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Confidence Intervals for Random Forests:The Jackknife and the Infinitesimal Jackknife
bagging jackknife methods Monte Carlo noise variance estimation
2015/8/21
We study the variability of predictions made by bagged learners and random forests, and show how to estimate standard errors for these methods. Our work builds on variance estimates for bagging propos...
Adaptive confidence intervals for regression functions under shape constraints
Adaptation confidence interval convex function coverage probability expected length minimax estimation modulus of continuity monotone func-tion nonparametric regression shape constraint white noise model
2013/6/14
Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of conf...
Confidence in a Neutrino Mass Hierarchy Determination
Confidence Neutrino Mass Hierarchy Determination
2013/6/17
In the next decade, a number of experiments will attempt to determine the neutrino mass hierarchy. Feasibility studies for such experiments generally determine the expected value of Delta chi^2. As th...
Anti-Concentration and Honest Adaptive Confidence Bands
Anti-Concentration Honest Adaptive Confidence Bands
2013/4/28
Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the Smirnov-Bickel-Rosenblatt (SBR) condition; see e.g. Gine and Nickl (2010). This co...
On confidence intervals in regression that utilize uncertain prior information about a vector parameter
Frequentist confidence interval Prior information Linear regression
2013/4/28
Consider a linear regression model with n-dimensional response vector, p-dimensional regression parameter beta and independent normally distributed errors. Suppose that the parameter of interest is th...
The cost of using exact confidence intervals for a binomial proportion
Asymptotic expansion binomial distribution expected length sample size determination proportion
2013/4/27
When computing a confidence interval for a binomial proportion p one must choose between using an exact interval, which has a coverage probability of at least 1-{\alpha} for all values of p, and a sho...
On asymptotically optimal confidence regions and tests for high-dimensional models
asymptotically optimal confidence regions tests for high-dimensional models
2013/4/27
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easi...
Variance estimation and asymptotic confidence bands for the mean estimator of sampled functional data with high entropy unequal probability sampling designs
covariance function finite population Hajek approximation Horvitz-Thompso estimator Kullback-Leibler divergence rejective sampling unequal probability sampling without replacement
2012/11/23
For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson estimator can be approximated by the H\'ajek formula. The interest of this asymptotic varia...
Confidence Sets in Sparse Regression
composite testing problem high-dimensional inference detection boundary
2012/11/22
The problem of constructing confidence sets in the high dimensional linear model with $n$ response variables and $p$ parameters, possibly $p \ge n$, is considered. Necessary and sufficient conditions ...
Adaptive Markov Chain Monte Carlo confidence intervals
Adaptive Markov Chain Monte Carlo confidence intervals
2012/11/22
In Adaptive Markov Chain Monte Carlo (AMCMC) simulation, classical estimators of asymptotic variances are inconsistent in general. In this work we establish that despite this inconsistency, confidence...
Guaranteed Conservative Fixed Width Confidence Intervals Via Monte Carlo Sampling
Guaranteed Conservative Fixed Width Confidence Intervals Monte Carlo Sampling
2012/9/17
Monte Carlo methods are used to approximate the means,? of random variablesY, whose distributions are not known explicitly. The key idea is that the
average of a random sample,Y1,...,Yn, tends to 礱sn...
Adaptive confidence bands in the nonparametric fixed design regression model
Adaptive confidence bands nonparametric fixed design regression model
2012/9/19
In this note, we consider the problem of existence of adaptive confidence bands in the fixed design regression model, adapting ideas in Hoffmann and Nickl [10] to the present case. In the course of th...
Latent variable models are frequently used to identify structure in dichotomous network
data, in part because they give rise to a Bernoulli product likelihood that is both well un-
derstood and cons...
High-dimensional instrumental variables regression and confidence sets
Instrumental variables sparsity STIV estimator endogeneity high-dimensional regression conic programming optimal instruments hereroscedasticity confidence intervals non-Gaussian errors variable selection unknown variance sign consistency
2011/6/17
We propose an instrumental variables method for estimation in linear models with endogenous
regressors in the high-dimensional setting where the sample size n can be smaller than the number
of possi...
Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data
CLT functional data local polynomial smoothing maximal inequalities space of continuous functions suprema of Gaussian processes survey sampling weighted crossvalidation
2011/6/17
When collections of functional data are too large to be exhaustively observed, survey
sampling techniques provide an e ective way to estimate global quantities such as
the population mean function. ...