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While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set --`inferring the uncertainty of model parameters on the basis of observations' -- has been continually pursued by many statisticians. To…
In recent years the ultrahigh dimensional linear regression problem has attracted enormous attentions from the research community. Under the sparsity assumption most of the published work is devoted to the selection and estimation of the…
Fisher's Method of Maximum Likelihood is shown to be a procedure for the construction of likelihood intervals or regions, instead of a procedure of point estimation. Based on Fisher's articles and books it is justified that by estimation…
Fisher's fiducial probability has recently received renewed attention under the name confidence. In this paper, we reformulate it within an extended-likelihood framework, a representation that helps to resolve many long-standing…
Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…
There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not…
In this paper, the authors first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with non-probability survey samples, and highlight the important…
In this paper, a new three-parameter lifetime distribution is introduced and many of its standard properties are discussed. These include shape of the probability density function, hazard rate function and its shape, quantile function,…
In this paper, we develop statistical inference techniques for the unknown coefficient functions and single-index parameters in single-index varying-coefficient models. We first estimate the nonparametric component via the local linear…
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…
Intuitively, unfamiliarity should lead to lack of confidence. In reality, current algorithms often make highly confident yet wrong predictions when faced with relevant but unfamiliar examples. A classifier we trained to recognize gender is…
Maximum likelihood (ML) estimation is widely used in statistics. The h-likelihood has been proposed as an extension of Fisher's likelihood to statistical models including unobserved latent variables of recent interest. Its advantage is that…
Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to…
In the context of the usual calibration model, we consider the case in which the independent variable is unobservable, but a pre-fixed value on its surrogate is available. Thus, considering controlled variables and assuming that the…
Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…
Estimating the difference between two binomial proportions will be investigated, where Bayesian, frequentist and fiducial (BFF) methods will be considered. Three vague priors will be used, the Jeffreys prior, a divergence prior and the…
This paper introduces a first implementation of a novel likelihood-ratio-based approach for constructing confidence intervals for neural networks. Our method, called DeepLR, offers several qualitative advantages: most notably, the ability…
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…
Clinical prediction models enable healthcare professionals to estimate individual outcomes using patient characteristics. Current sample size guidelines for developing or updating models with continuous outcomes aim to minimise overfitting…
Autoregressive moving average (ARMA) models are widely used for analyzing time series data. However, standard likelihood-based inference methodology for ARMA models has avoidable limitations. We show that currently accepted standards for…