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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Maximum likelihood estimation with flow data ： ウィキペディア英語版 Maximum likelihood estimation with flow data Maximum Likelihood Estimation with flow data is a parametric approach to deal with flow sampling data. Assume that we have observations of ''ai'' the time a person enters the state of interest, some observables xi, and the censoring of the flow data takes on a particular form. In particular $t\_i\; =\; \backslash min(t\_i^U,L)$, where is the observed duration outcome, $t\_i^U$ is the underlying continuous variable and is the censoring threshold.〔 Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass.〕 For instance, when thinking about unemployment spells, is the data of entering unemployment, is a vector of worker characteristics, and is the observed unemployment duration. If we only follow the workers for a certain period of time, this variable is necessarily a censored version of the true unemployment duration. Two key assumptions allow for setting up the loglikelihood. First, a distributional form for the latent variable $t\_i^U$ needs to be assumed. Second, independence between the true duration and the starting point of the spell is assumed, i.e., :$F(t\_i^U\; \backslash lor\; x\_i,\; a\_i,\; L)\; =\; F(t\_i^U\; \backslash lor\; x\_i)$ where ''F'' is the conditional distribution of the underlying duration variable〔Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass.〕. This latter assumption allows us to model the probability that the variable is censored, i.e., :$\backslash Pr(t\_i^U\; \backslash ge\; L\; \backslash lor\; x\_i)\; =\; 1\; -\; F(L\; \backslash lor\; x\_i)$ which leads to the following log likelihood: :$\backslash sum\_^n\; (d\_i\; log(f(t\_i\; \backslash lor\; x\_i))\; +\; (1-d\_i)\; log(1-F(L\; \backslash lor\; x\_i\; )))$ where ''f'' is the density associated with the distribution and is an indicator denoting whether .〔Hayashi, F. (2000): Econometrics. Princeton University Press, New Jersey.〕 Additionally, it is possible to have the threshold vary at the observational level, by replacing by in the formulas above. 〔 Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass.〕 Tests of specification in duration models encompass testing for the validity of the imposed functional form. Tests of restrictions on the functional form are similar to those testing for unobserved heterogeneity, where the restriction imposes no such heterogeneity. Nevertheless, it is often desirable to test for such heterogeneity, as this can bias the estimation of the hazard rate.〔 Cameron A. C. and P. K. Trivedi (2005): Microeconometrics: Methods and Applications. Cambridge University Press, New York.〕 Similarly, tests for censoring exist that compare the distribution of the generalized error under the censored and the uncensored assumption. 〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maximum likelihood estimation with flow data」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.