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Vergleich Von Funktionalen Und Strukturellen Messfehlerverfahren

Vergleich Von Funktionalen Und Strukturellen Messfehlerverfahren

          
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About the Book

In dieser Arbeit werden verschiedene Schatzverfahren bei Messfehlermodellen, insbesondere bei polynomialen und Poisson FV-Regressionen verglichen. Das Hauptaugenmerk liegt dabei auf den Parameterschatzungen, bei den quadratischen Messfehlermodellen werden auch die Schatzungen der Extremwerte der Parabel einer genaueren Betrachtung unterzogen. Die Analyse der Eigenschaften der Verfahren geschieht sowohl auf rechnerischem Weg als auch mit Hilfe von Simulationen und Beispieldaten. Neben dem Benchmark-Schatzer, der nur als Vergleich dienen kann, und dem naiven Verfahren, das die Messfehler schlichtweg ignoriert, werden das naiv-korrigierte (NK), das SimEx-, das (M)ALS- bzw. CS-Verfahren sowie die Regressionskalibrierung (RK), und das SQS-Verfahren bei Normalverteilung untersucht. Eine weiterfuhrende Variante des SQS-Verfahrens, die MSQS-Schatzung, wird im Zuge der Untersuchung der Missspezifikationen ebenfalls analysiert. Dabei wird die zugrundegelegte Verteilung durch eine Mischung von Normalverteilungen approximiert. In der Regel reichen hier hochstens drei Komponenten um die Verteilung der latenten Variable zu approximieren. Grundsatzlich lasst sich festhalten, dass der naive Schatzer und teilweise auch der SimEx-Schatzer stark verzerren. Ersteres liegt am Messfehlerprozess, letzteres ist grosstenteils auf nicht-optimale Extrapolationsfunktionen zuruckzufuhren. Bei normalverteilten latenten Variablen schneidet die Regressionskalibrierung sehr gut ab, abgesehen von den Absolutgliedern, die in der Regel nicht konsistent geschatzt werden. Der naiv-korrigierte Schatzer liefert in den untersuchten Modellen auch dort konsistente Schatzungen, hat aber den Nachteil, dass die Korrekturfaktoren fur FV-Regressionen explizit errechnet werden mussen. Das SQS-Verfahren ist in der klassischen Situation konsistent, flexibel und effektiv. Das CS-Verfahren, das bei den Polynomen auch MALS-Verfahren bezeichnet wird, ist unabhangig von der Verteilung der latenten Variablen. Es liefert bei hoheren Fallzahlen und moderaten Messfehlervarianzen robuste Schatzwerte. Bei geringen Fallzahlen und/oder hoheren Messfehlervarianzen ist es vereinzelt anfallig fur grobe Fehlschatzungen. Es kann hier zu numerischen Problemen und damit zu unplausiblen Parameterschatzungen kommen. Dies durfte in der Praxis aber kaum eine Rolle spielen, da diese Falle oft einfach zu erkennen sind. Neben dem CS-Verfahren liefert auch das MSQS-Verfahren regelmassig sehr gute Ergebnisse, falls die latente Kovariable nicht normalverteilt ist. Diese Schatzwerte hangen von der Gute der Approximation der Verteilung der latenten Kovariablen durch endlich viele Mischverteilungen ab. Naturgemass kann dies als zusatzliche Fehlerquelle dienen.


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Product Details
  • ISBN-13: 9783832505615
  • Publisher: Logos Verlag Berlin
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 0 mm
  • Width: 145 mm
  • ISBN-10: 383250561X
  • Publisher Date: 15 May 2004
  • Height: 210 mm
  • No of Pages: 147
  • Series Title: German
  • Weight: 700 gr


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