Confidence Corridors for Multivariate Generalized Quantile Regression

We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric estimator and the true function of interest, which follow after a series of approximation steps including a Bahadur representation, a new strong approximation theorem, and exponential tail inequalities for Gaussian random fields. As a byproduct we also obtain multivariate confidence corridors for the regression function in the classical mean regression. To deal with the problem of slowly decreasing error in coverage probability of the asymptotic confidence corridors, which results in meager coverage for small sample sizes, a simple bootstrap procedure is designed based on the leading term of the Bahadur representation. The finite-sample properties of both procedures are investigated by means of a simulation study and it is demonstrated that the bootstrap procedure considerably outperforms the asymptotic bands in terms of coverage accuracy. Finally, the bootstrap confidence corridors are used to study the efficacy of the National Supported Work Demonstration, which is a randomized employment enhancement program launched in the 1970s. This article has supplementary materials online.     

Robust inference for group sequential trials

For ethical reasons, group sequential trials were introduced to allow trials to stop early in the event of extreme results. Endpoints in such trials are usually mortality or irreversible morbidity. For a given endpoint, the norm is to use a single test statistic and to use that same statistic for each analysis. This approach is risky because the test statistic has to be specified before the study is unblinded, and there is loss in power if the assumptions that ensure optimality for each analysis are not met. To minimize the risk of moderate to substantial loss in power due to a suboptimal choice of a statistic, a robust method was developed for nonsequential trials. The concept is analogous to diversification of financial investments to minimize risk. The method is based on combining P values from multiple test statistics for formal inference while controlling the type I error rate at its designated value.This article evaluates the performance of 2 P value combining methods for group sequential trials. The emphasis is on time to event trials although results from less complex trials are also included. The gain or loss in power with the combination method relative to a single statistic is asymmetric in its favor. Depending on the power of each individual test, the combination method can give more power than any single test or give power that is closer to the test with the most power. The versatility of the method is that it can combine P values from different test statistics for analysis at different times. The robustness of results suggests that inference from group sequential trials can be strengthened with the use of combined tests.     

Scrutinizing an algorithmic technique: the Bayes classifier as interested reading of reality

ABSTRACT

This paper outlines the notion of ‘algorithmic technique’ as a middle ground between concrete, implemented algorithms and the broader study and theorization of software. Algorithmic techniques specify principles and methods for doing things in the medium of software and they thus constitute units of knowledge and expertise in the domain of software making. I suggest that algorithmic techniques are a suitable object of study for the humanities and social science since they capture the central technical principles behind actual software, but can generally be described in accessible language. To make my case, I focus on the field of information ordering and, first, discuss the wider historical trajectory of formal or ‘mechanical’ reasoning applied to matters of commerce and government before, second, moving to the investigation of a particular algorithmic technique, the Bayes classifier. This technique is explicated through a reading of the original work of M. E. Maron in the early 1960 and presented as a means to subject empirical, ‘datafied’ reality to an interested reading that confers meaning to each variable in relation to an operational goal. After a discussion of the Bayes classifier in relation to the question of power, the paper concludes by coming back to its initial motive and argues for increased attention to algorithmic techniques in the study of software.     

All Data are Wrong,but Some are Useful? Advocating the Need for Data Auditing

In a recent article from the Annals of Applied Statistics, Cox discussed the main phases of applied statistical research ranging from clarifying study objectives to final data analysis and interpreting results. As an incidental remark to these main phases, we advocate that beyond cleaning and preprocessing the data, it is a good practice to audit the data to determine if they can be trusted at all. A case study based on Ghanaian Official Fishery Statistics is used to illustrate this need, with Benford's law being the tool used to carrying out the data audit. Supplementary materials for this article are available online.     

Computationally and statistically efficient model fitting techniques

A significant challenge in fitting metamodels of large-scale simulations with sufficient accuracy is in the computational time required for rigorous statistical validation. This paper addresses the statistical computation issues associated with the Bootstrap and modified PRESS statistic, which yield key metrics for error measurements in metamodelling validation. Experimentation is performed on different programming languages, namely, MATLAB, R, and Python, and implemented on different computing architectures including traditional multicore personal computers and high-power clusters with parallel computing capabilities. This study yields insight into the effect that programming languages and computing architecture have on the computational time for simulation metamodel validation. The experimentation is performed across two scenarios with varying complexity.     

On the asymptotic normality of the R-estimators of the slope parameters of simple linear regression models with associated errors

ABSTRACT

The purpose of this paper is to prove, under mild conditions, the asymptotic normality of the rank estimator of the slope parameter of a simple linear regression model with stationary associated errors. This result follows from a uniform linearity property for linear rank statistics that we establish under general conditions on the dependence of the errors. We prove also a tightness criterion for weighted empirical process constructed from associated triangular arrays. This criterion is needed for the proofs which are based on that of Koul [Behavior of robust estimators in the regression model with dependent errors. Ann Stat. 1977;5(4):681–699] and of Louhichi [Louhichi S. Weak convergence for empirical processes of associated sequences. Ann Inst Henri Poincaré Probabilités Statist. 2000;36(5):547–567].     

Asymptotic behaviour of proportions of observations in random regions determined by central order statistics from stationary processes

In this paper, we show that proportions of observations that fall into a random region determined by a given Borel set and a central order statistic converge almost surely, provided that the corresponding population quantile is unique. We also describe three types of possible asymptotic behaviour of these proportions in the case of non-unique population quantile. As an application of our findings we establish limiting properties of numbers of ties with a central order statistics in a discrete sample. Our results are derived not only for independent and identically distributed observations but more generally for strictly stationary and ergodic sequences of random variables.     

Multiple comparisons in two-factor testing of psychophysical thresholds by the delta test method

We propose an algorithm of multiple comparisons in two-factor testing of psychophysical thresholds. We use logistic regression combined with guessing rate and adopt the step-down procedure with Ryan–Einot–Gabriel–Welsch (REGW) significance levels for multiple test. We test hypotheses of main effects and interaction in two-factor problem by using the delta test statistics.