The foundations of econometrics-are there any

The conclusions of alogically consistent economic theory which strictly adheres to Aristotle's axioms of logic are factually true if its sufficient conditions are all factually true. Alternatively, if a conclusion of such a theory is false, then at- least one of its assumptions is false. Unfortunately, the factual truth of sufficient conditions cannot be established because the problem of induction i s impossible t o solve. It is algo true that the falsity of a conclusion cannot be established in the presence of uncertainty. While the philosophy of instrumentalism applied to sufficient and logically consistent explanations may provide useful solutions to immediate practical problems, the principles of simplicity, parsimony and profligacy--all of them requiring conditional deductive arguments--are useless as criteria for model choice.     

GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar–Fisz transform

Summary.  We consider the stochastic mechanisms behind the data that were collected by the solar X-ray sensor (XRS) on board the GOES-8 satellite. We discover and justify a non-trivial mean–variance relationship within the XRS data. Transforming such data so that their variance is stable and its distribution is taken closer to the Gaussian distribution is the aim of many techniques (e.g. Anscombe and Box–Cox). Recently, new techniques based on the Haar–Fisz transform have been introduced that use a multiscale method to transform and stabilize data with a known mean–variance relationship. In many practical cases, such as the XRS data, the variance of the data can be assumed to increase with the mean, but other characteristics of the distribution are unknown. We introduce a method, the data-driven Haar–Fisz transform, which uses the Haar–Fisz transform but also estimates the mean–variance relationship. For known noise distributions, the data-driven Haar–Fisz transform is shown to be competitive with the fixed Haar–Fisz methods. We show how our data-driven Haar–Fisz transform method denoises the XRS series where other existing methods fail.     

Feature significance in generalized additive models

This paper develops inference for the significance of features such as peaks and valleys observed in additive modeling through an extension of the SiZer-type methodology of Chaudhuri and Marron (1999) and Godtliebsen et al. (2002, 2004) to the case where the outcome is discrete. We consider the problem of determining the significance of features such as peaks or valleys in observed covariate effects both for the case of additive modeling where the main predictor of interest is univariate as well as the problem of studying the significance of features such as peaks, inclines, ridges and valleys when the main predictor of interest is geographical location. We work with low rank radial spline smoothers to allow to the handling of sparse designs and large sample sizes. Reducing the problem to a Generalised Linear Mixed Model (GLMM) framework enables derivation of simulation-based critical value approximations and guards against the problem of multiple inferences over a range of predictor values. Such a reduction also allows for easy adjustment for confounders including those which have an unknown or complex effect on the outcome. A simulation study indicates that our method has satisfactory power. Finally, we illustrate our methodology on several data sets.     

Model-based clustering for social networks

Summary.  Network models are widely used to represent relations between interacting units or actors. Network data often exhibit transitivity, meaning that two actors that have ties to a third actor are more likely to be tied than actors that do not, homophily by attributes of the actors or dyads, and clustering. Interest often focuses on finding clusters of actors or ties, and the number of groups in the data is typically unknown. We propose a new model, the latent position cluster model , under which the probability of a tie between two actors depends on the distance between them in an unobserved Euclidean 'social space', and the actors' locations in the latent social space arise from a mixture of distributions, each corresponding to a cluster. We propose two estimation methods: a two-stage maximum likelihood method and a fully Bayesian method that uses Markov chain Monte Carlo sampling. The former is quicker and simpler, but the latter performs better. We also propose a Bayesian way of determining the number of clusters that are present by using approximate conditional Bayes factors. Our model represents transitivity, homophily by attributes and clustering simultaneously and does not require the number of clusters to be known. The model makes it easy to simulate realistic networks with clustering, which are potentially useful as inputs to models of more complex systems of which the network is part, such as epidemic models of infectious disease. We apply the model to two networks of social relations. A free software package in the R statistical language, latentnet, is available to analyse data by using the model.     

Identity for the NPMLE in Censored Data Models

We derive an identity for nonparametric maximum likelihood estimators (NPMLE) and regularized MLEs in censored data models which expresses the standardized maximum likelihood estimator in terms of the standardized empirical process. This identity provides an effective starting point in proving both consistency and efficiency of NPMLE and regularized MLE. The identity and corresponding method for proving efficiency is illustrated for the NPMLE in the univariate right-censored data model, the regularized MLE in the current status data model and for an implicit NPMLE based on a mixture of right-censored and current status data. Furthermore, a general algorithm for estimation of the limiting variance of the NPMLE is provided. This revised version was published online in July 2006 with corrections to the Cover Date.     

NONPARAMETRIC AUTOCOVARIANCE FUNCTION ESTIMATION

Nonparametric estimators of autocovariance functions for non-stationary time series are developed. The estimators are based on straightforward nonparametric mean function estimation ideas and allow use of any linear smoother (e.g. smoothing spline, local polynomial). The paper studies the properties of the estimators, and illustrates their usefulness through application to some meteorological and seismic time series.     

Measuring the complexity of generalized linear hierarchical models

Measuring a statistical model's complexity is important for model criticism and comparison. However, it is unclear how to do this for hierarchical models due to uncertainty about how to count the random effects. The authors develop a complexity measure for generalized linear hierarchical models based on linear model theory. They demonstrate the new measure for binomial and Poisson observables modeled using various hierarchical structures, including a longitudinal model and an areal‐data model having both spatial clustering and pure heterogeneity random effects. They compare their new measure to a Bayesian index of model complexity, the effective number p_D of parameters (Spiegelhalter, Best, Carlin & van der Linde 2002); the comparisons are made in the binomial and Poisson cases via simulation and two real data examples. The two measures are usually close, but differ markedly in some instances where p_D is arguably inappropriate. Finally, the authors show how the new measure can be used to approach the difficult task of specifying prior distributions for variance components, and in the process cast further doubt on the commonly‐used vague inverse gamma prior.     

Informing the Public About Uncertain Risks

Many problems arise in connection with the communication of risk information. In this article the content of the information communicated is taken as a starting-point for analyzing the risk communication process. We studied the way in which authorities communicated health risks to local residents in Dutch soil pollution situations and found that communication problems were characterized more by misunderstanding and conflict between parties with different views and interests than by a lack of understanding. Therefore, it is important to look more closely at the way the communicators of information (in our cases, officials) select risk information from risk assessments, and to study the effects that the information selected has on the receivers (in our cases, residents). Both the process of selection by the officials and the process of interpretation by the residents will be shown to be influenced by the different institutional backgrounds. The article presents a new approach to risk communication. Both the risk information presented by the authorities and the public reactions to this risk information are considered to reflect the institutional background of authorities and residents, and can be analyzed in these terms. Such an approach has consequences for the study of risk communication and the manner in which it is practiced.