Improvement of the Predicted Least-Squares-Estimates in Multiple Linear Regression by Means of an Examination of Residuals.
Improving both domain and total area estimation by composition.
In this article we propose small area estimators for both the small and large area parameters. When the objective is to estimate parameters at both levels, optimality is achieved by a sample design that combines fixed and proportional allocation. In such a design, one fraction of the sample is distributed proportionally among the small areas and the rest is evenly distributed. Simulation is used to assess the performance of the direct estimator and two composite small area estimators, for a range...
Improving small area estimation by combining surveys: new perspectives in regional statistics.
A national survey designed for estimating a specific population quantity is sometimes used for estimation of this quantity also for a small area, such as a province. Budget constraints do not allow a greater sample size for the small area, and so other means of improving estimation have to be devised. We investigate such methods and assess them by a Monte Carlo study. We explore how a complementary survey can be exploited in small area estimation. We use the context of the Spanish Labour Force Survey...
Inference for random effects in prime basis factorials using commutative Jordan algebras
Commutative Jordan algebras are used to drive an highly tractable framework for balanced factorial designs with a prime number p of levels for their factors. Both fixed effects and random effects models are treated. Sufficient complete statistics are obtained and used to derive UMVUE for the relevant parameters. Confidence regions are obtained and it is shown how to use duality for hypothesis testing.
Inference in linear models with inequality constrained parameters
In many econometric applications there is prior information available for some or all parameters of the underlying model which can be formulated in form of inequality constraints. Procedures which incorporate this prior information promise to lead to improved inference. However careful application seems to be necessary. In this paper we will review some methods proposed in the literature. Among these there are inequality constrained least squares (ICLS), constrained maximum likelihood (CML) and...
Inference on the location parameter of exponential populations
Studentization and analysis of variance are simple in Gaussian families because X̅ and S² are independent random variables. We exploit the independence of the spacings in exponential populations with location λ and scale δ to develop simple ways of dealing with inference on the location parameter, namely by developing an analysis of scale in the homocedastic independent k-sample problem.
Influence diagnostics in exponentiated-Weibull regression models with censored data.
Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from the error assumptions and the presence of outliers and influential observations with the fitted models. The literature provides plenty of approaches for detecting outlying or influential observations in data sets. In this paper, we follow the local influence approach (Cook 1986) in detecting influential observations with exponentiated-Weibull regression models. The relevance of the...
Insensitivity region for variance components in general linear model
In linear regression models the estimator of variance components needs a suitable choice of a starting point for an iterative procedure for a determination of the estimate. The aim of this paper is to find a criterion for a decision whether a linear regression model enables to determine the estimate reasonably and whether it is possible to do so when using the given data.
Instrumental weighted variables under heteroscedasticity. Part I – Consistency
The proof of consistency instrumental weighted variables, the robust version of the classical instrumental variables is given. It is proved that all solutions of the corresponding normal equations are contained, with high probability, in a ball, the radius of which can be selected - asymptotically - arbitrarily small. Then also -consistency is proved. An extended numerical study (the Part II of the paper) offers a picture of behavior of the estimator for finite samples under various types and levels...
Instrumental weighted variables under heteroscedasticity. Part II – Numerical study
Results of a numerical study of the behavior of the instrumental weighted variables estimator – in a competition with two other estimators – are presented. The study was performed under various frameworks (homoscedsticity/heteroscedasticity, several level and types of contamination of data, fulfilled/broken orthogonality condition). At the beginning the optimal values of eligible parameters of estimatros in question were empirically established. It was done under the various sizes of data sets and...
Interval estimation in two way nested unbalanced random model.
The present paper deals with interval estimation of variance components in two way nested unbalanced random model. Employing a suitable transformation a statistic has been developed and its distribution is well approximated by chi-square. The confidence intervals for variance components and the simultaneous confidence interval for their ratios have been derived.
Interval linear regression analysis based on Minkowski difference – a bridge between traditional and interval linear regression models
In this paper, we extend the traditional linear regression methods to the (numerical input)-(interval output) data case assuming both the observation/measurement error and the indeterminacy of the input-output relationship. We propose three different models based on three different assumptions of interval output data. In each model, the errors are defined as intervals by solving the interval equation representing the relationship among the interval output, the interval function and the interval...
Intrinsic linearization of nonlinear regression by principal components method.
Intrinsic priors for hypothesis testing in normal regression models.
Testing that some regression coefficients are equal to zero is an important problem in many applications. Homoscedasticity is not necessarily a realistic condition in this setting and, as a consequence, no frequentist test there exist. Approximate tests have been proposed. In this paper a Bayesian analysis of this problem is carried out, from a default Bayesian model choice perspective. Explicit expressions for intrinsic priors are provided, and it is shown that the corresponding Bayes factor is...
Inversion of partitioned matrices in investigation of the twoepoch linear model with the nuisance parameters
The estimation procedures in the multiepoch (and specially twoepoch) linear regression models with the nuisance parameters that were described in [2], Chapter 9, frequently need finding the inverse of a partitioned matrix. We use different kinds of such inversion in dependence on simplicity of the result, similarly as in well known Rohde formula for partitioned matrix. We will show some of these formulas, also methods how to get the other formulas, and then we applicate the formulas in estimation...
Inverting covariance matrices
Some useful tools in modelling linear experiments with general multi-way classification of the random effects and some convenient forms of the covariance matrix and its inverse are presented. Moreover, the Sherman-Morrison-Woodbury formula is applied for inverting the covariance matrix in such experiments.