Application des modèles statistiques spatio-temporels aux échantillonnages forestiers successifs

1992 ◽  
Vol 22 (12) ◽  
pp. 1988-1995 ◽  
Author(s):  
François Houllier ◽  
Jean-Claude Pierrat
Keyword(s):  
Forest Decline ◽  
Sampling Strategy ◽  
Partial Replacement ◽  
General Interest ◽  
Regionalized Variables ◽  
Modèles Statistiques ◽  
Temporal Structures ◽  
Best Linear Unbiased ◽  
Temporal And Spatial ◽  
Best Linear Unbiased Estimators

When surveying the same forest on several successive occasions, sampling intensity may be reduced without any loss of precision by taking into account the spatial and temporal structures of the estimated variable. The theory of regionalized variables (RV) generalizes and improves the estimators derived from the classical sampling with partial replacement (SPR) theory. A general model accounting for both temporal and spatial structures is presented in the context of successive inventories. The best linear unbiased estimators (Blue) are derived by using the kriging technique. A comparison of RV and SPR estimators on a simple numerical example reveals that the variance can be overestimated with the classical estimators. An application to a forest decline survey illustrates how this theory may be used to choose and optimize a sampling strategy. Finally, the general interest as well as some practical problems of RV theory are discussed.

scholarly journals Matrix rank and inertia formulas in the analysis of general linear models

2017 ◽  
Vol 15 (1) ◽  
pp. 126-150 ◽  
Author(s):  
Yongge Tian
Keyword(s):  
Statistical Analysis ◽  
Least Squares ◽  
Linear Models ◽  
Linear Regression Analysis ◽  
Ordinary Least Squares ◽  
Covariance Matrices ◽  
General Linear ◽  
General Linear Models ◽  
Best Linear Unbiased ◽  
Best Linear Unbiased Estimators

Abstract Matrix mathematics provides a powerful tool set for addressing statistical problems, in particular, the theory of matrix ranks and inertias has been developed as effective methodology of simplifying various complicated matrix expressions, and establishing equalities and inequalities occurred in statistical analysis. This paper describes how to establish exact formulas for calculating ranks and inertias of covariances of predictors and estimators of parameter spaces in general linear models (GLMs), and how to use the formulas in statistical analysis of GLMs. We first derive analytical expressions of best linear unbiased predictors/best linear unbiased estimators (BLUPs/BLUEs) of all unknown parameters in the model by solving a constrained quadratic matrix-valued function optimization problem, and present some well-known results on ordinary least-squares predictors/ordinary least-squares estimators (OLSPs/OLSEs). We then establish some fundamental rank and inertia formulas for covariance matrices related to BLUPs/BLUEs and OLSPs/OLSEs, and use the formulas to characterize a variety of equalities and inequalities for covariance matrices of BLUPs/BLUEs and OLSPs/OLSEs. As applications, we use these equalities and inequalities in the comparison of the covariance matrices of BLUPs/BLUEs and OLSPs/OLSEs. The work on the formulations of BLUPs/BLUEs and OLSPs/OLSEs, and their covariance matrices under GLMs provides direct access, as a standard example, to a very simple algebraic treatment of predictors and estimators in linear regression analysis, which leads a deep insight into the linear nature of GLMs and gives an efficient way of summarizing the results.

Estimation of the Parameters of Triangular Distribution by Order Statistics

2003 ◽  
Vol 54 (1-2) ◽  
pp. 45-56 ◽  
Author(s):  
Philip Samuel ◽  
P. Yageen Thomas
Keyword(s):  
Order Statistics ◽  
Triangular Distribution ◽  
Unbiased Estimators ◽  
Product Moments ◽  
Scale Parameters ◽  
U Statistics ◽  
Best Linear Unbiased ◽  
Best Linear Unbiased Estimators ◽  
Moments Of Order Statistics ◽  
Single And Product Moments

In this paper, we derive explicit expressions for the single and product moments of order statistics arising from the standard triangular distribution. Best linear unbiased estimators of the location and scale parameters of a triangular distribution based on order statistics are obtained. The efficiencies of these estimators are also compared with estimators based on U-statistics

Theory of best integer equivariant estimation for contaminated normal and multivariate t-distribution with applications

2021 ◽  
Author(s):  
Peter Teunissen
Keyword(s):  
Normal Distribution ◽  
Least Squares ◽  
Unbiased Estimation ◽  
Multivariate T Distribution ◽  
Integer Least Squares ◽  
Wide Range ◽  
Best Linear Unbiased ◽  
Best Linear Unbiased Estimators ◽  
T Distribution ◽  
Multivariate T

<p>Best integer equivariant (BIE) estimators provide minimum mean squared error (MMSE) solutions to the problem of GNSS carrier-phase ambiguity resolution for a wide range of distributions. The associated BIE estimators are universally optimal in the sense that they have an accuracy which is never poorer than that of any integer estimator and any linear unbiased estimator. Their accuracy is therefore always better or the same as that of Integer Least-Squares (ILS) estimators and Best Linear Unbiased Estimators (BLUEs).</p><p>Current theory is based on using BIE for the multivariate normal distribution. In this contribution this will be generalized to the contaminated normal distribution and the multivariate t-distribution, both of which have heavier tails than the normal. Their computational formulae are presented and discussed in relation to that of the normal distribution. In addition a GNSS real-data based analysis is carried out to demonstrate the universal MMSE properties of the BIE estimators for GNSS-baselines and associated parameters.</p><p> </p><p><strong>Keywords: </strong>Integer equivariant (IE) estimation · Best integer equivariant (BIE) · Integer Least-Squares (ILS) . Best linear unbiased estimation (BLUE) · Multivariate contaminated normal · Multivariate t-distribution . Global Navigation Satellite Systems (GNSSs)</p>

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