Invariant co-ordinate selection

Summary.  A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based on the eigenvalue–eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant co-ordinate system for the multivariate data. Consequently, we view this method as a method for invariant co-ordinate selection . By plotting the data with respect to this new invariant co-ordinate system, various data structures can be revealed. For example, under certain independent components models, it is shown that the invariant co- ordinates correspond to the independent components. Another example pertains to mixtures of elliptical distributions. In this case, it is shown that a subset of the invariant co-ordinates corresponds to Fisher's linear discriminant subspace, even though the class identifications of the data points are unknown. Some illustrative examples are given.     

Statisticians in European regulatory agencies

The UK body of statisticians in the pharmaceutical industry, PSI, has called on heads of European regulatory agencies responsible for assessing applications for marketing authorizations for new medicines in the EU to employ full time statisticians. In order to assess the present situation a survey has been conducted to identify the number of agencies employing one or more full time statisticians. Out of 29 responding agencies, 12 employed one or more statisticians on a full time basis, whereas 17 did not. Among these 17, 7 involved external experts on a regular basis, 5 involved external statisticians on a case‐by‐case basis, whereas 5 never involved external statistical expertise. Failure to involve statisticians in the assessment of efficacy and safety of medicines does not automatically lead to reports of low quality or invalid assessment of benefit‐risk. However, in depth knowledge of statistical methodology is often necessary to uncover weaknesses and potentially biased efficacy estimates. This might be of importance for the final opinion on granting a marketing authorization, and statistical review should therefore be conducted by those who are professionally expert in the area. A positive trend toward an increased involvement of statistical expertise in the European network of regulatory agencies is observed. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

Combined asymmetric spatial weights matrix with application to housing prices

In this study, a combined asymmetric spatial weights matrix is proposed for capturing the unequal spatial dependence of housing prices, where the advantage of this matrix was demonstrated by a non-nested hypothesis test. To explore the heterogeneous spatial impacts of urban essential characteristics on housing prices over the eastern, central, and western regions of China, after the Lagrange multiplier and likelihood ratio tests, the spatial Durbin model using the proposed weights matrix was applied to each region. The estimation results showed that the direct impacts of college and new employment were significantly negative in the eastern region, but not significant in the central and western regions. By contrast, the direct impacts of hospitals and scenic spots were significantly positive in eastern China, but not significant in central and western China. In addition, the indirect impacts of the four variables were not significant in the three regions. These results suggest that in eastern China, the government may increase the requirements for using medical resources and close tourist attractions in a single city to cool down the skyrocketing housing prices in this area.     

Palm Distributions for Log Gaussian Cox Processes

This paper establishes a remarkable result regarding Palm distributions for a log Gaussian Cox process: the reduced Palm distribution for a log Gaussian Cox process is itself a log Gaussian Cox process that only differs from the original log Gaussian Cox process in the intensity function. This new result is used to study functional summaries for log Gaussian Cox processes.