Review of the Stata statistical package

Statistics and Computing -     

Almost nonparametric inference for repeated measures in mixture models

We consider ways to estimate the mixing proportions in a finite mixture distribution or to estimate the number of components of the mixture distribution without making parametric assumptions about the component distributions. We require a vector of observations on each subject. This vector is mapped into a vector of 0s and 1s and summed. The resulting distribution of sums can be modelled as a mixture of binomials. We then work with the binomial mixture. The efficiency and robustness of this method are compared with the strategy of assuming multivariate normal mixtures when, typically, the true underlying mixture distribution is different. It is shown that in many cases the approach based on simple binomial mixtures is superior.     

A multi-resolution census algorithm for calculating vortex statistics in turbulent flows

Summary.  The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than extract the coherent portion of the image from the background variation, as in the classical signal-plus-noise model, we present a model for individual vortices using the non-decimated discrete wavelet transform. A template image, which is supplied by the user, provides the features to be extracted from the vorticity field. By transforming the vortex template into the wavelet domain, specific characteristics that are present in the template, such as size and symmetry, are broken down into components that are associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the vorticity field in the wavelet domain. Since all levels of the template decomposition may be used to model each level in the field decomposition, the resulting model need not be identical to the template. Application to a vortex census algorithm that records quantities of interest (such as size, peak amplitude and circulation) as the vorticity field evolves is given. The multiresolution census algorithm extracts coherent structures of all shapes and sizes in simulated vorticity fields and can reproduce known physical scaling laws when processing a set of vorticity fields that evolve over time.     

Concomitant record ranked set sampling

In this work, we define a new method of ranked set sampling (RSS) which is suitable when the characteristic (variable) Y of primary interest on the units is jointly distributed with an auxiliary characteristic X on which one can take its measurement on any number of units, so that units having record values on X alone are ranked and retained for making measurement on Y. We name this RSS as concomitant record ranked set sampling (CRRSS). We propose estimators of the parameters associated with the variable Y of primary interest based on observations of the proposed CRRSS which are applicable to a very large class of distributions viz. Morgenstern family of distributions. We illustrate the application of CRRSS and our estimation technique of parameters, when the basic distribution is Morgenstern-type bivariate logistic distribution. A primary data collected by CRRSS method is demonstrated and the obtained data used to illustrate the results developed in this work.     

Business-Cycle Analysis With a Markov-Switching Model

This article explores the Hamilton Markov-switching model through an analysis of the business cycles of eight developed market economies. Forecasting and specification tests suggest only marginal improvements over linear autoregressive models. Yet filtered and smoothed conditional probabilities indicate turning points in business cycles that closely correlate with turning points from traditional methods. Tests regarding the asymmetry of business cycles reject the null of symmetry for most countries.     

Markov-switching generalized additive models

We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for nonparametrically estimating the functional form of the effect of the covariates in such a regression model, assuming an additive structure of the predictor. The resulting class of Markov-switching generalized additive models is immensely flexible, and contains as special cases the common parametric Markov-switching regression models and also generalized additive and generalized linear models. The feasibility of the suggested maximum penalized likelihood approach is demonstrated by simulation. We further illustrate the approach using two real data applications, modelling (i) how sales data depend on advertising spending and (ii) how energy price in Spain depends on the Euro/Dollar exchange rate.     

Penalized likelihood and Bayesian function selection in regression models

Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive predictors has been considered only more recently. Several competing suggestions have been developed at about the same time and often do not refer to each other. This article provides a state-of-the-art review on function selection, focusing on penalized likelihood and Bayesian concepts, relating various approaches to each other in a unified framework. In an empirical comparison, also including boosting, we evaluate several methods through applications to simulated and real data, thereby providing some guidance on their performance in practice.     

Weak Identification in Fuzzy Regression Discontinuity Designs

In fuzzy regression discontinuity (FRD) designs, the treatment effect is identified through a discontinuity in the conditional probability of treatment assignment. We show that when identification is weak (i.e., when the discontinuity is of a small magnitude), the usual t-test based on the FRD estimator and its standard error suffers from asymptotic size distortions as in a standard instrumental variables setting. This problem can be especially severe in the FRD setting since only observations close to the discontinuity are useful for estimating the treatment effect. To eliminate those size distortions, we propose a modified t-statistic that uses a null-restricted version of the standard error of the FRD estimator. Simple and asymptotically valid confidence sets for the treatment effect can be also constructed using this null-restricted standard error. An extension to testing for constancy of the regression discontinuity effect across covariates is also discussed. Supplementary materials for this article are available online.