Lori A. Thombs

Bootstrap Prediction Intervals for Autoregression

Abstract The nonparametric bootstrap is applied to the problem of prediction in autoregression. Let {Y t : t = 0, ±1, ±2, …} be a stationary autoregressive process of known order p [AR(p)]. Given a realization of the series up to time t, (y 1, y 2, …., y t ), a 100β% prediction interval for Y t+k is desired. Standard forecasting techniques, which assume that the error sequence of the process {Y t } is Gaussian, rely on the fact that the conditional distribution of Y t+k , given the data, is Gaussian as well. As a nonparametric alternative, the bootstrap provides an estimate of the conditional distribution of Y t+k . The method is similar to other applications of the bootstrap for linear models, because the residuals are resampled. The proposed methodology represents a different approach, since an alternative representation for AR(p) series is used, allowing for bootstrap replicates generated backward in time. It follows that the resulting replicates all have the same conditionally fixed values at the end ...

Inference for Autocorrelations under Weak Assumptions

Abstract In this article we consider the large-sample behavior of estimates of autocorrelations and autoregressive moving average (ARMA) coefficients, as well as their distributions, under weak conditions. Specifically, the usual text book formulas for variances of these estimates are based on strong assumptions and should not be routinely applied without careful consideration. Such is the case when the time series follows an ARMA process with uncorrelated innovations that may not be assumed to be independent and identically distributed. As a specific case, it is well known that if the process is independent and identically distributed, then the sample autocorrelation estimates, scaled by the square root of the sample size, are asymptotically standard normal. This result is used extensively as a diagnostic check on the residuals of a fitted model, or as an initial test on the observed time series to determine whether further model fitting is warranted. In this article we show that this result can be quite...

Spectral characteristics of aging postural control

Abstract The purpose of this study was to apply techniques of spectral analysis to the study of postural control and determine if aging results in changes to spectral parameters obtained from postural forces. Subjects were young adults and elderly who live independently and had no difficulty performing tasks of daily living. Ground reaction forces were obtained from a measurement plat-form during repeated trials of static standing. Forces were analyzed using spectral analysis and selected parameters (central tendency and dispersion) were extracted from averaged spectral data. Significant differences were observed between age groups in all parameters extracted from spectra obtained from medial-lateral postural forces. Similar results were not obtained for data in the anterior-posterior direction. Results suggest that aging affects the spectral characteristics of postural forces used to maintain stability in the m-l direction.

Effects Of Seat‐Surface Inclination On Postural Stability And Function Of The Upper Extremities Of Children With Cerebral Palsy

This study investigated the effects of seat‐surface inclination on parameters of postural stability and functional use of the upper extremity. 10 non‐impaired children and 10 children with cerebral palsy, aged between four and 15 years, were studied. Seat‐suface inclinations of 0d̀, 5d̀ anteriorly and 5d̀ posteriorly were used as the experimental conditions. Significant differences were observed on most dependent measures between the two groups. The results suggest that anteriorly tilting the seats of children with cerebral palsy may disturb postural stability, without improving performance of the upper extremity.

Spectral characteristics of ageing postural control

Abstract The purpose of this study was to apply techniques of spectral analysis to the study of postural control and determine if ageing results in changes to spectral parameters obtained from postural forces. Subjects were young adults and elderly who live independently and had no difficulty performing tasks of daily living. Ground reaction forces were obtained from a measurement platform during repeated trials of static standing. Forces were analysed using spectral analysis and selected parameters (central tendency and dispersion) were extracted from averaged spectral data. Significant differences were observed between age groups in all parameters extracted from spectra obtained from medial-lateral postural forces. Similar results were not obtained for data in the anterior-posterior direction. Results suggest that ageing affects the spectral characteristics of postural forces used to maintain stability in the m-I direction.

A Dynamic Programming Based Pruning Method for Decision Trees

This paper concerns a decision-tree pruning method, a key issue in the development of decision trees. We propose a new method that applies the classical optimization technique, dynamic programming, to a decision-tree pruning procedure. We show that the proposed method generates a sequence of pruned trees that are optimal with respect to tree size. The dynamic-programming-based pruning (DPP) algorithm is then compared with cost-complexity pruning (CCP) in an experimental study. The results of our study indicate that DPP performs better than CCP in terms of classification accuracy.

Control charts for detecting cyclical behavior

One way that a process can be out of statistical control is that the process mean can follow a cyclical pattern over time. This out-of-control condition leads to increased variability in the variable of interest over any production interval. Recently, a control chart based on a common time series technique, the periodogram, was proposed as a means of detecting cyclical behavior of the process mean. We show that this control chart is not able to detect certain periodicities and that it does not make use of all available information when multiple observations are taken at each sampling time. Using a multiple regression approach, we present modifications of the periodogram approach that produce control charts sensitive to a wider range of periodicities and use all available information. We compare the average run lengths of the procedures.

Spectral signature of forces to discriminate perturbations in standing posture

This study proposes a methodology for the collection and analysis of the spectral characteristics of human movement patterns. Specifically, the purpose of this study was to determine the reliability of the spectral signature obtained from postural forces and the usefulness of the technique in identifying perturbations in standing posture. Data collected included trials of the experimental protocol under normal standing conditions and under three experimental conditions designed to perturb stability. Results of this investigation indicated that spectral signatures created from ground forces using the methodology proposed in this study were highly reliable within individuals and across different testing sessions. These data further indicate that spectral signatures obtained from ground reaction forces during standing provide a sensitive indicator of an individuals postural stability.

Local Bandwidth Selection for Density Estimation

The problem of choosing a local value of the bandwidth h for a kernel density estimate is considered. Estimates of the density f at a given point are needed in the estimation of the asymptotic standard error or sample quantiles and in some kernel regression estimators based on random design points. The value of the bandwidth that minimizes the asymptotic MSE of the kernel estimate at the point x involves both f(x) and f″(x). In this paper we show that the “solve-the-equation” bandwidth selection method of Sheather (1986) produces an estimate of the asymptotically optimal h which has relative rate of convergence of n-2/9. We also show how higher order kernel estimates of f″ can be used to improve this rate to n-2/5. How much reliance can be placed on these theoretical results is investigated through a simulation study which compares the performance of a number of different selection methods

Elementary statistics laboratory

Students in elementary statistics traditionally see experiments and data as words and numbers in a text. They receive little exposure to the important statistical activities of sample selection, data collection, experimental design, development of statistical models, the need for randomization, selection of factors, etc. They often leave the first course without a firm understanding of the role of applied statistics or of the statistician in scientific investigations. In an attempt to improve elementary statistics education, we have developed a statistics laboratory similar to those of other elementary science courses. We will discuss our experiences in teaching a laboratory component with the traditional elementary statistics course. In each lab session, students, working in teams, discuss the design of an experiment, carry out the experiment, and analyze their data using Minitab on a Macintosh or MS-DOS based computer. The students then individually either answer a series of short answer questions or wr...