Non-Parametric Identification and Estimation of the Number of Components in Multivariate Mixtures

Kasahara, Hiroyuki; Shimotsu, Katsumi

doi:10.1111/rssb.12022

Cited by 64 publications

(49 citation statements)

References 45 publications

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“…This is not true in the NLSY79 Cohort of the National Longitudinal Survey of Youth.3 SeeKasahara and Shimotsu (2014) andBonhomme et al (2016) for a discussion of this assumption Hu and Sasaki (2016). This is not true in the NLSY79 Cohort of the National Longitudinal Survey of Youth.3 SeeKasahara and Shimotsu (2014) andBonhomme et al (2016) for a discussion of this assumption Hu and Sasaki (2016).…”

mentioning

confidence: 99%

Finite mixture models with one exclusion restriction

Adams

2016

The Econometrics Journal

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This paper characterizes the identified set for finite mixture models with one exclusion restriction on the data-generating process. It provides necessary and sufficient conditions on the observed data for point identification and for when the identified set has measure zero. The results are illustrated in a simulation study and with data from a randomized controlled trial on chemotherapy for colon cancer as well as with data from an observational study used to estimate returns to schooling.

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confidence: 99%

Finite mixture models with one exclusion restriction

Adams

2016

The Econometrics Journal

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“…This result relates directly to a recent contribution of Kasahara and Shimotsu [2014]. Moreover, a consistent estimator of p is easily formed via a sequential-testing procedure based on infering the rank of an empirical analog of the P({i 1 , i 2 }).…”

Section: Givenmentioning

confidence: 84%

“…Such an approach would be in line with Allman, Matias and Rhodes [2009] and with Kasahara and Shimotsu [2014] but is not attractive for the construction of estimators. An alternative approach that has the advantage of yielding nice estimators is to consider a discretization in the frequency domain, as was recently done for a special case of (4.2) in Bonhomme, Jochmans and Robin [2013].…”

Section: Mixtures Of Continuous Measuresmentioning

confidence: 99%

Nonparametric spectral-based estimation of latent structures

Bonhomme¹,

Jochmans²,

Robin³

2014

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We present a constructive identification proof of p-linear decompositions of q-way arrays. The analysis is based on the joint spectral decomposition of a set of matrices. It has applications in the analysis of a variety of latent-structure models, such as q-variate mixtures of p distributions. As such, our results provide a constructive alternative to Allman, Matias and Rhodes [2009]. The identification argument suggests a joint approximate-diagonalization estimator that is easy to implement and whose asymptotic properties we derive. We illustrate the usefulness of our approach by applying it to nonparametrically estimate multivariate finite-mixture models and hidden Markov models. Terms of use: Documents in1. Introduction. Longitudinal data are since long known to be a powerful tool to establish the nonparametric identification of latent structures. Early results on the identifiability of multivariate finite mixtures of Bernouilli distributions were derived by Green [1951] and Anderson [1954], and have been extended by Kasahara and Shimotsu [2009]. More recently, Hall and Zhou [2003] showed that mixtures of two arbitary distributions are generally identified as soon as three measurements are available, provided the component distributions are linearly independent and the outcomes satisfy a conditional-independence restriction. Allman, Matias and Rhodes [2009] have demonstrated that this result carries over to mixtures of more components. Their approach can be applied to a more general class of latent structures that feature some form of conditional independence, such as hidden Markov models with finite state spaces (see Petrie [1969] for seminal work on this) and to random-graph models. We note that, although the availability of two measurements can suffice in problems featuring additive structures, the work of Henry, Kitamura and Salanié [2013] shows that two measurements will only deliver set-identification of parameters in more general latent-structure models. Li and Vuong [1998], Bordes, Mottelet andVandekerkhove [2006], and Gassiat and Rousseau [2013], among others, present results for additive models.The work of Allman, Matias and Rhodes [2009] builds heavily on algebraic results for multiway arrays due to Kruskal [1976;1977]. Although widely applicable, this approach is not constructive. Given identification, some authors have set out to develop methods to estimate latent structures. Benaglia, Chauveau and Hunter [2009] and Levine, Hunter and...

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“…Moreover, in the nonparametric context, there may be multiple K for which a decomposition as in (2.1) can be obtained. Kasahara and Shimotsu (2014) show that a lower bound on K is identified under weak conditions.…”

Section: Regime-switching Modelsmentioning

confidence: 89%

Nonparametric estimation of non-exchangeable latent-variable models

Bonhomme

Jochmans

Robin

2017

Journal of Econometrics

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We propose a two-step method to nonparametrically estimate multivariate models in which the observed outcomes are independent conditional on a discrete latent variable. Applications include microeconomet-ric models with unobserved types of agents, regime-switching models, and models with misclassification error. In the first step, we estimate weights that transform moments of the marginal distribution of the data into moments of the conditional distribution of the data for given values of the latent variable. In the second step, these conditional moments are estimated as weighted sample averages. We illustrate the method by estimating a model of wages with unobserved heterogeneity on PSID data.

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Non-Parametric Identification and Estimation of the Number of Components in Multivariate Mixtures

Cited by 64 publications

References 45 publications

Finite mixture models with one exclusion restriction

Finite mixture models with one exclusion restriction

Nonparametric spectral-based estimation of latent structures

Nonparametric estimation of non-exchangeable latent-variable models

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