Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment

Standard methods of estimation for autoregressive models are known to be biased in finite samples, which has implications for estimation, hypothesis testing, confidence interval construction and forecasting. Three methods of bias reduction are considered here: first-order bias correction, FOBC, where the total bias is approximated by the O(T^-1) bias; bootstrapping; and recursive mean adjustment, RMA. In addition, we show how first-order bias correction is related to linear bias correction. The practically important case where the AR model includes an unknown linear trend is considered in detail. The fidelity of nominal to actual coverage of confidence intervals is also assessed. A simulation study covers the AR(1) model and a number of extensions based on the empirical AR(p) models fitted by Nelson & Plosser (1982). Overall, which method dominates depends on the criterion adopted: bootstrapping tends to be the best at reducing bias, recursive mean adjustment is best at reducing mean squared error, whilst FOBC does particularly well in maintaining the fidelity of confidence intervals.     

The muse as mother

This paper suggests that the concept of the muse in relation to the creative process is more than a myth or cultural artifact. It is argued that the muse is a psychic recollection of our memories of the female who presided over our first experiences of consciousness as we traversed the borders of inner and outer reality—that is, the mother. The shift of consciousness required in creative activity triggers recall of this figure. Object relations theory, recent findings from infant research, and the intuitive observations of several authors are used to support this thesis. Clinical examples illustrate the application of this concept in treatment.     

Testing parameter of the power series distribution of a zero inflated power series model

The Zero Inflated Power Series Distribution (ZIPSD) contains two parameters. The first parameter indicates inflation of zero and the other parameter is that of the Power Series distribution. We provide three asymptotic tests for testing the parameter of Power Series distribution, using an unconditional (standard) likelihood approach, a conditional likelihood approach and a test based on sample mean, respectively. The performance of these three tests has been studied for Zero Inflated Poisson Distribution (ZIPD). Asymptotic Confidence Intervals for the parameter are also provided.     

Transformations for Smooth Regression Models with Multiplicative Errors

We consider whether one should transform to estimate nonparametrically a regression curve sampled from data with a constant coefficient of variation, i.e. with multiplicative errors. Kernel-based smoothing methods are used to provide curve estimates from the data both in the original units and after transformation. Comparisons are based on the mean-squared error (MSE) or mean integrated squared error (MISE), calculated in the original units. Even when the data are generated by the simplest multiplicative error model, the asymptotically optimal MSE (or MISE) is surprisingly not always obtained by smoothing transformed data, but in many cases by directly smoothing the original data. Which method is optimal depends on both the regression curve and the distribution of the errors. Data-based procedures which could be useful in choosing between transforming and not transforming a particular data set are discussed. The results are illustrated on simulated and real data.     

Point and confidence interval estimates for a global maximum via extreme value theory

The aim of this paper is to provide some practical aspects of point and interval estimates of the global maximum of a function using extreme value theory. Consider a real-valued function f:D→? defined on a bounded interval D such that f is either not known analytically or is known analytically but has rather a complicated analytic form. We assume that f possesses a global maximum attained, say, at u*∈D with maximal value x*=max _u  f(u)?f(u*). The problem of seeking the optimum of a function which is more or less unknown to the observer has resulted in the development of a large variety of search techniques. In this paper we use the extreme-value approach as appears in Dekkers et al. [A moment estimator for the index of an extreme-value distribution, Ann. Statist. 17 (1989), pp. 1833–1855] and de Haan [Estimation of the minimum of a function using order statistics, J. Amer. Statist. Assoc. 76 (1981), pp. 467–469]. We impose some Lipschitz conditions on the functions being investigated and through repeated simulation-based samplings, we provide various practical interpretations of the parameters involved as well as point and interval estimates for x*.     

Posterior consistency of logistic Gaussian process priors in density estimation

We establish weak and strong posterior consistency of Gaussian process priors studied by Lenk [1988. The logistic normal distribution for Bayesian, nonparametric, predictive densities. J. Amer. Statist. Assoc. 83 (402), 509–516] for density estimation. Weak consistency is related to the support of a Gaussian process in the sup-norm topology which is explicitly identified for many covariance kernels. In fact we show that this support is the space of all continuous functions when the usual covariance kernels are chosen and an appropriate prior is used on the smoothing parameters of the covariance kernel. We then show that a large class of Gaussian process priors achieve weak as well as strong posterior consistency (under some regularity conditions) at true densities that are either continuous or piecewise continuous.     

A Conversation With Virus X: Outing a Malevolent and Subversive Force in Parents' Lives

The following conversation describes a narrative means of uncovering (or ‘deconstructing’) some of the invisible forces that undermine parents' capacities in caring for their children in preferred ways. In the authors' experience, parents can be hugely resourceful and provide a clear account of what they ‘should’ be doing, yet seem unable to act upon their own good advice — it is as though an external agent, named below as ‘Virus X’, prevents them from being the parents they would like to be. Through naming this external agent, identifying its influences and noticing parents' acts of resistance in the face of these influences, antidotes to Virus X can be developed. This paper describes the development of such an approach within a child behaviour management group. In keeping with the playful approach encouraged by narrative therapy, the authors of this paper join forces to act as investigative journalists in exposing Virus X to the readers.     

The Return of Non‐DAC Donors to Africa: New Prospects for African Development?

This article examines the consequences of the return to Africa of donors that are not members of the OECD's Development Assistance Committee (DAC). It categorises these donors according to form, content, size and modality of their aid. It finds that their return increases external financial flows, in particular to countries not targeted by DAC donors. Moreover, for some donors like China and India the flows are closely related to other financial flow s such as trade and investment. Furthermore, it finds that the return of non‐DAC donors may conflict with plans to harmonise aid and may simultaneously raise transaction costs for recipients.