An invariance principle for triangular arrays of dependent variables with application to autocovariance estimation

The invariance principle for triangular arrays of dependent variables is studied. We use the concept of mixingale, proposed by McLeish (1975). Uniform bounds are imposed on the growth of conditional expectations with respect to distant predecessors. The theorem is applied to invariance principles for autocovariance estimates based on triangular arrays of time-series data for weak mixing sequences and linear processes. Such results are required for bootstrap applications.     

Optimal experiments in the presence of a learning effect: a problem suggested by software production

In software engineering empirical comparisons of different ways of writing computer code are often made. This leads to the need for planned experimentation and has recently established a new area of application of DoE. This paper is motivated by an experiment on the production of multimedia services on the web, performed at the Telecom Research Centre in Turin, where two different ways of developing code, with or without a framework, were compared. As the experiment progresses, the programmers performance improves as he/she undergoes a learning process; this must be taken into account as it may affect the outcome of the trial. In this paper we discuss statistical models and D-optimal plans for such experiments and indicate some heuristics which allow a much speedier search for the optimum. Solutions differ according to whether we assume that the learning process depends or not on the treatments.     

The Iowa Gambling Treatment Program: Treatment Outcomes for a Follow-up Sample

The Iowa Gambling Treatment Program (IGTP) amassed participant data for gamblers and concerned others of gamblers over 4 years (1997–2001). Data collection opportunities included: (1) crisis contacts, (2) placement screening, (3) admission, (4) treatment services, (5) discharge, and (6) follow-up. Among followed gamblers, 74% of treatment completers, 49% of substantial treatment completers, and 36% of dropouts and referrals were abstaining from gambling at 6-month follow-up. The reduction in dollars lost to gambling was similar; 85% of treatment completers, 88% of substantial treatment completers, and 65% of others reduced their dollars lost per week. Although more extensive follow-up efforts are needed to properly evaluate the effectiveness of the IGTP, these results suggest that the IGTP shows promise.     

The automatic percentile method: Accurate confidence limits in parametric models

The problem of constructing confidence limits for a scalar parameter is considered. Under weak conditions, Efron's accelerated bias-corrected bootstrap confidence limits are correct to second order in parametric familles. In this article, a new method, called the automatic percentile method, for setting approximate confidence limits is proposed as an attempt to alleviate two problems inherent in Efron's method. The accelerated bias-corrected method is not fully automatic, since it requires the calculation of an analytical adjustment; furthermore, it is typically not exact, though for many situations, particularly scalar-parameter familles, exact answers are available. In broader generality, the proposed method is exact when exact answers exist, and it is second-order accurate otherwise. The automatic percentile method is automatic, and for scalar parameter models it can be iterated to achieve higher accuracy, with the number of computations being linear in the number of iterations. However, when nuisance parameters are present, only second-order accuracy seems obtainable.     

Subsampling Intervals in Autoregressive Models with Linear Time Trend

A new method is proposed for constructing confidence intervals in autoregressive models with linear time trend. Interest focuses on the sum of the autoregressive coefficients because this parameter provides a useful scalar measure of the long‐run persistence properties of an economic time series. Since the type of the limiting distribution of the corresponding OLS estimator, as well as the rate of its convergence, depend in a discontinuous fashion upon whether the true parameter is less than one or equal to one (that is, trend‐stationary case or unit root case), the construction of confidence intervals is notoriously difficult. The crux of our method is to recompute the OLS estimator on smaller blocks of the observed data, according to the general subsampling idea of Politis and Romano (1994a), although some extensions of the standard theory are needed. The method is more general than previous approaches in that it works for arbitrary parameter values, but also because it allows the innovations to be a martingale difference sequence rather than i.i.d. Some simulation studies examine the finite sample performance.