7,522 research outputs found
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 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, , 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 , . Suppose , are independent
realizations from a completely unknown . 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 to
depend on . 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 and be independent
-dimensional multivariate normal vectors with common unknown mean .
Based on observing , we consider the problem of estimating the true
predictive density of 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
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