scholarly journals Improving the Cavalieri estimator under non-equidistant sampling and dropouts

2020 ◽  
Vol 39 (3) ◽  
pp. 197-212
Author(s):  
Mads Stehr ◽  
Markus Kiderlen
Keyword(s):  
Stationary Point ◽  
Random Sampling ◽  
Convex Bodies ◽  
Three Dimensional ◽  
Estimation Procedure ◽  
Volume Estimation ◽  
Bounded Interval ◽  
Variance Estimators ◽  
Stationary Point Process ◽  
General Estimation

Motivated by the stereological problem of volume estimation from parallel section profiles, the so-called Newton-Cotes integral estimators based on random sampling nodes are analyzed. These estimators generalize the classical Cavalieri estimator and its variant for non-equidistant sampling nodes, the generalized Cavalieri estimator, and have typically a substantially smaller variance than the latter. The present paper focuses on the following points in relation to Newton-Cotes estimators: the treatment of dropouts, the construction of variance estimators, and, finally, their application in volume estimation of convex bodies.Dropouts are eliminated points in the initial stationary point process of sampling nodes, modeled by independent thinning. Among other things, exact representations of the variance are given in terms of the thinning probability and increments of the initial points under two practically relevant sampling models. The paper presents a general estimation procedure for the variance of Newton-Cotes estimators based on the sampling nodes in a bounded interval. Finally, the findings are illustrated in an application of volume estimation for three-dimensional convex bodies with sufficiently smooth boundaries.

scholarly journals Comparison of Variance Estimators for Systematic Environmental Sample Surveys: Considerations for Post-Stratified Estimation

Forests ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 772
Author(s):  
Bryce Frank ◽  
Vicente J. Monleon
Keyword(s):  
Random Sampling ◽  
Simple Random Sampling ◽  
National Forest Inventory ◽  
Point Estimation ◽  
Systematic Sampling ◽  
Sampling Variance ◽  
Variance Estimators ◽  
The Past ◽  
Point Estimators ◽  
Species Specific

The estimation of the sampling variance of point estimators under two-dimensional systematic sampling designs remains a challenge, and several alternative variance estimators have been proposed in the past few decades. In this work, we compared six alternative variance estimators under Horvitz-Thompson (HT) and post-stratification (PS) point estimation regimes. We subsampled a multitude of species-specific forest attributes from a large, spatially balanced national forest inventory to compare the variance estimators. A variance estimator that assumes a simple random sampling design exhibited positive relative bias under both HT and PS point estimation regimes ranging between 1.23 to 1.88 and 1.11 to 1.78 for HT and PS, respectively. Alternative estimators reduced this positive bias with relative biases ranging between 1.01 to 1.66 and 0.90 to 1.64 for HT and PS, respectively. The alternative estimators generally obtained improved efficiencies under both HT and PS, with relative efficiency values ranging between 0.68 to 1.28 and 0.68 to 1.39, respectively. We identified two estimators as promising alternatives that provide clear improvements over the simple random sampling estimator for a wide variety of attributes and under HT and PS estimation regimes.

On projected thick sections of stationary point processes and Boolean models

1996 ◽  
Vol 28 (2) ◽  
pp. 335-335
Author(s):  
Markus Kiderlen
Keyword(s):  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
Linear Subspace ◽  
Isotropic Case ◽  
Thick Section ◽  
Boolean Models ◽  
Dimensional Linear Subspace ◽  
Stationary Point Process ◽  
Stationary Point Processes

For a stationary point process X of convex particles in ℝd the projected thick section process X(L) on a q-dimensional linear subspace L is considered. Formulae connecting geometric functionals, e.g. the quermass densities of X and X(L), are presented. They generalize the classical results of Miles (1976) and Davy (1976) which hold only in the isotropic case.

