Related papers: Breakthrough in Interval Data Fitting II. From Ran…
Multivariate meta-analysis is gaining prominence in evidence synthesis research because it enables simultaneous synthesis of multiple correlated outcome data, and random-effects models have generally been used for addressing between-studies…
The current standard for confidence interval construction in the context of a possibly misspecified model is to use an interval based on the sandwich estimate of variance. These intervals provide asymptotically correct coverage, but…
The recent decade has seen an enormous rise in the popularity of deep learning and neural networks. These algorithms have broken many previous records and achieved remarkable results. Their outstanding performance has significantly sped up…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
By combining a bound on the absolute value of the difference of mutual information between two joint probablity distributions with a fixed variational distance, and a bound on the probability of a maximal deviation in variational distance…
Evaluating treatment effect heterogeneity widely informs treatment decision making. At the moment, much emphasis is placed on the estimation of the conditional average treatment effect via flexible machine learning algorithms. While these…
We compute bias, variance, and approximate confidence intervals for the efficiency of a random selection process under various special conditions that occur in practical data analysis. We consider the following cases: a) the number of…
We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. We are mainly…
In the domain of physics experiments, data fitting is a pivotal technique for extracting insights from both experimental and simulated datasets. This article presents an approximation method designed to estimate the systematic errors…
Objective: This paper proposes a framework to support the scientific research of standards so that they can be better measured, evaluated, and designed. Methods: Beginning with the notion of common models, the framework describes the…
The behaviors of various confidence/credible interval constructions are explored, particularly in the region of low statistics where methods diverge most. We highlight a number of challenges, such as the treatment of nuisance parameters,…
A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…
Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
Using theoretical and numerical results, we document the accuracy of commonly applied variational Bayes methods across a range of state space models. The results demonstrate that, in terms of accuracy on fixed parameters, there is a clear…
Difference-in-differences (DID) is one of the most popular tools used to evaluate causal effects of policy interventions. This paper extends the DID methodology to accommodate interval outcomes, which are often encountered in empirical…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
The construction of numerical value scales (or priority values) is a recurrent topic in decision-aiding research. However, in real contexts, uncertainty and limited cognitive precision often lead decision-makers to provide interval…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
Bayesian inference is widely used in many different fields to test hypotheses against observations. In most such applications, an assumption is made of precise input values to produce a precise output value. However, this is unrealistic for…