Topic
Fiducial inference
About: Fiducial inference is a research topic. Over the lifetime, 2254 publications have been published within this topic receiving 154871 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: This paper describes simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters, and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalizedlinear models, linear mixed effects models, the Cox model, robust linear models, etc.
Abstract: Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth
10,545 citations
Book•
01 Jan 1965TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Abstract: Algebra of Vectors and Matrices. Probability Theory, Tools and Techniques. Continuous Probability Models. The Theory of Least Squares and Analysis of Variance. Criteria and Methods of Estimation. Large Sample Theory and Methods. Theory of Statistical Inference. Multivariate Analysis. Publications of the Author. Author Index. Subject Index.
8,300 citations
TL;DR: In this article, it was shown that ignoring the process that causes missing data when making sampling distribution inferences about the parameter of the data, θ, is generally appropriate if and only if the missing data are missing at random and the observed data are observed at random, and then such inferences are generally conditional on the observed pattern of missing data.
Abstract: Two results are presented concerning inference when data may be missing. First, ignoring the process that causes missing data when making sampling distribution inferences about the parameter of the data, θ, is generally appropriate if and only if the missing data are “missing at random” and the observed data are “observed at random,” and then such inferences are generally conditional on the observed pattern of missing data. Second, ignoring the process that causes missing data when making Bayesian inferences about θ is generally appropriate if and only if the missing data are missing at random and the parameter of the missing data is “independent” of θ. Examples and discussion indicating the implications of these results are included.
8,197 citations
Book•
01 Jan 1980TL;DR: The Classical Inference Approach for the General Linear Model, Statistical Decision Theory and Biased Estimation, and the Bayesian Approach to Inference are reviewed.
Abstract: SAMPLING THEORY AND BAYESIAN APPROACHES TO INFERENCE. The Classical Inference Approach for the General Linear Model. Statistical Decision Theory and Biased Estimation. The Bayesian Approach to Inference. INFERENCE IN GENERAL STATISTICAL MODELS AND TIME SERIES. Some Asymptotic Theory and Other General Results for the Linear Statistical Model. Nonlinear Statistical Models. Time Series. DYNAMIC SPECIFICATIONS. Autocorrelation. Finite Distributed Lags. Infinite Distributed Lags. SOME ALTERNATIVE COVARIANCE STRUCTURES. Heteroskedasticity. Disturbance--Related Sets of Regression Equations. Inference in Models that Combine Time Series and Cross--Sectional Data. INFERENCE IN SIMULTANEOUS EQUATION MODELS. Specification and Identification in Simultaneous Equation Models. Estimation and Inference in a System of Simultaneous Equations. Multiple Time Series and Systems of Dynamic Simultaneous Equations. FURTHER MODEL EXTENSIONS. Unobservable Variables. Qualitative and Limited Dependent Variable Models. Varying and Random Coefficient Models. Non--Normal Disturbances. On Selecting the Set of Aggressors. Multicollinearity. Appendices.
4,469 citations
Book•
01 Jun 1973
TL;DR: In this article, the effect of non-normality on inference about a population mean with generalizations was investigated. But the authors focused on the effect on the mean with information from more than one source.
Abstract: Nature of Bayesian Inference Standard Normal Theory Inference Problems Bayesian Assessment of Assumptions: Effect of Non-Normality on Inferences About a Population Mean with Generalizations Bayesian Assessment of Assumptions: Comparison of Variances Random Effect Models Analysis of Cross Classification Designs Inference About Means with Information from More than One Source: One-Way Classification and Block Designs Some Aspects of Multivariate Analysis Estimation of Common Regression Coefficients Transformation of Data Tables References Indexes.
3,896 citations