Multivariate Lorenz dominance based on zonoids

The classical Lorenz curve visualizes and measures the disparity of items which are characterized by a single variable: The more the curve bends, the more scatter the data. Recently a general approach has been proposed and investigated that measures the disparity of multidimensioned items regardless of their dimension. This paper surveys various generalizations of Lorenz curve and Lorenz dominance for multidimensional data. Firstly, the Lorenz zonoid of multivariate data and, more general, of a random vector is introduced. Then three multivariate extensions of univariate Lorenz dominance are surveyed and contrasted, the set inclusion of lift zonoids, the scaled convex order, and the price Lorenz order. The latter is based on the set inclusion of extended Lorenz zonoids. Finally, a decomposition of the multivariate volume-Gini mean difference is given.     

Bootstrapping a hedonic price index: experience from used cars data

Every hedonic price index is an estimate of an unknown economic parameter. It depends, in practice, on one or more random samples of prices and characteristics of a certain good. Bootstrap resampling methods provide a tool for quantifying sampling errors. Following some general reflections on hedonic elementary price indices, this paper proposes a case-based, a model-based, and a wild bootstrap approach for estimating confidence intervals for hedonic price indices. Empirical results are obtained for a data set on used cars in Switzerland. A simple and an enhanced adaptive semi-logarithmic model are fit to monthly samples, and bootstrap confidence intervals are estimated for Jevons-type hedonic elementary price indices.     

Consistency of completely outlier-adjusted simultaneous redescending M-estimators of location and scale

This paper gives conditions for the consistency of simultaneous redescending M-estimators for location and scale. The consistency postulates the uniqueness of the parameters μ and σ, which are defined analogously to the estimations by using the population distribution function instead of the empirical one. The uniqueness of these parameters is no matter of course, because redescending ψ- and χ-functions, which define the parameters, cannot be chosen in a way that the parameters can be considered as the result of a common minimizing problem where the sum of ρ-functions of standardized residuals is to be minimized. The parameters arise from two minimizing problems where the result of one problem is a parameter of the other one. This can give different solutions. Proceeding from a symmetrical unimodal distribution and the usual symmetry assumptions for ψ and χ leads, in most but not in all cases, to the uniqueness of the parameters. Under this and some other assumptions, we can also prove the consistency of the according M-estimators, although these estimators are usually not unique even when the parameters are. The present article also serves as a basis for a forthcoming paper, which is concerned with a completely outlier-adjusted confidence interval for μ. So we introduce a ñ where data points far away from the bulk of the data are not counted at all.     

Assessing the bias due to non-coverage of residential movers in the German Microcensus Panel: an evaluation using data from the Socio-Economic Panel

The German Microcensus (MC) is a large scale rotating panel survey over three years. The MC is attractive for longitudinal analysis over the entire participation duration because of the mandatory participation and the very high case numbers (about 200000 respondents). However, as a consequence of the area sampling that is used for the MC, residential mobility is not covered and consequently statistical information at the new residence is lacking in the MC sample. This raises the question whether longitudinal analyses, like transitions between labour market states, are biased and how different methods perform that promise to reduce such a bias. Similar problems occur also for other national Labour Force Surveys (LFS) which are rotating panels and do not cover residential mobility, see Clarke and Tate (2002). Based on data of the German Socio-Economic Panel (SOEP), which covers residential mobility, we analysed the effects of missing data of residential movers by the estimation of labour force flows. By comparing the results from the complete SOEP sample and the results from the SOEP, restricted to the non-movers, we concluded that the non-coverage of the residential movers can not be ignored in Rubin’s sense. With respect to correction methods we analysed weighting by inverse mobility scores and log-linear models for partially observed contingency tables. Our results indicate that weighting by inverse mobility scores reduces the bias to about 60% whereas the official longitudinal weights obtained by calibration result in a bias reduction of about 80%. The estimation of log-linear models for non-ignorable non-response leads to very unstable results.     

