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Least squares approximation in Bayesian analysis.

Michel Mouchart, Léopold Simar (1980)

Trabajos de Estadística e Investigación Operativa

This paper presents in a simple and unified framework the Least-Squares approximation of posterior expectations. Particular structures of the sampling process and of the prior distribution are used to organize and to generalize previous results. The two basic structures are obtained by considering unbiased estimators and exchangeable processes. These ideas are applied to the estimation of the mean. Sufficient reduction of the data is analysed when only the Least-Squares approximation is involved....

Least squares estimator consistency: a geometric approach

João Tiago Mexia, João Lita da Silva (2006)

Discussiones Mathematicae Probability and Statistics

Consistency of LSE estimator in linear models is studied assuming that the error vector has radial symmetry. Generalized polar coordinates and algebraic assumptions on the design matrix are considered in the results that are established.

Likelihood and parametric heteroscedasticity in normal connected linear models

Joao Tiago Mexia, Pedro Corte Real (2000)

Discussiones Mathematicae Probability and Statistics

A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.

Likelihood and quasi - likelihood estimation of transition probabilities

Ewa Bakinowska, Radosław Kala (2004)

Discussiones Mathematicae Probability and Statistics

In the paper two approaches to the problem of estimation of transition probabilities are considered. The approach by McCullagh and Nelder [5], based on the independent model and the quasi-likelihood function, is compared with the approach based on the marginal model and the standard likelihood function. The estimates following from these two approaches are illustrated on a simple example which was used by McCullagh and Nelder.

Likelihood and the Bayes procedure.

Hirotugu Akaike (1980)

Trabajos de Estadística e Investigación Operativa

In this paper the likelihood function is considered to be the primary source of the objectivity of a Bayesian method. The necessity of using the expected behaviour of the likelihood function for the choice of the prior distribution is emphasized. Numerical examples, including seasonal adjustment of time series, are given to illustrate the practical utility of the common-sense approach to Bayesian statistics proposed in this paper.

Likelihood for random-effect models (with discussion).

Youngjo Lee, John A. Nelder (2005)

SORT

For inferences from random-effect models Lee and Nelder (1996) proposed to use hierarchical likelihood (h-likelihood). It allows influence from models that may include both fixed and random parameters. Because of the presence of unobserved random variables h-likelihood is not a likelihood in the Fisherian sense. The Fisher likelihood framework has advantages such as generality of application, statistical and computational efficiency. We introduce an extended likelihood framework and discuss why...

Linear comparative calibration with correlated measurements

Gejza Wimmer, Viktor Witkovský (2007)

Kybernetika

The paper deals with the linear comparative calibration problem, i. e. the situation when both variables are subject to errors. Considered is a quite general model which allows to include possibly correlated data (measurements). From statistical point of view the model could be represented by the linear errors-in-variables (EIV) model. We suggest an iterative algorithm for estimation the parameters of the analysis function (inverse of the calibration line) and we solve the problem of deriving the...

Linear error propagation law and nonlinear functions

Lubomír Kubáček, Eva Tesaříková (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Linear error propagation law (LEPL) has been using frequently also for nonlinear functions. It can be adequate for an actual situation however it need not be so. It is useful to use some rule in order to recognize whether LEPL is admissible. The aim of the paper is to find such rule.

Linear model with nuisance parameters and with constraints on useful and nuisance parameters

Pavla Kunderová, Jaroslav Marek (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The properties of the regular linear model are well known (see [1], Chapter 1). In this paper the situation where the vector of the first order parameters is divided into two parts (to the vector of the useful parameters and to the vector of the nuisance parameters) is considered. It will be shown how the BLUEs of these parameters will be changed by constraints given on them. The theory will be illustrated by an example from the practice.

Linear versus quadratic estimators in linearized models

Lubomír Kubáček (2004)

Applications of Mathematics

In nonlinear regression models an approximate value of an unknown parameter is frequently at our disposal. Then the linearization of the model is used and a linear estimate of the parameter can be calculated. Some criteria how to recognize whether a linearization is possible are developed. In the case that they are not satisfied, it is necessary to take into account either some quadratic corrections or to use the nonlinear least squares method. The aim of the paper is to find some criteria for an...

Linearization conditions for regression models with unknown variance parameter

Anna Jenčová (2000)

Applications of Mathematics

In the case of the nonlinear regression model, methods and procedures have been developed to obtain estimates of the parameters. These methods are much more complicated than the procedures used if the model considered is linear. Moreover, unlike the linear case, the properties of the resulting estimators are unknown and usually depend on the true values of the estimated parameters. It is sometimes possible to approximate the nonlinear model by a linear one and use the much more developed linear...

Linearization regions for a confidence ellipsoid in singular nonlinear regression models

Lubomír Kubáček, Eva Tesaříková (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A construction of confidence regions in nonlinear regression models is difficult mainly in the case that the dimension of an estimated vector parameter is large. A singularity is also a problem. Therefore some simple approximation of an exact confidence region is welcome. The aim of the paper is to give a small modification of a confidence ellipsoid constructed in a linearized model which is sufficient under some conditions for an approximation of the exact confidence region.

Linearization regions for confidence ellipsoids

Lubomír Kubáček, Eva Tesaříková (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

If an observation vector in a nonlinear regression model is normally distributed, then an algorithm for a determination of the exact ( 1 - α ) -confidence region for the parameter of the mean value of the observation vector is well known. However its numerical realization is tedious and therefore it is of some interest to find some condition which enables us to construct this region in a simpler way.

Currently displaying 561 – 580 of 1241