Related papers: Estimation in Discrete Parameter Models
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed…
Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…
This paper generalizes recent proposals of density forecasting models and it develops theory for this class of models. In density forecasting, the density of observations is estimated in regions where the density is not observed.…
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…
Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…
The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling and systematic sampling. This volume is a collection of five papers. The following problems…
Social sampling is a novel randomized message passing protocol inspired by social communication for opinion formation in social networks. In a typical social sampling algorithm, each agent holds a sample from the empirical distribution of…
Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…
Modeling and understanding multivariate extreme events is challenging, but of great importance in various applications - e.g. in biostatistics, climatology, and finance. The separating Hill estimator can be used in estimating the extreme…
One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for…
This paper explores strong and weak consistency of M-estimators for non-identically distributed data, extending prior work. Emphasis is given to scenarios where data is viewed as a triangular array, which encompasses distributional…
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…
The proliferation of science and technology has led to the prevalence of voluminous data sets that are distributed across multiple machines. It is an established fact that conventional statistical methodologies may be unfeasible in the…
A finite set is "hidden" if its elements are not directly enumerable or if its size cannot be ascertained via a deterministic query. In public health, epidemiology, demography, ecology and intelligence analysis, researchers have developed a…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…