Semiparametric multinomial logit models for analysing consumer choice behaviour

The multinomial logit model (MNL) is one of the most frequently used statistical models in marketing applications. It allows one to relate an unordered categorical response variable, for example representing the choice of a brand, to a vector of covariates such as the price of the brand or variables characterising the consumer. In its classical form, all covariates enter in strictly parametric, linear form into the utility function of the MNL model. In this paper, we introduce semiparametric extensions, where smooth effects of continuous covariates are modelled by penalised splines. A mixed model representation of these penalised splines is employed to obtain estimates of the corresponding smoothing parameters, leading to a fully automated estimation procedure. To validate semiparametric models against parametric models, we utilise different scoring rules as well as predicted market share and compare parametric and semiparametric approaches for a number of brand choice data sets.     

A structured variational learning approach for switching latent factor models

A data-driven approach for modeling volatility dynamics and co-movements in financial markets is introduced. Special emphasis is given to multivariate conditionally heteroscedastic factor models in which the volatilities of the latent factors depend on their past values, and the parameters are driven by regime switching in a latent state variable. We propose an innovative indirect estimation method based on the generalized EM algorithm principle combined with a structured variational approach that can handle models with large cross-sectional dimensions. Extensive Monte Carlo simulations and preliminary experiments with financial data show promising results.     

A new approach to the measurement of polarization for grouped data

In this paper we develop a measure of polarization for discrete distributions of non-negative grouped data. The measure takes into account the relative sizes and homogeneities of individual groups as well as the heterogeneities between all pairs of groups. It is based on the assumption that the total polarization within the distribution can be understood as a function of the polarizations between all pairs of groups. The measure allows information on existing groups within a population to be used directly to determine the degree of polarization. Thus the impact of various classifications on the degree of polarization can be analysed. The treatment of the distribution’s total polarization as a function of pairwise polarizations allows statements concerning the effect of an individual pair or an individual group on the total polarization.     

Adaptive thresholding of sequences with locally variable strength

This paper addresses, via thresholding, the estimation of a possibly sparse signal observed subject to Gaussian noise. Conceptually, the optimal threshold for such problems depends upon the strength of the underlying signal. We propose two new methods that aim to adapt to potential local variation in this signal strength and select a variable threshold accordingly. Our methods are based upon an empirical Bayes approach with a smoothly variable mixing weight chosen via either spline or kernel based marginal maximum likelihood regression. We demonstrate the excellent performance of our methods in both one and two-dimensional estimation when compared to various alternative techniques. In addition, we consider the application to wavelet denoising where reconstruction quality is significantly improved with local adaptivity.     

Sequential monitoring of minimum variance portfolio

This paper evaluates the economic effect of monitoring the minimum variance portfolio weights, which depend solely on the covariance matrix of returns. The investor decides whether the portfolio composition providing the smallest portfolio variance remains optimal at the beginning of every new investment period. For this purpose changes in the optimal weights are sequentially detected by means of EWMA control charts. Signals obtained from monitoring are used for improvement of the covariance matrix estimation procedure. The investment strategy exploiting signals from control charts is compared with a number of alternative approaches in the empirical study.     

Frequentist,Bayes, or Other?

ABSTRACT

Both philosophically and in practice, statistics is dominated by frequentist and Bayesian thinking. Under those paradigms, our courses and textbooks talk about the accuracy with which true model parameters are estimated or the posterior probability that they lie in a given set. In nonparametric problems, they talk about convergence to the true function (density, regression, etc.) or the probability that the true function lies in a given set. But the usual paradigms' focus on learning the true model and parameters can distract the analyst from another important task: discovering whether there are many sets of models and parameters that describe the data reasonably well. When we discover many good models we can see in what ways they agree. Points of agreement give us more confidence in our inferences, but points of disagreement give us less. Further, the usual paradigms’ focus seduces us into judging and adopting procedures according to how well they learn the true values. An alternative is to judge models and parameter values, not procedures, and judge them by how well they describe data, not how close they come to the truth. The latter is especially appealing in problems without a true model.     

