NFL Draftnikology: Euclidean Metrics and Other Approaches to Scoring Ranking Predictions

With viewership of NFL (National Football League) football in the US rising above 20 million, interest in the NFL Draft has also been at all-time highs in recent years. Much of this interest is directed toward the “NFL draftniks” who provide draft predictions—so-called “mock drafts”—leading up to the NFL Draft. Despite increasing interest in “NFL draftnikology,” the scoring methodology used to evaluate mock NFL drafts lags far behind. This study offers a few alternative approaches, including a Euclidean metrics approach to evaluating mock NFL drafts. The usefulness of our methodologies extends to evaluation of economic and financial analysts.     

Approximate mrpp p-values obtained from four exact moments

A F0RTRAN-77 subroutine for a general version of multi-response permutation procedures (MRPP) is described. The exact four moments are employed in conjunction with the Pearson type I, type III, and type VI distributions to calculate the associated P-values.     

Mixture Representation of the Maximum Entropy Density Through Archimedean Copulas

In this article, we obtain a mixture representation of the maximum entropy density introduced by Rodrigues (2004 Rodrigues , J. ( 2004 ). An entropy model for dependent variables . Commun. Statist. Theor. Meth. 4 ( 33 ): 979 – 990 . [Google Scholar]) via Laplace approximation. This representation suggests, as in Sklar (1959 Sklar , A. ( 1959 ). Fonctions de répartition à ndimensions et marges . Publications de l 'Université de Paris 8 : 229 – 231 . [Google Scholar]), a dependence structure through Archimedean copulas independently of the specified marginal distributions. This result can be used as a natural Bayesian and non Bayesian procedure to estimate the dependence function and the marginal, separately.     

Statistical Comparison of the Goodness of Fit Delivered by Five Families of Distributions Used in Distribution Fitting

A basic assumption in distribution fitting is that a single family of distributions may deliver useful representation to the universe of available distributions. To date, little study has been conducted to compare the relative effectiveness of these families. In this article, five families are compared by fitting them to a sample of 20 distributions, using 2 fitting objectives: minimization of the L ₂ norm and four-moment matching. Values of L ₂ norm associated with the fitted families are used as input data to test for significant differences. The Pearson family and the RMM (Response Modeling Methodology) family significantly outperforms all other families.     

Inverse Circular–Linear/Linear–Circular Regression

We propose two distance-based methods and two likelihood-based methods of inversely regressing a linear predictor on a circular variable, and of inversely regressing a circular predictor on a linear variable. An asymptotic result on least circular distance estimators is provided in the Appendix. We present likelihood-based methods for symmetrical and asymmetrical errors in each situation. The utility of our methodology in each situation is illustrated by applying it to real data sets in engineering and environmental science. We then compare their performances using a cross validation method.     

Minimum anderson-darling estimation

The Anderson-Darling distance d(F_n ,F_0,) between the empirical distribution function F_n and the hypothesized model F₀ is minimized to produce estimators with good robustness and efficiency properties. In addition, the residual distance d_min = min₀d(F_n,F₀.) is availabe to assess model validity. The approximate distribution-free character of nd_min is studied using monte carlo methods.     

An information-theoretic approach to incorporating prior information in binomial sampling

The incorporation of prior information about θ, where θ is the success probability in a binomial sampling model, is an essential feature of Bayesian statistics. Methodology based on information-theoretic concepts is introduced which (a) quantifies the amount of information provided by the sample data relative to that provided by the prior distribution and (b) allows for a ranking of prior distributions with respect to conservativeness, where conservatism refers to restraint of extraneous information about θ which is embedded in any prior distribution. In effect, the most conservative prior distribution from a specified class (each member o f which carries the available prior information about θ) is that prior distribution within the class over which the likelihood function has the greatest average domination. The most conservative prior distributions from five different families of prior distributions over the interval (0,1) including the beta distribution are determined and compared for three situations: (1) no prior estimate of θ is available, (2) a prior point estimate or θ is available, and (3) a prior interval estimate of θ is available. The results of the comparisons not only advocate the use of the beta prior distribution in binomial sampling but also indicate which particular one to use in the three aforementioned situations.     

A target distribution model for nonparametric density estimation

In this paper a model is proposed which represents a wide class of continuous distributions. It is shown how the parameters of this model can be estimated leading to a distribution estimator and a corresponding density estimator. An important property of this estimator is that it can be structured to reflect a priori knowledge of the unknown distribution.

Finally, some examples are shown and some comparisons made with kernel and orthogonal series estimators.     

A structural model for the markov chain of change in vote intention

Assuming a first-order Markov chain, we propose a structural model for the transition probabilities in vote intention. The proposed model utilizes the ordering among the categories representing vote intentions and carries the flavor of distance models. It also allows a stochastic ordering among distributions reflecting the extent of change. The model is easy to fit and provides a nice interpretation of the data. The model is applied to a panel study of vote intention acquired through six successive interviews before the 1940 Presidential election in Erie County, Ohio.     

中国绿色全要素生产率测算及分解:1985~2010

现有文献在我国全要素生产率方面已经得到了很多有价值的研究结论,但不可否认的是,单纯考虑中国经济增长而忽略了资源环境因素对经济质量的影响是片面的。与类似研究相比,本文在生产率测量框架体系中引入了资源环境因素,从而为我国经济增长质量的测度提供一个更为科学的方法。文章分别运用基于DEA的Malmquist生产率指数和基于方向性距离函数的Malmquist-Luenberger生产率指数对1985～2010年间中国绿色全要素生产率进行了测算及分解。研究发现,不考虑资源环境因素会高估全要素生产率,从而对我国经济增长质量做出较为乐观的判断;我国全要素生产率增长主要来源于技术进步;考察期内我国绿色全要素生产率呈现“先升后降再平稳”的时间趋势特征,且显示出较大的地区差异。