Likelihood-based Imprecise Regression

We introduce a new approach to regression with imprecisely observed data, combining likelihood inference with ideas from imprecise probability theory, and thereby taking different kinds of uncertainty into account. The approach is very general and applicable to various kinds of imprecise data, not only to intervals. In the present paper, we propose a regression method based on this approach, where no parametric distributional assumption is needed and interval estimates of quantiles of the error distribution are used to identify plausible descriptions of the relationship of interest. Therefore, the proposed regression method is very robust. We apply our robust regression method to an interesting question in the social sciences. The analysis, based on survey data, yields a relatively imprecise result, reflecting the high amount of uncertainty inherent in the analyzed data set

Different distance measures for fuzzy linear regression with Monte Carlo methods

The aim of this study was to determine the best distance measure for estimating the fuzzy linear regression model parameters with Monte Carlo (MC) methods. It is pointed out that only one distance measure is used for fuzzy linear regression with MC methods within the literature. Therefore, three different definitions of distance measure between two fuzzy numbers are introduced. Estimation accuracies of existing and proposed distance measures are explored with the simulation study. Distance measures are compared to each other in terms of estimation accuracy; hence this study demonstrates that the best distance measures to estimate fuzzy linear regression model parameters with MC methods are the distance measures defined by Kaufmann and Gupta (Introduction to fuzzy arithmetic theory and applications. Van Nostrand Reinhold, New York, 1991), Heilpern-2 (Fuzzy Sets Syst 91(2):259–268, 1997) and Chen and Hsieh (Aust J Intell Inf Process Syst 6(4):217–229, 2000). One the other hand, the worst distance measure is the distance measure used by Abdalla and Buckley (Soft Comput 11:991–996, 2007; Soft Comput 12:463–468, 2008). These results would be useful to enrich the studies that have already focused on fuzzy linear regression models

ANCOVA: A global test based on a robust measure of location or quantiles when there is curvature

For two independent groups, let $M_j(x)$ be some conditional measure of location for the $j$th group associated with some random variable $Y$, given that some covariate $X=x$. When $M_j(x)$ is a robust measure of location, or even some conditional quantile of $Y$, given $X$, methods have been proposed and studied that are aimed at testing $H_0$: $M_1(x)=M_2(x)$ that deal with curvature in a flexible manner. In addition, methods have been studied where the goal is to control the probability of one or more Type I errors when testing $H_0$ for each $x \in \{x_1, \ldots, x_p\}$. This paper suggests a method for testing the global hypothesis $H_0$: $M_1(x)=M_2(x)$ for $\forall x \in \{x_1, \ldots, x_p\}$ when using a robust or quantile location estimator. An obvious advantage of testing $p$ hypotheses, rather than the global hypothesis, is that it can provide information about where regression lines differ and by how much. But the paper summarizes three general reasons to suspect that testing the global hypothesis can have more power. 2 Data from the Well Elderly 2 study illustrate that testing the global hypothesis can make a practical difference.Comment: 23 pp 2 Figure

Intraday forecasts of a volatility index: Functional time series methods with dynamic updating

As a forward-looking measure of future equity market volatility, the VIX index has gained immense popularity in recent years to become a key measure of risk for market analysts and academics. We consider discrete reported intraday VIX tick values as realisations of a collection of curves observed sequentially on equally spaced and dense grids over time and utilise functional data analysis techniques to produce one-day-ahead forecasts of these curves. The proposed method facilitates the investigation of dynamic changes in the index over very short time intervals as showcased using the 15-second high-frequency VIX index values. With the help of dynamic updating techniques, our point and interval forecasts are shown to enjoy improved accuracy over conventional time series models.Comment: 29 pages, 5 figures, To appear at the Annals of Operations Researc

P-P Total Cross Sections at VHE from Accelerator Data

Comparison of P-P total cross-sections estimations at very high energies - from accelerators and cosmic rays - shows a disagreement amounting to more than 10 %, a discrepancy which is beyond statistical errors. Here we use a phenomenological model based on the Multiple-Diffraction approach to successfully describe data at accelerator energies. The predictions of the model are compared with data On the basis of regression analysis we determine confident error bands, analyzing the sensitivity of our predictions to the employed data for extrapolation. : using data at 546 and 1.8 TeV, our extrapolations for p-p total cross-sections are only compatible with the Akeno cosmic ray data, predicting a slower rise with energy than other cosmic ray results and other extrapolation methods. We discuss our results within the context of constraints in the light of future accelerator and cosmic ray experimental results.Comment: 26 pages aqnd 11 figure

The effect of interstimulus interval on sequential effects in absolute identification

In absolute identification experiments, the participant is asked to identify stimuli drawn from a small set of items which differ on a single physical dimension (e.g., 10 tones which vary in frequency). Responses in these tasks show a striking pattern of sequential dependencies: The current response assimilates towards the immediately preceding stimulus but contrasts with the stimuli further back in the sequence. This pattern has been variously interpreted as resulting from confusion of items in memory, shifts in response criteria, or the action of selective attention, and these interpretations have been incorporated into competing formal models of absolute identification performance. In two experiments, we demonstrate that lengthening the time between trials increases contrast to both the previous stimulus and the stimulus two trials back. This surprising pattern of results is difficult to reconcile with the idea that sequential dependencies result from memory confusion or from criterion shifts, but is consistent with an account that emphasizes selective attention. </jats:p