Thomas Mikosch (University of Copenhagen)
19 January 2017**CANCELED**
The auto- and cross-distance correlation functions of a multivariate time series and their sample versions
Feuerverger (1993) and Székely, Rizzo and Bakirov (2007) introduced the notion of distance covariance/correlation as a measure of independence/dependence between two vectors of arbitrary dimension and provided limit theory for the sample versions based on an i.i.d. sequence. The main idea is to use characteristic functions to test for independence between vectors, using the standard property that the characteristic function of two independent vectors factorizes. Distance covariance is a weighted version of the squared distance between the joint characteristic function of the vectors and the product of their marginal characteristic functions. Similar ideas have been used in the literature for various purposes: goodness-of-fit tests, change point detection, testing for independence of variables, etc; see work by Meintanis, Huškova, and many others. In contrast to Székely et al. who use a weight function which is infinite on the axes, the latter authors choose probability density weights. Z. Zhou (2012) extended distance correlation to time series models for testing dependence/independence in a time series at a given lag. He assumed a “ physical dependence measure''. In our work we consider the distance covariance/correlation for general weight measures, finite or infinite on the axes or at the origin. These include the choice of Székely et al., probability and various Lévy measures. The sample versions of distance covariance/correlation are obtained by replacing the characteristic functions by their sample versions. We show consistency under ergodicity and weak convergence to an unfamiliar limit distribution of the scaled auto- and cross-distance covariance/correlation functions under strong mixing. We also study the auto-distance correlation function of the residual process of an autoregressive process. The limit theory is distinct from the corresponding theory of an i.i.d. noise process. We illustrate the theory for simulated and real data examples.
Kirill Evdokimov (Princeton University)
16 March 2017
Efficient Estimation with a Finite Number of Simulation Draws per Observation
In microeconometric applications, simulation methods such as the Method of Simulated Moments (MSM) and Indirect Inference (II) typically provide consistent and asymptotically normal estimators when a finite number of simulation draws per observation is used. However, these estimators are inefficient, unless the number of simulation draws per observation is large (theoretically, infinite). This paper argues that this inefficiency can be attributed to the standard estimators ignoring important information about the estimation problem. The paper proves that asymptotically efficient estimation is possible with as little as one simulation draw per observation, as long as the estimators make proper use of the available information. Moreover, such efficient estimators can be taken to be simple modifications of the standard MSM and II estimators with nearly no additional computational or programming burden. In practice, the possibility of using just one simulation draw per observation could significantly reduce the estimation time for models, in which evaluation at each simulation draw and parameter value is time-consuming. This in particular includes models that require numerical computation of an optimal choice, decision, or equilibrium for each simulation draw. Such models are widespread in empirical microeconomics, including industrial organization and labor economics. To establish the properties of the new estimators, the paper develops an asymptotic theory of estimation and inference in (possibly non-smooth) moment condition models with a large number of moments. This asymptotic theory covers both the extremum and quasi-Bayesian estimators.
Zhipeng Liao (UCLA)
6 April 2017
A Uniform Vuong Test for Semi/Nonparametric Models
This paper proposes a new Vuong test for the statistical comparison of semi/non-parametric models based on a general quasi-likelihood ratio criterion. An important feature of the new test is its uniformly exact asymptotic size in the overlapping nonnested case, as well as in the easier nested and strictly nonnested cases. The uniform size control is achieved without using pretesting, sample-splitting, or simulated critical values. We also show that the test has nontrivial power against all ƴn-local alternatives and against some local alternatives that converge to the null faster than ƴn. Finally, we provide a framework for conducting uniformly valid post Vuong test inference for model parameters. The finite sample performance of the uniform test and that of the post Vuong test inference procedure are illustrated in a mean-regression example by Monte Carlo.
Co-Author Xiaoxia Shi
Drew Creal (University of Chicago)
20 April 2017
Liangjun Su (Singarpore Management University)
4 May 2017
Martin Weidner (UCL)
30 May 2017