Variablen. Damit können – anders als bei der linearen Regression – Anwendungen behandelt werden, bei denen beide Variablen und messfehlerbehaftet sind. (de) |
| rdfs:label | Orthogonale Regression (de) Total least squares (en) Метод наименьших полных квадратов (ru) |
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