Some properties of tests for parameters that can be arbitrarily close to being unidentified

Confidence intervals for parameters that can be arbitrarily close to being unidentified are unbounded with positive probability [e.g. Dufour, J.-M., 1997. Some impossibility theorems in econometrics with applications to instrumental variables and dynamic models. Econometrica 65, 1365–1388; Pfanzagl, J. 1998. The nonexistence of confidence sets for discontinuous functionals. Journal of Statistical Planning and Inference 75, 9–20], and the asymptotic risks of their estimators are unbounded [Pötscher, B.M., 2002. Lower risk bounds and properties of confidence sets for ill-posed estimation problems with applications to spectral density and persistence estimation, unit roots, and estimation of long memory parameters. Econometrica 70, 1035–1065]. We extend these “impossibility results” and show that all tests of size α concerning parameters that can be arbitrarily close to being unidentified have power that can be as small as α for any sample size even if the null and the alternative hypotheses are not adjacent. The results are proved for a very general framework that contains commonly used models.     

Noninformative priors for the normal variance ratio

In this paper, we consider noninformative priors for the ratio of variances in two normal populations. We develop first and second order matching priors. We find that the second order matching prior matches alternative coverage probabilities up to the second order and is also a HPD matching prior. It turns out that among the reference priors, only one-at-a-time reference prior satisfies a second order matching criterion. Our simulation study indicates that the one-at-a-time reference prior performs better than other reference priors in terms of matching the target coverage probabilities in a frequentist sense. This work is supported by Korea Research Foundation Grant (KRF-2004-002-C00041).     

A Bayesian approach to non-parametric monotone function estimation

Summary.  The paper proposes two Bayesian approaches to non-parametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay that allows unconstrained estimation. The second approach uses a Bayesian regression spline model of Smith and Kohn with a mixture distribution of constrained normal distributions as the prior for the regression coefficients to ensure the monotonicity of the resulting function estimate. The small sample properties of the two function estimators across a range of functions are provided via simulation and compared with existing methods. Asymptotic results are also given that show that Bayesian methods provide consistent function estimators for a large class of smooth functions. An example is provided involving economic demand functions that illustrates the application of the constrained regression spline estimator in the context of a multiple-regression model where two functions are constrained to be monotone.     

A queuing-theory-based approach to evaluate the efficiency of a network of automated stations and of a communication system

The Regional Meteorological Service for the Emilia-Romagna Region manages a network of automatic weather stations equipped with electronic sensors suitable for measuring meteorological parameters. The automatic stations consist of electronic instruments, which are subject to failures at more or less frequent intervals. A summary of their performance is necessary. In this paper, we compare the results of the summary, such as the contiguous absence or simultaneous inactivity of different stations, with theoretical simulations in order to evaluate the nature and recurrence of the failures. A single- and multi-server queue simulation model was also used to evaluate the performance of the data transmission system, so as to optimize the communications system.     

A note on modelling underreported Poisson counts

In this paper we present a parsimonious model for the analysis of underreported Poisson count data. In contrast to previously developed methods, we are able to derive analytic expressions for the key marginal posterior distributions that are of interest. The usefulness of this model is explored via a re-examination of previously analysed data covering the purchasing of port wine (Ramos, 1999).     

Shrinkage Structure of Partial Least Squares

Partial least squares regression (PLS) is one method to estimate parameters in a linear model when predictor variables are nearly collinear. One way to characterize PLS is in terms of the scaling (shrinkage or expansion) along each eigenvector of the predictor correlation matrix. This characterization is useful in providing a link between PLS and other shrinkage estimators, such as principal components regression (PCR) and ridge regression (RR), thus facilitating a direct comparison of PLS with these methods. This paper gives a detailed analysis of the shrinkage structure of PLS, and several new results are presented regarding the nature and extent of shrinkage.     

GNR, MGR, and exact misspeclfication testing

The Gauss-Newton regression (GNR) is widely used to compute Lagrange multiplier statistics. A regression described by Milliken and Graybill yields an exact F test in a certain class of nonlinear models which are linear under the null. This paper shows that the Milliken-Graybill regression is a GNR. Hence one interpretation of Milliken-Graybill is that they identified a class of nonlinear models for which the GNR yields an exact test.     

Risk of Disclosure, Perceptions of Risk, and Concerns about Privacy and Confidentiality as Factors in Survey Participation

This article reports on a web-based vignette experiment investigating how likely subjects would be to participate in surveys varying in topic sensitivity and risk of disclosure. A total of 3,672 participants each responded to a series of eight vignettes, along with a variety of background questions, concerns about confidentiality, trust in various institutions, and the like.Vignettes were randomly assigned to respondents, such that each respondent was exposed to four levels of disclosure risk for each level of topic sensitivity (high versus low). Half the sample was assigned to receive a confidentiality statement for all eight vignettes, while the other half received no mention of confidentiality in the vignettes. The order of presentation of vignettes was randomized for each respondent.Respondents were also asked for their subjective perceptions of risk, harm, and social as well as personal benefits for one of the eight vignettes. Adding these questions permits us to examine how objective risk information presented by the researcher relates to the subjective perception of risk by the participant, and to assess the importance of both for their willingness to participate in the surveys described.Under conditions resembling those of real surveys, objective risk information does not affect willingness to participate. On the other hand, topic sensitivity does have such effects, as do general attitudes toward privacy and survey organizations as well as subjective perceptions of risk, harm, and benefits. We discuss the limitations and implications of these findings.