Validation of Random Sampling as an Estimation Procedure for Lyme Disease Surveillance in Massachusetts and Minnesota

2016 ◽  
Vol 65 (2) ◽  
pp. 266-274 ◽  
Author(s):  
J. Bjork ◽  
C. Brown ◽  
H. Friedlander ◽  
E. Schiffman ◽  
D. Neitzel
Keyword(s):  
Lyme Disease ◽  
Random Sampling ◽  
Disease Surveillance ◽  
Estimation Procedure

Spatial Models of Sugars and Their Compounds

2021 ◽  
Vol 11 (2) ◽  
pp. 9-22
Author(s):  
Gennadiy Vladimirovich Zhizhin
Keyword(s):  
Convex Bodies ◽  
Three Dimensional ◽  
Spatial Models ◽  
Higher Dimensions ◽  
Three Dimensional Images

The images of saccharide and polysaccharide molecules in spaces of various dimensions are considered. A method has been developed for obtaining simplified three-dimensional images of sugar molecules and their chains based on their images in spaces of higher dimensions. It was found that three-dimensional images of furanose and pyranose molecules fundamentally differ from each other to form convex and, accordingly, non-convex bodies. This leads to fundamental differences in the structure of polysaccharides from these molecules.

Improved Random Sampling Consistency Algorithm Employed in Three-Dimensional Point Cloud Registration

2018 ◽  
Vol 55 (10) ◽  
pp. 101104
Author(s):  
刘美菊 Liu Meiju ◽  
王旭东 Wang Xudong ◽  
李凌燕 Li Lingyan ◽  
高恩阳 Gao Enyang
Keyword(s):  
Random Sampling ◽  
Point Cloud ◽  
Three Dimensional ◽  
Point Cloud Registration

On the weak convergence of a class of estimators of the variance-time curve of a weakly stationary point process

1977 ◽  
Vol 14 (01) ◽  
pp. 114-126 ◽  
Author(s):  
A. M. Liebetrau
Keyword(s):  
Weak Convergence ◽  
Gaussian Process ◽  
Point Process ◽  
Stationary Point ◽  
Stationary Gaussian Process ◽  
Time Curve ◽  
Second Moment ◽  
Stationary Point Process ◽  
Class Of Estimators

The second-moment structure of an estimator V*(t) of the variance-time curve V(t) of a weakly stationary point process is obtained in the case where the process is Poisson. This result is used to establish the weak convergence of a class of estimators of the form Tβ (V*(tTα ) – V(tTα )), 0 < α < 1, to a non-stationary Gaussian process. Similar results are shown to hold when α = 0 and in the case where V(tTα ) is replaced by a suitable estimator.

Selective interaction of a Poisson and renewal process: first-order stationary point results

1970 ◽  
Vol 7 (02) ◽  
pp. 359-372 ◽  
Author(s):  
A. J. Lawrance
Keyword(s):  
Stationary Point ◽  
Joint Distribution ◽  
Point Processes ◽  
First Order ◽  
Response Interval ◽  
Selective Interaction ◽  
Counting Distribution ◽  
Stationary Point Process ◽  
Equilibrium Process ◽  
Stationary Point Processes

The simple stationarity of a previously derived equilibrium process of responses in a renewal inhibited stationary point process is established by deriving the joint distribution of the number of responses in contiguous intervals in the process. For a renewal inhibited Poisson process the variancetime function of the process is obtained; the distribution of an arbitrary between-response interval and the synchronous counting distribution are also derived following analytic justification of the required results. These results strengthen earlier results in the theory of stationary point processes. Three other point processes arising from the interaction are briefly discussed.

Some multivariate generalizations of results in univariate stationary point processes

1977 ◽  
Vol 14 (04) ◽  
pp. 748-757 ◽  
Author(s):  
Mark Berman
Keyword(s):  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
Stationary Point Process ◽  
Stationary Point Processes

Some relationships are derived between the asynchronous and partially synchronous counting and interval processes associated with a multivariate stationary point process. A few examples are given to illustrate some of these relationships.

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