Statistics development: statistical methods meeting the user’s needs

Statistical methods have the potential of being effectively used by industrial practitioners if they satisfied two criteria: functionality and usability. Statistical methods are usually the product of statistical research activities of universities and other research organizations. Some already satisfy these criteria; however, many do not. The effect is that potentially relevant methods are not used in practice as often as they could be. In this paper we will present an approach regarding ‘statistics development,’ in which the end-user is given a central position, so that the results from statistical research aim to meet the needs and requirements of the practitioner. Examples of known and new methods will be presented, and we will discuss issues such as education in statistics, the link with statistical consultancy and publication of methods through various channels.     

Diagonal uniform association symmetry modelsfor cumulative probabilities in square tables

For the analysis of square contingency tables with ordered categories, Tomizawa (1991) considered the diagonal uniform association symmetry (DUS) model, which has a multiplicative form for cell probabilities and has the structure of uniform association in the tables constructed using two diagonals that are equidistant from the main diagonal. This paper proposes another DUS model which has a similar multiplicative form for cumulative probabilities. The model indicates that the odds that an observation will fall in row category i or below and column category i+k or above, instead of in column category i or below and row category i+k or above, increase (decrease) exponentially as the cutpoint i increases for a fixed k. Examples are given.     

A Critical Look at Some Analyses of Major League Baseball Salaries

At a data analysis exposition sponsored by the Section on Statistical Graphics of the ASA in 1988, 15 groups of statisticians analyzed the same data about salaries of major league baseball players. By examining what they did, what worked, and what failed, we can begin to learn about the relative strengths and weaknesses of different approaches to analyzing data. The data are rich in difficulties. They require reexpression, contain errors and outliers, and exhibit nonlinear relationships. They thus pose a realistic challenge to the variety of data analysis techniques used. The analysis groups chose a wide range of model-fitting methods, including regression, principal components, factor analysis, time series, and CART. We thus have an effective framework for comparing these approaches so that we can learn more about them. Our examination shows that approaches commonly identified with Exploratory Data Analysis are substantially more effective at revealing the underlying patterns in the data and at building parsimonious, understandable models that fit the data well. We also find that common data displays, when applied carefully, are often sufficient for even complex analyses such as this.     

Colours and Cocktails: Compositional Data Analysis 2013 Lancaster Lecture

The different constituents of physical mixtures such as coloured paint, cocktails, geological and other samples can be represented by d‐dimensional vectors called compositions with non‐negative components that sum to one. Data in which the observations are compositions are called compositional data. There are a number of different ways of thinking about and consequently analysing compositional data. The log‐ratio methods proposed by Aitchison in the 1980s have become the dominant methods in the field. One reason for this is the development of normative arguments converting the properties of log‐ratio methods to ‘essential requirements’ or Principles for any method of analysis to satisfy. We discuss different ways of thinking about compositional data and interpret the development of the Principles in terms of these different viewpoints. We illustrate the properties on which the Principles are based, focussing particularly on the key subcompositional coherence property. We show that this Principle is based on implicit assumptions and beliefs that do not always hold. Moreover, it is applied selectively because it is not actually satisfied by the log‐ratio methods it is intended to justify. This implies that a more open statistical approach to compositional data analysis should be adopted.     

A Hausman test for Brownian motion

New tests are proposed for the specification of the intraday price process of a risky asset, based on open, high, low, and close prices. Under the null of a Brownian process we derive two stochastically independent, unbiased volatility estimators. For a Hausman specification test we prove its equivalence with an F-test, consider its robustness against variation in drift and volatility, and analyze the power against an Ornstein–Uhlenbeck process, as well as a random walk with alternative distributions.     

