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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...
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...
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...
A Normal Hierarchical Model and Minimum Contrast Estimation for Random Intervals
random intervals Normality hierarchical Choquet functional minimum contrast estimator strong consistency asymptotic normality.
2012/9/19
Many statistical data are imprecise due to factors such as mea-surement errors, computation errors, and lack of information. In such cases, data are better represented by intervals rather thanby singl...
Confidence intervals for sensitivity indices using reduced-basis metamodels
sensitivity analysis reduced basis method Sobol indices bootstrap method Monte Carlo method
2011/3/24
Global sensitivity analysis is often impracticable for complex and time demanding numerical models, as it requires a large number of runs. The reduced-basis approach provides a way to replace the orig...
Chi-square Intervals for a Poisson Parameter - Bayes, Classical and Structural
Confidence interval coverage probability estimation interval Poisson
2011/3/18
The 'standard' confidence interval for a Poisson parameter is only one of a number of estimation intervals based on the chi-square distribution that may be used in the estimation of the mean or mean r...
Asymptotic multivariate normality for the subseries values of a general statistic form a stationary sequence - with applications to nonparametric confidence intervals
Asymptotic multivariate the subseries values of a general statistic a stationary sequence
2009/9/23
Asymptotic multivariate normality for the subseries values of a general statistic form a stationary sequence - with applications to nonparametric confidence intervals。
ON THE CONSTRUCTION AND PROPERTIES OF BOOTSTRAP-t PREDICTION INTERVALS FOR STATIONARY TIME SERIES
Prediction intervals sieve bootstrap-t method of sieves
2009/9/18
We consider the construction of unconditional bootstrap-
t prediction intervals for stationary time series. Our approach
relies on the sieve bootstrap resampling scheme introduced by
Biihlmann.
Ba...
In this paper, we develop a general theory on the coverage probability of random inter-
vals defined in terms of discrete random variables with continuous parameter spaces. The
theory shows that the...
On the frequentist coverage of Bayesian credible intervals for lower bounded means
Bayesian credible sets restricted parameter space frequentist coverage probability logconcavity
2009/9/16
For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, we investigate the frequentist performance of the $100(1-alpha)%$ Bayesian HPD credible set associated...
Exact confidence intervals for the Hurst parameter of a fractional Brownian motion
Concentration inequalities exact confidence intervals fractional Brownian motion Hurst parameter
2009/9/16
In this short note, we show how to use concentration inequalities in order to build exact confidence intervals for the Hurst parameter associated with a one-dimensional fractional Brownian motion.
Functional asymptotic confidence intervals for a common mean of independent random variables
Lindeberg's condition symmetric random variable Student statistic Student process Wiener process functional central limit theorem
2009/9/16
We consider independent random variables (r.v.'s) with a common mean $mu$ that either satisfy Lindeberg's condition, or are symmetric around $mu$. Present forms of existing functional central limit th...