Related papers: Estimating the Maximum Expected Value: An Analysis…
When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…
Extreme value analysis in the presence of censoring is receiving much attention as it has applications in many disciplines, including survival and reliability studies. Estimation of extreme value index (EVI) is of primary importance as it…
The exact expression is derived for the expected value, $< {p_i}> $, for the parameter for any bin $i$ of a histogram following a multinomial distribution derived by sorting $N$ observations into bins of $B$ classes, if $n_i$ of the…
Randomized artificial neural networks such as extreme learning machines provide an attractive and efficient method for supervised learning under limited computing ressources and green machine learning. This especially applies when equipping…
In this paper we propose an optimal predictor of a random variable that has either an infinite mean or an infinite variance. The method consists of transforming the random variable such that the transformed variable has a finite mean and…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…
Unbiased and consistent variance estimators generally do not exist for design-based treatment effect estimators because experimenters never observe more than one potential outcome for any unit. The problem is exacerbated by interference and…
This paper presents a theory of error in cross-validation testing of algorithms for predicting real-valued attributes. The theory justifies the claim that predicting real-valued attributes requires balancing the conflicting demands of…
In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of…
The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al. 2012), bearing a simple estimator with pleasing computational and statistical properties. Being able…
Traditionally model averaging has been viewed as an alternative to model selection with the ultimate goal to incorporate the uncertainty associated with the model selection process in standard errors and confidence intervals by using a…
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…
The estimated accuracy of a classifier is a random quantity with variability. A common practice in supervised machine learning, is thus to test if the estimated accuracy is significantly better than chance level. This method of signal…
The aim of the paper is to derive the numerical least-squares estimator for mean and variance of random variable. In order to do so the following questions have to be answered: (i) what is the statistical model for the estimation procedure?…
We study a linear high-dimensional regression model in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no response $Y$. We do not make any sparsity assumptions on the vector of…
In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard…
We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). Bayesian hierarchical models are popular for their ability to model complex dependence structures and…
We consider estimating an expected infinite-horizon cumulative discounted cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…