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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...
We study precise conditions under which the cyclic regenerative confidence intervals of Sargent and Shanthikumar are asymptotically valid. We also obtain an optimal way of implementing the cyclic rege...
Coverage Error for Confidence Intervals Arising in Simulation Output Analysis
Coverage Error Confidence Intervals Arising Simulation Output Analysis
2015/7/8
Coverage error asymptotics for confidence intervals arising in simulation are discussed~ Asymptotic expansions, to order O(n-1) (n is the sample size), are given for confidence intervals associated wi...
Confidence Regions for Stochastic Approximation Algorithms
Confidence Regions Stochastic Approximation Algorithms
2015/7/8
In principle, known central limit theorems for stochastic approximation schemes permit the simulationist to provide confidence regions for both the optimum and optimizer of a stochastic optimization p...
Robustness Properties and Confidence Interval Reliability
Robustness Properties Confidence Interval Reliability
2015/7/6
In this chapter, we discuss the robustness and reliability of the estimators of the probability of a rare event (or, more generally, of the expectation of some function of rare events) with respect to...
Asymptotic Validity of Batch Means Steady-State Confidence Intervals
Asymptotic Validity Batch Means Steady-State Confidence Intervals
2015/7/6
Themethod of batch means is a widely applied procedure for constructing steady-state confidence intervals. The traditional theoretical support for the method of batch means has rested on the assumptio...
Simulation-Based Confidence Bounds for Two-Stage Stochastic Programs
Stochastic programming Linear programming Probability theory
2015/7/6
This paper provides a rigorous asymptotic analysis and justification of upper and lower confidence bounds proposed by Dantzig and Infanger (1995) for an iterative sampling-based decomposition algorith...
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 ...