Re-figuring Federalism: Nation and State in Health Reform's Next Round

Reviews the evolution of national healthcare reform movements and the relationship between the federal and state governments, with international comparisons. Outlines differences to be resolved over Medicaid and other programs under a reformed system

In-season prediction of batting averages: A field test of empirical Bayes and Bayes methodologies

Batting average is one of the principle performance measures for an individual baseball player. It is natural to statistically model this as a binomial-variable proportion, with a given (observed) number of qualifying attempts (called ``at-bats''), an observed number of successes (``hits'') distributed according to the binomial distribution, and with a true (but unknown) value of $p_i$ that represents the player's latent ability. This is a common data structure in many statistical applications; and so the methodological study here has implications for such a range of applications. We look at batting records for each Major League player over the course of a single season (2005). The primary focus is on using only the batting records from an earlier part of the season (e.g., the first 3 months) in order to estimate the batter's latent ability, $p_i$, and consequently, also to predict their batting-average performance for the remainder of the season. Since we are using a season that has already concluded, we can then validate our estimation performance by comparing the estimated values to the actual values for the remainder of the season. The prediction methods to be investigated are motivated from empirical Bayes and hierarchical Bayes interpretations. A newly proposed nonparametric empirical Bayes procedure performs particularly well in the basic analysis of the full data set, though less well with analyses involving more homogeneous subsets of the data. In those more homogeneous situations better performance is obtained from appropriate versions of more familiar methods. In all situations the poorest performing choice is the na\"{{\i}}ve predictor which directly uses the current average to predict the future average.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS138 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Statistical properties of the method of regularization with periodic Gaussian reproducing kernel

The method of regularization with the Gaussian reproducing kernel is popular in the machine learning literature and successful in many practical applications. In this paper we consider the periodic version of the Gaussian kernel regularization. We show in the white noise model setting, that in function spaces of very smooth functions, such as the infinite-order Sobolev space and the space of analytic functions, the method under consideration is asymptotically minimax; in finite-order Sobolev spaces, the method is rate optimal, and the efficiency in terms of constant when compared with the minimax estimator is reasonably high. The smoothing parameters in the periodic Gaussian regularization can be chosen adaptively without loss of asymptotic efficiency. The results derived in this paper give a partial explanation of the success of the Gaussian reproducing kernel in practice. Simulations are carried out to study the finite sample properties of the periodic Gaussian regularization.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000045

Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of normal means

We consider the classical problem of estimating a vector \bolds{\mu}=(\mu_1,...,\mu_n) based on independent observations $Y_i\sim N(\mu_i,1)$, $i=1,...,n$. Suppose $\mu_i$, $i=1,...,n$ are independent realizations from a completely unknown $G$. We suggest an easily computed estimator \hat{\bolds{\mu}}, such that the ratio of its risk E(\hat{\bolds{\mu}}-\bolds{\mu})^2 with that of the Bayes procedure approaches 1. A related compound decision result is also obtained. Our asymptotics is of a triangular array; that is, we allow the distribution $G$ to depend on $n$. Thus, our theoretical asymptotic results are also meaningful in situations where the vector \bolds{\mu} is sparse and the proportion of zero coordinates approaches 1. We demonstrate the performance of our estimator in simulations, emphasizing sparse setups. In ``moderately-sparse'' situations, our procedure performs very well compared to known procedures tailored for sparse setups. It also adapts well to nonsparse situations.Comment: Published in at http://dx.doi.org/10.1214/08-AOS630 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ski areas, weather and climate: Time series models for New England case studies

Wintertime warming trends experienced in recent decades, and predicted to increase in the future, present serious challenges for ski areas and whole regions that depend on winter tourism. Most research on this topic examines past or future climate-change impacts at yearly to decadal resolution, to obtain a perspective on climate-change impacts. We focus instead on local-scale impacts of climate variability, using detailed daily data from two individual ski areas. Our analysis fits ARMAX (autoregressive moving average with exogenous variables) time series models that predict day-to-day variations in skier attendance from a combination of mountain and urban weather, snow cover and cyclical factors. They explain half to two-thirds of the variation in these highly erratic series, with no residual autocorrelation. Substantively, model results confirm the backyard hypothesis that urban snow conditions significantly affect skier activity; quantify these effects alongside those of mountain snow and weather; show that previous-day conditions provide a practical time window; find no monthly effects net of weather; and underline the importance of a handful of high-attendance days in making or breaking the season. Viewed in the larger context of climate change, our findings suggest caution regarding the efficacy of artificial snowmaking as an adaptive strategy, and of smoothed yearly summaries to characterize the timing-sensitive impacts of weather (and hence, high-variance climate change) on skier activity. These results elaborate conclusions from our previous annual-level analysis. More broadly, they illustrate the potential for using ARMAX models to conduct integrated, dynamic analysis across environmental and social domains

Admissible predictive density estimation

Let $X|\mu\sim N_p(\mu,v_xI)$ and $Y|\mu\sim N_p(\mu,v_yI)$ be independent $p$-dimensional multivariate normal vectors with common unknown mean $\mu$. Based on observing $X=x$, we consider the problem of estimating the true predictive density $p(y|\mu)$ of $Y$ under expected Kullback--Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Bayes rules is a complete class, and that the easily interpretable conditions of Brown and Hwang [Statistical Decision Theory and Related Topics (1982) III 205--230] are sufficient for a formal Bayes rule to be admissible.Comment: Published in at http://dx.doi.org/10.1214/07-AOS506 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org