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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...
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...
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...
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...
Lack of confidence in ABC model choice
Lack of confidence ABC model choice Approximate Bayesian computation
2011/3/24
Approximate Bayesian computation (ABC) have become a essential tool for the analysis of complex stochastic models. Earlier, Grelaud et al. (2009) advocated the use of ABC for Bayesian model choice in ...
Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds
Concentration Inequalities Confidence Bands Density Estimators
2011/3/21
Let $X_1,...,X_n$ be a random sample from some unknown probability density $f$ defined on a compact homogeneous manifold $\mathbf M$ of dimension $d \ge 1$. Consider a 'needlet frame' $\{\phi_{j \eta}...
Confidence Sets in Time--Series Filtering
Information Theory (cs.IT) Statistics Theory (math.ST)
2010/12/17
The problem of filtering of finite--alphabet stationary ergodic time series is considered. A method for constructing a confidence set for the (unknown) signal is proposed, such that the resulting set ...
On construction of the smallest one-sided confidence interval for the difference of two proportions
Binomial distribution coverage probability minimum effectivedose multiple tests Poisson distribution set inclusion
2010/3/11
For any class of one-sided 1− confidence intervals with a certain
monotonicity ordering on the random confidence limit, the smallest
interval, in the sense of the set inclusion for the differ...
Confidence bands in density estimation
Adaptive estimation limit theorem density estimation extremes Gaussian processes wavelet estimators kernel estimators
2010/3/11
we construct adaptive confidence bands that are honest for all densities
in a “generic” subset of the union of t-H¨older balls, 0 < t r,
where r is a fixed but arbitrary integer. The exceptional (...
Admissibility of the usual confidence interval in linear regression
admissibility compromise decision theory confidence interval decisiontheory
2010/3/9
Consider a linear regression model with independent and identically normally distributed
random errors. Suppose that the parameter of interest is a specified linear
combination of the regression par...