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2013-03-15T07:22:40Z

Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q584783

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	~~Wilber Berryhill~~ is the ~~title his parents gave him~~ and ~~he completely digs that title~~. ~~What I adore doing~~ is ~~football but I don~~'~~t have~~ the ~~time recently~~. ~~For many years she~~'~~s been working as~~ a ~~travel agent~~. ~~Ohio~~ is ~~exactly where his house~~ is and ~~his family members enjoys it~~.<br><br>~~Here is my web site psychic readings (~~[~~http:~~//~~Formalarmour~~.~~com/index~~.~~php?do~~=~~/profile~~-~~26947~~/~~info~~/ ~~formalarmour.com~~])		The '''Hausman test''' (also called the '''Wu–Hausman test''', '''Hausman specification test''', and '''Durbin–Wu–Hausman test''') is a [[statistical hypothesis test]] in [[econometrics]] named after [[James Durbin]],<ref name=Durbin/> De-Min Wu<ref name=Wu/> and [[Jerry A. Hausman]].<ref name=Hausman/>{{citation needed\|date=February 2012}}{{clarify\|reason=who calls this \|date=February 2012}} The test evaluates the [[Statistical significance\|significance]]{{clarify\|reason=what do you mean significance? do you mean efficiency? \|date=May 2012}} of an [[estimator]] versus an alternative [[estimator]]. It helps one evaluate if a statistical model corresponds to the data.

			==Details==
			Consider the linear model ''y'' = ''bX'' + ''e'', where ''y'' is the dependent variable and ''X'' is vector of [[regressor]]s, ''b'' is a vector of coefficients and ''e'' is the [[error term]]. We have two estimators for ''b'': ''b''<sub>0</sub> and ''b''<sub>1</sub>. Under the [[null hypothesis]], both of these estimators are [[consistent estimator\|consistent]], but ''b''<sub>1</sub> is [[efficiency (statistics)\|efficient]] (has the smallest asymptotic variance), at least in the class of estimators containing ''b''<sub>0</sub>. Under the [[alternative hypothesis]], ''b''<sub>0</sub> is consistent, whereas ''b''<sub>1</sub> isn’t.

			Then the '''Wu–Hausman [[statistic]]''' is:<ref name=Greene/>

			: <math>H=(b_{1}-b_{0})'\big(\operatorname{Var}(b_{0})-\operatorname{Var}(b_{1})\big)^\dagger(b_{1}-b_{0}),</math>

			where <sup>†</sup> denotes the [[Moore–Penrose pseudoinverse]]. This statistic has asymptotically the [[chi-squared distribution]] with the number of degrees of freedom equal to the rank of matrix {{nowrap\|Var(''b''<sub>0</sub>) − Var(''b''<sub>1</sub>)}}.

			If we reject the null hypothesis, b<sub>1</sub> is inconsistent. This test can be used to check for the [[Endogeneity (economics)\|endogeneity]] of a variable (by comparing [[instrumental variable]] (IV) estimates to [[ordinary least squares]] (OLS) estimates). It can also be used to check the validity of extra [[instrumental variable\|instruments]] by comparing IV estimates using a full set of instruments ''Z'' to IV estimates that use a proper subset of ''Z''. Note that in order for the test to work in the latter case, we must be certain of the validity of the subset of ''Z'' and that subset must have enough instruments to identify the parameters of the equation.

			Hausman also showed that the covariance between an efficient estimator and the difference of an efficient and inefficient estimator is zero.

			==Panel data==
			Hausman test can be also used to differentiate between [[fixed effects model]] and [[random effects model]] in panel data. In this case, Random effects (RE) is preferred under the null hypothesis due to higher efficiency, while under the alternative Fixed effects (FE) is at least consistent and thus preferred.
			{\| class="wikitable"
			\|
			! H<sub>0</sub> is true
			! H<sub>1</sub> is true
			\|- align="center"
			\| ''b''<sub>1</sub> (RE estimator)
			\| Consistent <br> Efficient
			\| Inconsistent
			\|- align="center"
			\| ''b''<sub>0</sub> (FE estimator)
			\| Consistent <br> Inefficient
			\| Consistent
			\|}

			==See also==
			*[[Regression model validation]]

			==References==
			{{reflist\|refs=
			<ref name=Durbin>{{cite journal \| last=Durbin \| first=James \| year=1954 \| title=Errors in variables \| journal=[[Review of the International Statistical Institute]] \| volume=22 \| pages=23–32}}</ref>

			<ref name=Wu>{{cite journal \|last=Wu \|first=De-Min \|date=July 1973 \|title=Alternative Tests of Independence between Stochastic Regressors and Disturbances \|journal=[[Econometrica]] \|volume=41 \|issue=4 \|pages=733–750 \|issn=0012-9682 \|doi= \|jstor=1914093 }}</ref>

			<ref name=Hausman>{{cite journal \|authorlink=Jerry A. Hausman \|last=Hausman \|first=J. A. \|date=November 1978 \|title=Specification Tests in Econometrics \|journal=[[Econometrica]] \|volume=46 \|issue=6 \|pages=1251–1271 \|issn=0012-9682 \|doi= \|jstor=1913827 }}</ref>

			<ref name=Greene>{{cite book \|last=Greene \|first=William H. \|title=Econometric Analysis \|publisher=Pearson \|edition=6th \|year=2008 \|isbn=9780135132456 }}{{page needed\|date=February 2012}}</ref>
			}}

			[[Category:Econometrics]]
			[[Category:Statistical tests]]

en>Sun Creator: /* References */Typo fixing and checking, typos fixed: c.Letters, → c. Letters, using AWB (8097)

2012-08-08T16:31:46Z

References: Typo fixing and checking, typos fixed: c.Letters, → c. Letters, using AWB (8097)

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Wilber Berryhill is the title his parents gave him and he completely digs that title. What I adore doing is football but I don't have the time recently. For many years she's been working as a travel agent. Ohio is exactly where his house is and his family members enjoys it.<br><br>Here is my web site psychic readings ([http://Formalarmour.com/index.php?do=/profile-26947/info/ formalarmour.com])

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en>Addbot: Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q584783

en>Sun Creator: /* References */Typo fixing and checking, typos fixed: c.Letters, → c. Letters, using AWB (8097)