Related papers: Reducing bias and variance in quantile estimates w…
The distribution of the spacing, or the difference between consecutive order statistics, is known only for uniform and exponential random variates. We add here logistic and Gumbel variates, and present an estimator for distributions with a…
Traditional quantile estimators that are based on one or two order statistics are a common way to estimate distribution quantiles based on the given samples. These estimators are robust, but their statistical efficiency is not always good…
Let $F=F_N$ be the distribution of a finite real population of size $N$. Let $\widehat{F}=F_N$ be the empirical distribution of a sample of size $n$ drawn from the population without replacement. We prove the following remarkable {\it…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to…
Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely the ultimate convergence…
Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…
Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…
Quantiles, such as the median or percentiles, provide concise and useful information about the distribution of a collection of items, drawn from a totally ordered universe. We study data structures, called quantile summaries, which keep…
In this paper, we propose an empirical likelihood-based weighted estimator of regression parameter in quantile regression model with nonignorable missing covariates. The proposed estimator is computationally simple and achieves…
The manuscript discusses how to incorporate random effects for quantile regression models for clustered data with focus on settings with many but small clusters. The paper has three contributions: (i) documenting that existing methods may…
Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…
The use of quantiles to obtain insights about multivariate data is addressed. It is argued that incisive insights can be obtained by considering directional quantiles, the quantiles of projections. Directional quantile envelopes are…
Sensitivity forecasts inform the design of experiments and the direction of theoretical efforts. To arrive at representative results, Bayesian forecasts should marginalize their conclusions over uncertain parameters and noise realizations…
Bessel's correction adjusts the denominator in the sample variance formula from n to n-1 to ensure an unbiased estimator of the population variance. This paper provides rigorous algebraic derivations geometric interpretations and…
To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…
When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…
This paper develops theory for feasible estimators of finite-dimensional parameters identified by general conditional quantile restrictions, under much weaker assumptions than previously seen in the literature. This includes instrumental…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
We propose a general semi-supervised inference framework focused on the estimation of the population mean. As usual in semi-supervised settings, there exists an unlabeled sample of covariate vectors and a labeled sample consisting of…