Do Actions Speak Louder Than Words? Preschool Children's Use of the Verbal-Nonverbal Consistency Principle During Inconsistent Communications

The present study investigated whether preschool children could use the conventional actions speak louder than words principle (or the verbal-nonverbal consistency principle) to process information in situations where verbal cues contradict nonverbal cues. Three-, 4-, and 5-year-olds were shown a video in which an actor drank a beverage and made a verbal statement (e.g., I like it) that was inconsistent with her emotional expression (e.g., frowning), and were asked whether the actor liked or disliked the beverage. If children used the verbal-nonverbal consistency principle, they should respond according to the information conveyed by the actor's emotional expression. Results showed that when the message was more naturalistic, the majority of children tended to respond based on the actor's verbal message. However, when the inconsistency between the verbal and nonverbal messages was made salient, more children appeared to rely on the nonverbal cue. Younger children's reliance on verbal cues reported in previous research may be partly explained by the salience of the verbal message.     

Growth Curves with Explanatory Variables and Estimation of the Effect of Tagging

The von Bertalanffy growth model is extended to incorporate explanatory variables. The generalized model includes the switched growth model and the seasonal growth model as special cases, and can also be used to assess the tagging effect on growth. Distribution-free and consistent estimating functions are constructed for estimation of growth parameters from tag-recapture data in which age at release is unknown. This generalizes the work of James (1991, Biometrics 47 1519–1530) who considered the classical model and allowed for individual variability in growth. A real dataset from barramundi ( Lates calcarifer ) is analysed to estimate the growth parameters and possible effect of tagging on growth.     

Self‐consistent estimation of mean response functions and their derivatives

Many methods have been developed for the nonparametric estimation of a mean response function, but most of these methods do not lend themselves to simultaneous estimation of the mean response function and its derivatives. Recovering derivatives is important for analyzing human growth data, studying physical systems described by differential equations, and characterizing nanoparticles from scattering data. In this article the authors propose a new compound estimator that synthesizes information from numerous pointwise estimators indexed by a discrete set. Unlike spline and kernel smooths, the compound estimator is infinitely differentiable; unlike local regression smooths, the compound estimator is self‐consistent in that its derivatives estimate the derivatives of the mean response function. The authors show that the compound estimator and its derivatives can attain essentially optimal convergence rates in consistency. The authors also provide a filtration and extrapolation enhancement for finite samples, and the authors assess the empirical performance of the compound estimator and its derivatives via a simulation study and an application to real data. The Canadian Journal of Statistics 39: 280–299; 2011 © 2011 Statistical Society of Canada     

Posterior consistency of random effects models for binary data

In longitudinal studies or clustered designs, observations for each subject or cluster are dependent and exhibit intra-correlation. To account for this dependency, we consider Bayesian analysis for conditionally specified models, so-called generalized linear mixed model. In nonlinear mixed models, the maximum likelihood estimator of the regression coefficients is typically a function of the distribution of random effects, and so the misspecified choice of the distribution of random effects can cause bias in the estimator. To avoid the problem of the misspecification of the distribution of random effects, one can resort in nonparametric approaches. We give sufficient conditions for posterior consistency of the distribution of random effects as well as regression coefficients.     

Consistent Tests for Stochastic Dominance

Methods are proposed for testing stochastic dominance of any pre–specified order, with primary interest in the distributions of income. We consider consistent tests, that are similar to Kolmogorov–Smirnov tests, of the complete set of restrictions that relate to the various forms of stochastic dominance. For such tests, in the case of tests for stochastic dominance beyond first order, we propose and justify a variety of approaches to inference based on simulation and the bootstrap. We compare these approaches to one another and to alternative approaches based on multiple comparisons in the context of a Monte Carlo experiment and an empirical example.     

The Measurement of Intellectual Influence

This paper examines the problem of measuring intellectual influence based on data on citations between scholarly publications. We follow an axiomatic approach and find that the properties of invariance to reference intensity, weak homogeneity, weak consistency, and invariance to splitting of journals characterize a unique ranking method. This method is different from those regularly used in economics and other social sciences.     

Efficient Semiparametric Estimation of Censored and Truncated Regressions via a Smoothed Self‐Consistency Equation

An asymptotically efficient likelihood‐based semiparametric estimator is derived for the censored regression (tobit) model, based on a new approach for estimating the density function of the residuals in a partially observed regression. Smoothing the self‐consistency equation for the nonparametric maximum likelihood estimator of the distribution of the residuals yields an integral equation, which in some cases can be solved explicitly. The resulting estimated density is smooth enough to be used in a practical implementation of the profile likelihood estimator, but is sufficiently close to the nonparametric maximum likelihood estimator to allow estimation of the semiparametric efficient score. The parameter estimates obtained by solving the estimated score equations are then asymptotically efficient. A summary of analogous results for truncated regression is also given.     

New aspects of Bregman divergence in regression and classification with parametric and nonparametric estimation

In statistical learning, regression and classification concern different types of the output variables, and the predictive accuracy is quantified by different loss functions. This article explores new aspects of Bregman divergence (BD), a notion which unifies nearly all of the commonly used loss functions in regression and classification. The authors investigate the duality between BD and its generating function. They further establish, under the framework of BD, asymptotic consistency and normality of parametric and nonparametric regression estimators, derive the lower bound of their asymptotic covariance matrices, and demonstrate the role that parametric and nonparametric regression estimation play in the performance of classification procedures and related machine learning techniques. These theoretical results and new numerical evidence show that the choice of loss function affects estimation procedures, whereas has an asymptotically relatively negligible impact on classification performance. Applications of BD to statistical model building and selection with non‐Gaussian responses are also illustrated. The Canadian Journal of Statistics 37: 119‐139; 2009 © 2009 Statistical Society of Canada     

A weighted bootstrap approximation for comparing the error distributions in nonparametric regression

Several procedures have been proposed for testing the equality of error distributions in two or more nonparametric regression models. Here we deal with methods based on comparing estimators of the cumulative distribution function (CDF) of the errors in each population to an estimator of the common CDF under the null hypothesis. The null distribution of the associated test statistics has been approximated by means of a smooth bootstrap (SB) estimator. This paper proposes to approximate their null distribution through a weighted bootstrap. It is shown that it produces a consistent estimator. The finite sample performance of this approximation is assessed by means of a simulation study, where it is also compared to the SB. This study reveals that, from a computational point of view, the proposed approximation is more efficient than the one provided by the SB.     

Statistical Inference for Expectile‐based Risk Measures

Expectiles were introduced by Newey and Powell in 1987 in the context of linear regression models. Recently, Bellini et al. revealed that expectiles can also be seen as reasonable law‐invariant risk measures. In this article, we show that the corresponding statistical functionals are continuous w.r.t. the 1‐weak topology and suitably functionally differentiable. By means of these regularity results, we can derive several properties such as consistency, asymptotic normality, bootstrap consistency and qualitative robustness of the corresponding estimators in nonparametric and parametric statistical models.