相关论文: What Did Fisher Mean by An Estimate?

Fisher information is a measure of the best precision with which a parameter can be estimated from statistical data. It can also be defined for a continuous random variable without reference to any parameters, in which case it has a…

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,…

Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…

Maximum likelihood estimation (MLE) and heuristic predictive estimation (HPE) are two widely used approaches in industrial uncertainty analysis. We review them from the point of view of decision theory, using Bayesian inference as a gold…

This article includes a discussion of the ``lost submarine problem", following Morey \emph{et al} (2016). As the title of that paper suggests (\emph{The fallacy of placing confidence in confidence intervals}), the example is intended to…

Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to…

The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…

Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters - both their errors and covariances. In this short review, I outline a…

We review the introduction of likelihood functions and Fisher information in classical estimation theory, and we show how they can be defined in a very similar manner within quantum measurement theory. We show that the stochastic master…

We introduce Fisher consistency in the sense of unbiasedness as a desirable property for estimators of class prior probabilities. Lack of Fisher consistency could be used as a criterion to dismiss estimators that are unlikely to deliver…

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We…

Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We…

Profile likelihood provides a general framework to infer on a scalar parameter of a statistical model. A confidence interval is obtained by numerically finding the two abscissas where the profile log-likelihood curve intersects an…

Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…

The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…

Fisher developed his geometric model to support the micro-mutationalism hypothesis which claims that small mutations are more likely to be beneficial and therefore to contribute to evolution and adaptation. While others have provided a…

Fisher's fiducial argument is widely viewed as a failed version of Neyman's theory of confidence limits. But Fisher's goal -- Bayesian-like probabilistic uncertainty quantification without priors -- was more ambitious than Neyman's, and…

Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. A\"{\i}t-Sahalia [J. Finance 54 (1999)…

Estimation of mean shift in a temporally ordered sequence of random variables with a possible existence of change-point is an important problem in many disciplines. In the available literature of more than fifty years the estimation methods…