713 research outputs found
Optimal Estimation under Nonstandard Conditions
We analyze optimality properties of maximum likelihood (ML) and other estimators when the problem does not necessarily fall within the locally asymptotically normal (LAN) class, therefore covering cases that are excluded from conventional LAN theory such as unit root nonstationary time series. The classical HĂĄjek-Le Cam optimality theory is adapted to cover this situation. We show that the expectation of certain monotone âbowl-shapedâ functions of the squared estimation error are minimized by the ML estimator in locally asymptotically quadratic situations, which often occur in nonstationary time series analysis when the LAN property fails. Moreover, we demonstrate a direct connection between the (Bayesian property of) asymptotic normality of the posterior and the classical optimality properties of ML estimators
The bootstrap -A review
The bootstrap, extensively studied during the last decade, has become a powerful tool in different areas of Statistical Inference. In this work, we present the main ideas of bootstrap methodology in several contexts, citing the most relevant contributions and illustrating with examples and simulation studies some interesting aspects
Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process
A stationary Gaussian process is said to be long-range dependent (resp.,
anti-persistent) if its spectral density can be written as
, where (resp., ),
and is continuous and positive. We propose a novel Bayesian nonparametric
approach for the estimation of the spectral density of such processes. We prove
posterior consistency for both and , under appropriate conditions on the
prior distribution. We establish the rate of convergence for a general class of
priors and apply our results to the family of fractionally exponential priors.
Our approach is based on the true likelihood and does not resort to Whittle's
approximation.Comment: Published in at http://dx.doi.org/10.1214/11-AOS955 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Improved Cross-Entropy Method for Estimation
The cross-entropy (CE) method is an adaptive importance sampling procedure that has been successfully applied to a diverse range of complicated simulation problems. However, recent research has shown that in some high-dimensional settings, the likelihood ratio degeneracy problem becomes severe and the importance sampling estimator obtained from the CE algorithm becomes unreliable. We consider a variation of the CE method whose performance does not deteriorate as the dimension of the problem increases. We then illustrate the algorithm via a high-dimensional estimation problem in risk management
Parametric modeling of quantile regression coefficient functions with count data
AbstractApplying quantile regression to count data presents logical and practical complications which are usually solved by artificially smoothing the discrete response variable through jittering. In this paper, we present an alternative approach in which the quantile regression coefficients are modeled by means of (flexible) parametric functions. The proposed method avoids jittering and presents numerous advantages over standard quantile regression in terms of computation, smoothness, efficiency, and ease of interpretation. Estimation is carried out by minimizing a "simultaneous" version of the loss function of ordinary quantile regression. Simulation results show that the described estimators are similar to those obtained with jittering, but are often preferable in terms of bias and efficiency. To exemplify our approach and provide guidelines for model building, we analyze data from the US National Medical Expenditure Survey. All the necessary software is implemented in the existing R package
Laws and Limits of Econometrics
We start by discussing some general weaknesses and limitations of the econometric approach. A template from sociology is used to formulate six laws that characterize mainstream activities of econometrics and the scientific limits of those activities, we discuss some proximity theorems that quantify by means of explicit bounds how close we can get to the generating mechanism of the data and the optimal forecasts of next period observations using a finite number of observations. The magnitude of the bound depends on the characteristics of the model and the trajectory of the observed data. The results show that trends are more elusive to model than stationary processes in the sense that the proximity bounds are larger. By contrast, the bounds are of smaller order for models that are unidentified or nearly unidentified, so that lack or near lack of identification may not be as fatal to the use of a model in practice as some recent results on inference suggest, we look at one possible future of econometrics that involves the use of advanced econometric methods interactively by way of a web browser. With these methods users may access a suite of econometric methods and data sets online. They may also upload data to remote servers and by simple web browser selections initiate the implementation of advanced econometric software algorithms, returning the results online and by file and graphics downloads.Activities and limitations of econometrics, automated modeling, nearly unidentified models, nonstationarity, online econometrics, policy analysis, prediction, quantitative bounds, trends, unit roots, weak instruments
- âŠ