3,848 research outputs found
An autoregressive approach to house price modeling
A statistical model for predicting individual house prices and constructing a
house price index is proposed utilizing information regarding sale price, time
of sale and location (ZIP code). This model is composed of a fixed time effect
and a random ZIP (postal) code effect combined with an autoregressive
component. The former two components are applied to all home sales, while the
latter is applied only to homes sold repeatedly. The time effect can be
converted into a house price index. To evaluate the proposed model and the
resulting index, single-family home sales for twenty US metropolitan areas from
July 1985 through September 2004 are analyzed. The model is shown to have
better predictive abilities than the benchmark S&P/Case--Shiller model, which
is a repeat sales model, and a conventional mixed effects model. Finally, Los
Angeles, CA, is used to illustrate a historical housing market downturn.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS380 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Minimax Linear Estimation in a White Noise Problem
Linear estimation of f(x) at a point in a white noise model is considered. The exact linear minimax estimator of f(0) is found for the family of f(x) in which f′(x) is Lip (M). The resulting estimator is then used to verify a conjecture of Sacks and Ylvisaker concerning the near optimality of the Epanechnikov kernel
Bayesian Aspects of Some Nonparametric Problems
We study the Bayesian approach to nonparametric function estimation problems such as nonparametric regression and signal estimation. We consider the asymptotic properties of Bayes procedures for conjugate (= Gaussian) priors.
We show that so long as the prior puts nonzero measure on the very large parameter set of interest then the Bayes estimators are not satisfactory. More specifically, we show that these estimators do not achieve the correct minimax rate over norm bounded sets in the parameter space. Thus all Bayes estimators for proper Gaussian priors have zero asymptotic efficiency in this minimax sense.
We then present a class of priors whose Bayes procedures attain the optimal minimax rate of convergence. These priors may be viewed as compound, or hierarchical, mixtures of suitable Gaussian distributions
Bayesian Nonparametric Point Estimation Under a Conjugate Prior
Estimation of a nonparametric regression function at a point is considered. The function is assumed to lie in a Sobolev space, Sq, of order q. The asymptotic squared-error performance of Bayes estimators corresponding to Gaussian priors is investigated as the sample size, n, increases. It is shown that for any such fixed prior on Sq the Bayes procedures do not attain the optimal minimax rate over balls in Sq. This result complements that in Zhao (Ann. Statist. 28 (2000) 532) for estimating the entire regression function, but the proof is rather different
A Geometrical Explanation of Stein Shrinkage
Shrinkage estimation has become a basic tool in the analysis of high-dimensional data. Historically and conceptually a key development toward this was the discovery of the inadmissibility of the usual estimator of a multivariate normal mean.
This article develops a geometrical explanation for this inadmissibility. By exploiting the spherical symmetry of the problem it is possible to effectively conceptualize the multidimensional setting in a two-dimensional framework that can be easily plotted and geometrically analyzed. We begin with the heuristic explanation for inadmissibility that was given by Stein [In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, Vol. I (1956) 197–206, Univ. California Press]. Some geometric figures are included to make this reasoning more tangible. It is also explained why Stein’s argument falls short of yielding a proof of inadmissibility, even when the dimension, p, is much larger than p = 3.
We then extend the geometric idea to yield increasingly persuasive arguments for inadmissibility when p ≥ 3, albeit at the cost of increased geometric and computational detail
Are Large Language Models Ready for Healthcare? A Comparative Study on Clinical Language Understanding
Large language models (LLMs) have made significant progress in various
domains, including healthcare. However, the specialized nature of clinical
language understanding tasks presents unique challenges and limitations that
warrant further investigation. In this study, we conduct a comprehensive
evaluation of state-of-the-art LLMs, namely GPT-3.5, GPT-4, and Bard, within
the realm of clinical language understanding tasks. These tasks span a diverse
range, including named entity recognition, relation extraction, natural
language inference, semantic textual similarity, document classification, and
question-answering. We also introduce a novel prompting strategy,
self-questioning prompting (SQP), tailored to enhance LLMs' performance by
eliciting informative questions and answers pertinent to the clinical scenarios
at hand. Our evaluation underscores the significance of task-specific learning
strategies and prompting techniques for improving LLMs' effectiveness in
healthcare-related tasks. Additionally, our in-depth error analysis on the
challenging relation extraction task offers valuable insights into error
distribution and potential avenues for improvement using SQP. Our study sheds
light on the practical implications of employing LLMs in the specialized domain
of healthcare, serving as a foundation for future research and the development
of potential applications in healthcare settings.Comment: 19 pages, preprin
- …