Koen Jochmans

Estimating multivariate latent-structure models

A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden Markov models. The key step to show identification is the joint diagonalization of a set of matrices in the same non-orthogonal basis. An estimator of the latent-structure model may then be based on a sample version of this simultaneous-diagonalization problem. Simple algorithms are available for computation. Asymptotic theory is derived for this joint approximate-diagonalization estimator.

Inference on Mixtures Under Tail Restrictions

Two-component mixtures are nonparametrically identified under tail-dominance conditions on the component distributions if a source of variation is available that affects the mixing proportions but not the component distributions. We motivate these restrictions through several examples. One interesting example is a location model where the location parameter is subject to classical measurement error. The identification analysis suggests very simple closed-form estimators of the component distributions and mixing proportions based on ratios of intermediate quantiles. We derive their asymptotic properties using results on tail empirical processes, and we provide simulation evidence on their finite-sample performance.

LIKELIHOOD INFERENCE IN AN AUTOREGRESSION WITH FIXED EFFECTS

We calculate the bias of the profile score for the regression coefficients in a multistratum autoregressive model with stratum-specific intercepts. The bias is free of incidental parameters. Centering the profile score delivers an unbiased estimating equation and, upon integration, an adjusted profile likelihood. A variety of other approaches to constructing modified profile likelihoods are shown to yield equivalent results. However, the global maximizer of the adjusted likelihood lies at infinity for any sample size, and the adjusted profile score has multiple zeros. We argue that the parameters are local maximizers inside or on an ellipsoid centered at the maximum likelihood estimator.

Semiparametric Analysis of Network Formation

ABSTRACT We consider a statistical model for directed network formation that features both node-specific parameters that capture degree heterogeneity and common parameters that reflect homophily among nodes. The goal is to perform statistical inference on the homophily parameters while treating the node-specific parameters as fixed effects. Jointly estimating all parameters leads to incidental-parameter bias and incorrect inference. As an alternative, we develop an approach based on a sufficient statistic that separates inference on the homophily parameters from estimation of the fixed effects. The estimator is easy to compute and can be applied to both dense and sparse networks, and is shown to have desirable asymptotic properties under sequences of growing networks. We illustrate the improvements of this estimator over maximum likelihood and bias-corrected estimation in a series of numerical experiments. The technique is applied to explain the import and export patterns in a dense network of countries and to estimate a more sparse advice network among attorneys in a corporate law firm.

Inference On Two-Component Mixtures Under Tail Restrictions

Many econometric models can be analyzed as finite mixtures. We focus on two-component mixtures and we show that they are nonparametrically point identified by a combination of an exclusion restriction and tail restrictions. Our identification analysis suggests simple closed-form estimators of the component distributions and mixing proportions, as well as a specification test. We derive their asymptotic properties using results on tail empirical processes and we present a simulation study that documents their finite-sample performance.

Pairwise-comparison estimation with non-parametric controls

The purpose of this paper is the presentation of distribution theory for generic estimators based on the pairwise comparison of observations in problems where identification is achieved through the use of control functions. The controls can be specified semi- or non-parametrically. The criterion function may be non-smooth. The theory is applied to the estimation of the coefficients in a monotone linear-index model and to inference on the link function in a partially-linear transformation model. A number of simulation exercises serve to assess the small-sample performance of these techniques.