Is there a role for statisticians in pay equity?

After analyzing the salary structures of over 20 organizations in the process of implementing the requirements of the Pay Equity Act of the Province of Ontario, I found that one apparently invariant characteristic was the uniqueness of each salary structure — even among organizations with similar organizational structures. In almost every analysis, diagnostics suggested features of the gender gap that were not captured in the initial regression model. In studying a salary structure for the purposes of pay equity, the statistician is expected to help produce gender-neutral measures of the value of jobs and to estimate the shape and size of the gap between salaries of women and men for work of comparable value. We are expected to provide an “objective and unbiased” component to a very complex process fraught with subjectivity and bias. When we analyze real salary data with modern statistical tools, we generally find more questions than answers, yet we are expected to recommend some form of partial remedy for gender inequity within the legislated framework for pay equity plans. One (unsatisfying) solution to the dilemma would be to leave this type of work to analysts whose techniques don't confront them with the inadequacy of their models. This paper describes some experiences and observations gleaned from the analysis of real pay data for pay equity. It provides some answers, but they are, admittedly, much less compelling than the questions.     

Lottery qualities

The aim of this paper is to propose a model of decision-making for lotteries. Lottery qualities are the key concepts of the theory. Qualities allow the derivation of optimal decision-making processes and are taken explicitly into account for lottery evaluation. Our contribution explains the major violations of the expected utility theory for decisions on two-point lotteries and shows the necessity of giving explicit consideration to lottery qualities. Judged certainty equivalent and choice certainty equivalent concepts are discussed in detail along with the comparison of lotteries. Examples are provided by using different test results in the literature. JEL Classification D81     

Comparative Mixed Risk Aversion: Definition and Application to Self-Protection and Willingness to Pay

We analyze the optimal choices of agents with utility functions whose derivatives alternate in sign, an important class that includes most of the functions commonly used in economics and finance (Mixed Risk Aversion, MRA, Caballé and Pomansky, 1996). We propose a comparative mixed risk aversion definition for this class of utility functions, namely, More Risk Averse MRA, and provide a sufficient condition to compare individuals. We apply the model to optimal prevention and willingness to pay. More risk averse MRA agents spend less to reduce accident probabilities that are above 1/2. They spend more only when accident probabilities are below 1/2. Explanations in terms of risk premiums are provided. The results presented also allow for the presence of background risk.     

On principles and arguments to likelihood

Birnbaum (1962a) argued that the conditionality principle (C) and the sufficiency principle (S) implied the likelihood principle (L); he then argued (Birnbaum 1972) that C and a mathematical equivalence principle M implied L. Evans, Fraser, and Monette (1985a) gave reference details, and this paper gives proof that C alone implies L. The level of support by the profession for L is sharply less than that for S or even for C; thus the paradoxical nature of these results. In this regard, we elaborate on the Monette example (Fraser, Monette, and Ng 1984), which provides a strong case against L. We also examine closely the various proofs linking the principles and find that S and C can each be used operationally to suppress information otherwise deemed relevant. From another viewpoint this says that S and C can each be used in contexts that directly conflict with the original examples and motivations supporting them; the principles can thus be viewed as inappropriately used, or more strongly, as invalid. In either case, the result that C and S imply L or that C implies L can be regarded as noneffective in the context of discriminating applications. A resolution of the apparent anomalies can be obtained by allowing the statistical model to include ingredients additional to those usually present (particularly for subsequent use with conditionality), or alternatively by restricting the application of the principles to contexts where the conflicts would seem not to arise.     

On the influence of extreme parties in electoral competition with policy-motivated candidates

We study and compare equilibrium platforms in models of unidimensional electoral competition with two and four policy motivated parties. We first analyze the plurality game, where the party getting the most votes is elected and implements its proposed platform. Restrictions on the set of credible announcements are needed to get existence of equilibria. Comparing equilibria with two and four parties, we obtain that moderate parties react to the introduction of extreme parties by proposing the same or more extreme equilibrium platforms. We then study the proportional system, where the policy implemented is a weighted sum of the proposals, with the voting shares as weights. Here, the existence of extreme parties leads moderate ones to choose more centrist platforms. We finally test the robustness of our results with respect to, first, the enlargement of the strategy space to entry decisions and, second, to asymmetric distributions of voters' blisspoints.

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A Note on Computing the Noncentrality Parameter of the Noncentral F-Distribution

In this paper we present a modification to Newton's method that is suitable for computing percentage points as well as other parameter estimation. The method is locally quadratically convergent.     

A new proof of hsu's theorem in regression analysis– a coordinate-free approach

This paper provides a new proof of results by HSU (Statist. Res. Mem. 1938) and Drygas (Math. Operationsforsch. Statist. 1972) on estimating the variance σ²in HsU's regression model:By using a dispersion. mean-Correspondence the given problem in the theory of estimating the mean vector.