By R L Chambers
Read or Download Maximum likelihood estimation for sample surveys PDF
Best probability & statistics books
This IMA quantity in arithmetic and its functions instructions IN strong records AND DIAGNOSTICS is predicated at the complaints of the 1st 4 weeks of the six week IMA 1989 summer time application "Robustness, Diagnostics, Computing and photos in Statistics". a major goal of the organizers used to be to attract a vast set of statisticians operating in robustness or diagnostics into collaboration at the tough difficulties in those components, quite at the interface among them.
Bayesian Networks: An creation presents a self-contained advent to the speculation and purposes of Bayesian networks, a subject matter of curiosity and significance for statisticians, computing device scientists and people thinking about modelling complicated information units. the cloth has been largely established in lecture room educating and assumes a simple wisdom of likelihood, statistics and arithmetic.
Lacking facts research in perform offers functional tools for examining lacking facts in addition to the heuristic reasoning for figuring out the theoretical underpinnings. Drawing on his 25 years of expertise gaining knowledge of, instructing, and consulting in quantitative components, the writer provides either frequentist and Bayesian views.
A completely revised and up-to-date variation of this advent to trendy statistical tools for form research form research is a vital instrument within the many disciplines the place items are in comparison utilizing geometrical beneficial properties. Examples contain evaluating mind form in schizophrenia; investigating protein molecules in bioinformatics; and describing development of organisms in biology.
- Logic Colloquium '95. Proceedings of the Annual European Summer Meeting of the Association of Symbolic Logic, held in Haifa, Israel, August 9-18, 1995
- Smoothing Splines: Methods and Applications (Chapman & Hall CRC Monographs on Statistics & Applied Probability)
- Mathematical Methods of Statistics.
- Topics in statistical mechanics
- Statistics II for Dummies (For Dummies (Math & Science))
Extra info for Maximum likelihood estimation for sample surveys
For example, in a health survey, d may consist of height, weight, smoking status and other variables of interest. In principle, the value of this variable is observable for each of the N units that make up the surveyed population, which we denote by U . Let DU denote the matrix containing these N values. When the survey variable is a scalar, then DU becomes a vector of N elements, which we denote by the corresponding lower case dU . We assume that DU is generated from a distribution with density DU , which is completely known except for a parameter vector θ.
This leads −1 z s and µz = z U . to the maximum likelihood estimates ν = y s − σyz σzz Since −1 µd = ν + σdz σzz µz , it immediately follows from the invariance properties of maximum likelihood that the maximum likelihood estimate of µ is µ= = µd µz = −1 ν + σdz σzz µz µz −1 ds + σdz σzz (z U − z s ) zU . 5) is not the sample mean vector (ds , z s )T that maximizes log ds , zs , but rather this sample mean vector modified by the imbalance between the nonsample and sample z-values, as well as the strength of the relationship between d and z, as measured ILLUSTRATIVE EXAMPLES WITH COMPLETE RESPONSE 35 by the covariance terms in V.
The important concepts of sufficiency and ancillarity give a more refined view of where in the likelihood this information is and is not contained. We refer to ancillarity in this book so it is important to give a definition; however, we only use it occasionally so the following definitions can be skipped at a first reading. BIBLIOGRAPHIC NOTES 21 A statistic t(Dobs ) is a sufficient statistic for a model if the conditional distribution of Dobs given t(Dobs ) = t is the same for all distributions in the model.