STEIN'S METHOD AND THE BERRY-ESSÉEN THEOREM

Stein's method is used to prove the Lindeberg-Feller theorem and a generalization of the Berry-Esséen theorem. The arguments involve only manipulation of probability inequalities, and form an attractive alternative to the less direct Fourier-analytic methods which are traditionally employed.     

The fiducial argument and hacking's principle of irrelevance

In a searching analysis of the fiducial argument Hacking (1965) proposed the Principle of Irrelevance as a condition under which the argument is valid. His statement of the Principle was essentially non-mathematical and this paper presents a mathematical development of the Principle. The relationship with likelihood inference is explored and some of the proposed counter-examples to fiducial theory are considered. It is shown that even with the Principle of Irrelevance examples of non-uniqueness of fiducial distributions exist.     

Nonparametric regression estimates with censored data based on block thresholding method

Here we consider wavelet-based identification and estimation of a censored nonparametric regression model via block thresholding methods and investigate their asymptotic convergence rates. We show that these estimators, based on block thresholding of empirical wavelet coefficients, achieve optimal convergence rates over a large range of Besov function classes, and in particular enjoy those rates without the extraneous logarithmic penalties that are usually suffered by term-by-term thresholding methods. This work is extension of results in Li et al. (2008). The performance of proposed estimator is investigated by a numerical study.     

Bayesian inference with misspecified models

This article reviews Bayesian inference from the perspective that the designated model is misspecified. This misspecification has implications in interpretation of objects, such as the prior distribution, which has been the cause of recent questioning of the appropriateness of Bayesian inference in this scenario. The main focus of this article is to establish the suitability of applying the Bayes update to a misspecified model, and relies on representation theorems for sequences of symmetric distributions; the identification of parameter values of interest; and the construction of sequences of distributions which act as the guesses as to where the next observation is coming from. A conclusion is that a clear identification of the fundamental starting point for the Bayesian is described.     

On the recoding of continuous and bounded indexes to a binomial form: an application to quality-of-life scores

The statistical analysis of patient-reported outcomes (PROs) as endpoints has shown to be of great practical relevance. The resulting scores or indexes from the questionnaires used to measure PROs could be treated as continuous or ordinal. The goal of this study is to propose and evaluate a recoding process of the scores, so that they can be treated as binomial outcomes and, therefore, analyzed using logistic regression with random effects. The general methodology of recoding is based on the observable values of the scores. In order to obtain an optimal recoding, the evaluation of the recoding method is tested for different values of the parameters of the binomial distribution and different probability distributions of the random effects. We illustrate, evaluate and validate the proposed method of recoding with the Short Form-36 (SF-36) Survey and real data. The optimal recoding approach is very useful and flexible. Moreover, it has a natural interpretation, not only for ordinal scores, but also for questionnaires with many dimensions and different profiles, where a common method of analysis is desired, such as the SF-36.     

A time-varying measurement error model for age of onset of a psychiatric diagnosis: applied to first depressive episode diagnosed by the Composite International Diagnostic Interview (CIDI)

A substantial degree of uncertainty exists surrounding the reconstruction of events based on memory recall. This form of measurement error affects the performance of structured interviews such as the Composite International Diagnostic Interview (CIDI), an important tool to assess mental health in the community. Measurement error probably explains the discrepancy in estimates between longitudinal studies with repeated assessments (the gold-standard), yielding approximately constant rates of depression, versus cross-sectional studies which often find increasing rates closer in time to the interview. Repeated assessments of current status (or recent history) are more reliable than reconstruction of a person's psychiatric history based on a single interview. In this paper, we demonstrate a method of estimating a time-varying measurement error distribution in the age of onset of an initial depressive episode, as diagnosed by the CIDI, based on an assumption regarding age-specific incidence rates. High-dimensional non-parametric estimation is achieved by the EM-algorithm with smoothing. The method is applied to data from a Norwegian mental health survey in 2000. The measurement error distribution changes dramatically from 1980 to 2000, with increasing variance and greater bias further away in time from the interview. Some influence of the measurement error on already published results is found.     

On a bounded bimodal two-sided distribution fitted to the Old-Faithful geyser data

In this paper, we shall develop a novel family of bimodal univariate distributions (also allowing for unimodal shapes) and demonstrate its use utilizing the well-known and almost classical data set involving durations and waiting times of eruptions of the Old-Faithful geyser in Yellowstone park. Specifically, we shall analyze the Old-Faithful data set with 272 data points provided in Dekking et al. [3]. In the process, we develop a bivariate distribution using a copula technique and compare its fit to a mixture of bivariate normal distributions also fitted to the same bivariate data set. We believe the fit-analysis and comparison is primarily illustrative from an educational perspective for distribution theory modelers, since in the process a variety of statistical techniques are demonstrated. We do not claim one model as preferred over the other.     

Decomposing the predictive performance of the moving average trading rule of technical analysis: the contribution of linear and non-linear dependencies in stock returns

The main purpose of this work is to decompose the predictive performance of the moving average (MA) trading rule and find out the portion that could be attributed to the possible exploitation of linear and non-linear dependencies in stock returns. Data from the General Index of the Athens Stock Exchange, from the Standard and Poor-500 Index of the New York Stock Exchange and from the Austrian Traded Index of the Vienna Stock Exchange are filtered by linear filters so as the resulting simulated ‘returns’ exhibit no serial correlation. Applying MA trading rules to both the original and the simulated indices and using a new statistical testing procedure that takes into account the sensitivity of the performance of the trading rule as a function of the length of the MA it is found that the predictive performance of the trading rule is clearly weakened when applied to the simulated indices indicating that a substantial part of the rule's predictive performance is due to the exploitation of linear dependencies in stock returns. This weakening is uneven; in general the shorter the MA length the more pronounced the attenuation.     

Robust location estimation with missing data

In a missing data setting, we have a sample in which a vector of explanatory variables ${\bf x}_i$ is observed for every subject i, while scalar responses $y_i$ are missing by happenstance on some individuals. In this work we propose robust estimators of the distribution of the responses assuming missing at random (MAR) data, under a semiparametric regression model. Our approach allows the consistent estimation of any weakly continuous functional of the response's distribution. In particular, strongly consistent estimators of any continuous location functional, such as the median, L‐functionals and M‐functionals, are proposed. A robust fit for the regression model combined with the robust properties of the location functional gives rise to a robust recipe for estimating the location parameter. Robustness is quantified through the breakdown point of the proposed procedure. The asymptotic distribution of the location estimators is also derived. The proofs of the theorems are presented in Supplementary Material available online. The Canadian Journal of Statistics 41: 111–132; 2013 © 2012 Statistical Society of Canada