Title:Locally Adaptive Lag-Window Spectral Estimation
Date issued:Oct 1994
Abstract:We propose a procedure for the locally optimal window width in nonparametric spectral estimation, minimizing the asymptotic mean square error at a fixed frequency of a lag-window estimator. Our approach is based on an iterative plug-in scheme. Besides the estimation of a spectral density at a fixed frequency, e.g. at frequency zero, our procedure allows to perform nonparametric spectral estimation with variable window width which adapts to the smoothness of the true underlying density.
Pub info:Journal of Time Series Analysis, Vol.17
Date issued:Sep 1994
Abstract:Bagging predictors is a method for generating multiple versions of a predictor and using these to get an aggregated predictor. The aggregation averages over the versions when predicting a numerical outcome and does a plurality vote when predicting a class. The multiple versions are formed by making bootstrap replicates of the learning set and using these as new learning sets. Tests on real and simulated data sets using classification and regression trees and subset selection in linear regression show that bagging can give substantial gains in accuracy. The vital element is the instability of the prediction method. If perturbing the learning set can cause significant changes in the predictor constructed, then bagging can improve accuracy.
Title:Predicting multivariate responses in multiple linear regression
Author(s):Breiman, L.; Friedman, J. H.;
Date issued:August 1994
Keyword note:Breiman__Leo Friedman__J_H
Title:Resampling Fewer Than n Observations: Gains, Losses, and Remedies for Losses
Author(s):Bickel, P. J.; Götze, F.; van Zwet, W. R.;
Date issued:Aug 1994
Abstract:We discuss a number of resampling schemes in which $m=o(n)$ observations are resampled. We review nonparametric bootstrap failure and give results old and new on how the $m$ out of $n$ with replacement bootstraps and without replacement works. We extend work of Bickel and Yahav (1988) to show that $m$ out of $n$ bootstraps can be made second order correct, if the usual nonparametric bootstrap is correct and study how these extrapolation techniques work when the nonparametric bootstrap doesn't.
Keyword note:Bickel__Peter_John Gotze__Friedrich van_Zwet__W_R
Title:Some issues in the foundation of statistics
Author(s):Freedman, D. A.;
Date issued:August 1994
Title:Simultaneous Confidence Intervals for Linear Estimates of Linear Functionals
Author(s):Stark, P. B.;
Date issued:Aug 1994
Date modified:revised March, 1995
Abstract:This note presents three ways of constructing simultaneous confidence intervals for linear estimates of linear functionals in inverse problems, including ``Backus-Gilbert'' estimates. Simultaneous confidence intervals are needed to compare estimates, for example, to find spatial variations in a distributed parameter. The notion of simultaneous confidence intervals is introduced using coin tossing as an example before moving to linear inverse problems. The first method for constructing simultaneous confidence intervals is based on the Bonferroni inequality, and applies generally to confidence intervals for any set of parameters, from dependent or independent observations. The second method for constructing simultaneous confidence intervals in inverse problems is based on a ``global'' measure of fit to the data, which allows one to compute simultaneous confidence intervals for any number of linear functionals of the model that are linear combinations of the data mappings. This leads to confidence intervals whose widths depend on percentage points of the chi-square distribution with $n$ degrees of freedom, where $n$ is the number of data. The third method uses the joint normality of the estimates to find shorter confidence intervals than the other methods give, at the cost of evaluating some integrals numerically.
Title:Heuristics of instability and stabilization in model selection
Date issued:June 1994
Title:Some asymptotics of wavelet fits in the stationary error case
Author(s):Brillinger, D. R.;
Date issued:June 1994
Title:Consistency of Bayes estimates for nonparametric regression: normal theory
Author(s):Diaconis, P.; Freedman, D. A.;
Date issued:May 1994
Keyword note:Diaconis__Persi Freedman__David
Title:Looking at Markov Samplers through Cusum Path Plots:
Date issued:Jun 1994
Abstract:a simple diagnostic idea In this paper, we propose to monitor a Markov chain sampler using the cusum path plot of a chosen 1-dimensional summary statistic. We argue that the cusum path plot can bring out, more effectively than the sequential plot, those aspects of a Markov sampler which tell the user how quickly or slowly the sampler is moving around in its sample space, in the direction of the summary statistic. The proposal is then illustrated in four examples which represent situations where the cusum path plot works well and not well. Moreover, a rigorous analysis is given for one of the examples. We conclude that the cusum path plot is an effective tool for convergence diagnostics of a Markov sampler and for comparing different Markov samplers.
Title:Neighbourhood `correlation ratio' curves
Author(s):Doksum, K.; Froda, S.;
Date issued:April 1994
Keyword note:Doksum__Kjell_Andreas Froda__S
Title:Some properties of splitting criteria
Date issued:March 1994
Title:Estimating $L^1$ Error of Kernel Estimator: Monitoring Convergence of Markov Samplers
Date issued:Nov 1994
Abstract:In many Markov chain Monte Carlo problems, the target density function is known up to a normalization constant. In this paper, we take advantage of this knowledge to facilitate the convergence diagnostic of a Markov sampler by estimating the $L^1$ error of a kernel estimator. Firstly, we propose an estimator of the normalization constant which is shown to be asymptotically normal under mixing and moment conditions. Secondly, the $L^1$ error of the kernel estimator is estimated using the normalization constant estimator, and the ratio of the estimated $L^1$ error to the true $L^1$ error is shown to converge to 1 in probability under similar conditions. Thirdly, we propose a sequential plot of the estimated $L^1$ error as a tool to monitor the convergence of the Markov sampler. Finally, a 2-dimensional bimodal example is given to illustrate the proposal, and two Markov samplers are compared in the example using the proposed diagnostic plot.
Title:From association to causation via regression
Author(s):Freedman, David A.;
Date issued:Apr 1994
Abstract:For nearly a century, investigators in the social sciences have used regression models to deduce cause-and-effect relationships from patterns of association. Path models and automated search procedures are more recent developments. In my view, this enterprise has not been successful. The models tend to neglect the difficulties in establishing causal relations, and the mathematical complexities tend to obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C, ... hold, then H can be tested against the data. However, if A, B, C, ... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work-- a principle honored more often in the breach than the observance. I will discuss modeling techniques that seem to convert association into causation. The object is to clarify the differences among the various uses of regression, and the difficulties in making causal inferences by modeling.
Title:Inference in Hidden Markov Models I: Local Asymptotic Normality in the Stationary Case
Author(s):Bickel, P. J.; Ritov, Y.;
Date issued:Feb 1994
Date modified:revised April 1995
Abstract:Following up on Baum and Petrie (1966) we study likelihood based methods in hidden Markov models, where the hiding mechanism can lead to continuous observations and is itself governed by a parametric model. We show that procedures essentially equivalent to maximum likelihood estimates are asymptotically normal as expected and consistent estimates of their variance can be constructed, so that the usual inferential procedures are asymptotically valid.
Keyword note:Bickel__Peter_John Ritov__Yaacov