Parameter Estimation for Inhomogeneous Space‐Time Shot‐Noise Cox Point Processes

We consider the problem of parameter estimation for inhomogeneous space‐time shot‐noise Cox point processes. We explore the possibility of using a stepwise estimation method and dimensionality‐reducing techniques to estimate different parts of the model separately. We discuss the estimation method using projection processes and propose a refined method that avoids projection to the temporal domain. This remedies the main flaw of the method using projection processes – possible overlapping in the projection process of clusters, which are clearly separated in the original space‐time process. This issue is more prominent in the temporal projection process where the amount of information lost by projection is higher than in the spatial projection process. For the refined method, we derive consistency and asymptotic normality results under the increasing domain asymptotics and appropriate moment and mixing assumptions. We also present a simulation study that suggests that cluster overlapping is successfully overcome by the refined method.     

The questions of fit in the gregor mendel controversy

Ever since R. A. Fisher published his 1936 article , "Has Mendel's Work Been Rediscovered?", historians of both biclogy and statistics have been fascinated by the surprisingly high conformity between Gregor (Johann) Mendel's observed and expected ratios in his famous experiments with peas. Fisher's calculatftl x² statistic of the experiments, taken as a whole, suggested that results on a par or better than those Mendel reported coultl only be expected to occur about three times in every 100,000 attempts. The ensuing controversy as to whether or not the good Father "sophisticated" his data has continued to this very day. In recent years the controversy has focused upon the more technical question of what underlying genetic arrangement Mendel actually studied.

The statistical issues of the controversy are exam:.led in am historical and comparative perspective. The changes the controversy has gone through are evaluated, and the nature of its current, more biological, status is briefly discussed.     

Union List Management: The Initial Project and Afterwards

Abstract

Two additional libraries have now joined the West Texas Union List. One is a city-supported; the other, state-supported. These two libraries have also joined the Texas Statewide Union List of Serials. Fees for the West Texas Union List are invoiced to each member directly. So far fees for the Texas Statewide Union List have been absorbed by grants awarded the Texas State Library. At this time, the statewide list will be funded with grants for two more years.

Member libraries update information in different workflows and on different schedules. Union list coordinators learn that members will update the information in their union lists; when, will vary from library to library and from list to list. Agents and coordinators must be aware of the attitude each member library has towards the list. If the list is available on OCLC, some members may only update holdings when they replace the individual institutional list used in their library. If the list is stored on computer tape, some members may have been interested in it only because it could assist them in future serial automation projects and may not have given much thought to the importance of the list as an ongoing venture.

There may be a problem if the library staff responsible for updating the list was never really involved in the decision to join a union list and is not committed to the list beyond the initial project phase. In some cases the members have every intention of keeping the information current but are not good managers or communicators. The agent should ask what is being done and advise members on getting started, and might even offer to visit the library to assist in setting up the proper workflow.

Working with libraries involved in union list activities is a challenge. As with all management tasks, communication is the key to success. When users or members discover a problem, the group must solve it quickly or the list will lose its credibility. Each list must face the possibility that members may not want to retain membership. Some members may not want the list to grow in size, while others do. Interpreting standards and choosing bibliographic and holdings formats are potentially controversial issues.

If the members agree that the list is needed and if the list is important to them from the beginning, then they will be more flexible and understanding of the problems in each library, and more likely to contribute to keeping the list current. As the members learn to work together, their union list product becomes a major goal or interest. The list becomes a product that represents the work and cooperation of the group as a whole.     

Bayesian covariance matrix estimation using a mixture of decomposable graphical models

We present a Bayesian approach to estimating a covariance matrix by using a prior that is a mixture over all decomposable graphs, with the probability of each graph size specified by the user and graphs of equal size assigned equal probability. Most previous approaches assume that all graphs are equally probable. We show empirically that the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs in more efficiently estimating the covariance matrix. The prior requires knowing the number of decomposable graphs for each graph size and we give a simulation method for estimating these counts. We also present a Markov chain Monte Carlo method for estimating the posterior distribution of the covariance matrix that is much more efficient than current methods. Both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.