Consistency in systematic sampling for stereology

1996 ◽  
Vol 28 (2) ◽  
pp. 329-330
Author(s):  
X. Gual Arnau ◽  
L. M. Cruz-Orive
Keyword(s):  
Surface Area ◽  
Strong Consistency ◽  
Sufficient Conditions ◽  
Estimation Accuracy ◽  
Systematic Sampling ◽  
Geometrical Object ◽  
Important Prerequisite ◽  
Curve Length ◽  
Systematic Pattern

In design-based stereology, fixed parameters (such as volume, surface area, curve length, feature number, connectivity) of a non-random geometrical object are estimated by intersecting the object with randomly located and oriented geometrical probes (e.g. test slabs, planes, lines, points), [4], [5], [8], [11], [12]. Estimation accuracy may in principle be increased by increasing the number of probes, which are usually laid in a systematic pattern, [1], [2], [3], [7], [9], [10]. An important prerequisite to increase accuracy, however, is that the relevant estimators are unbiased and consistent. Our purpose is therefore to give sufficient conditions for the unbiasedness and strong consistency of design-based stereological estimators obtained by systematic sampling.

Consistency in systematic sampling for stereology

1996 ◽  
Vol 28 (02) ◽  
pp. 329-330
Author(s):  
X. Gual Arnau ◽  
L. M. Cruz-Orive
Keyword(s):  
Surface Area ◽  
Strong Consistency ◽  
Sufficient Conditions ◽  
Estimation Accuracy ◽  
Systematic Sampling ◽  
Geometrical Object ◽  
Important Prerequisite ◽  
Curve Length ◽  
Systematic Pattern

In design-based stereology, fixed parameters (such as volume, surface area, curve length, feature number, connectivity) of a non-random geometrical object are estimated by intersecting the object with randomly located and oriented geometrical probes (e.g. test slabs, planes, lines, points), [4], [5], [8], [11], [12]. Estimation accuracy may in principle be increased by increasing the number of probes, which are usually laid in a systematic pattern, [1], [2], [3], [7], [9], [10]. An important prerequisite to increase accuracy, however, is that the relevant estimators are unbiased and consistent. Our purpose is therefore to give sufficient conditions for the unbiasedness and strong consistency of design-based stereological estimators obtained by systematic sampling.

Consistency in systematic sampling

1996 ◽  
Vol 28 (4) ◽  
pp. 982-992 ◽  
Author(s):  
X. Gual Arnau ◽  
L. M. Cruz-Orive
Keyword(s):  
Sample Size ◽  
Surface Area ◽  
Strong Consistency ◽  
Sufficient Conditions ◽  
Estimation Accuracy ◽  
Systematic Sampling ◽  
Geometrical Object ◽  
Important Prerequisite ◽  
Systematic Pattern ◽  
Increase Sample Size

In design-based stereology, fixed parameters (such as volume, surface area, curve length, feature number, connectivity) of a non-random geometrical object are estimated by intersecting the object with randomly located and oriented geometrical probes (e.g. test slabs, planes, lines, points). Estimation accuracy may in principle be increased by increasing the number of probes, which are usually laid in a systematic pattern. An important prerequisite to increase accuracy, however, is that the relevant estimators are unbiased and consistent. The purpose of this paper is therefore to give sufficient conditions for the unbiasedness and strong consistency of design-based stereological estimators obtained by systematic sampling. Relevant mechanisms to increase sample size, compatible with stereological practice, are considered.

Consistency in systematic sampling

1996 ◽  
Vol 28 (04) ◽  
pp. 982-992 ◽  
Author(s):  
X. Gual Arnau ◽  
L. M. Cruz-Orive
Keyword(s):  
Sample Size ◽  
Surface Area ◽  
Strong Consistency ◽  
Sufficient Conditions ◽  
Estimation Accuracy ◽  
Systematic Sampling ◽  
Geometrical Object ◽  
Important Prerequisite ◽  
Systematic Pattern ◽  
Increase Sample Size

In design-based stereology, fixed parameters (such as volume, surface area, curve length, feature number, connectivity) of a non-random geometrical object are estimated by intersecting the object with randomly located and oriented geometrical probes (e.g. test slabs, planes, lines, points). Estimation accuracy may in principle be increased by increasing the number of probes, which are usually laid in a systematic pattern. An important prerequisite to increase accuracy, however, is that the relevant estimators are unbiased and consistent. The purpose of this paper is therefore to give sufficient conditions for the unbiasedness and strong consistency of design-based stereological estimators obtained by systematic sampling. Relevant mechanisms to increase sample size, compatible with stereological practice, are considered.

scholarly journals FIBRIN-TYPE FIBRINOID IN HUMAN PLACENTA: A STEREOLOGICAL ANALYSIS OF ITS ASSOCIATION WITH INTERVILLOUS VOLUME AND VILLOUS SURFACE AREA

2011 ◽  
Vol 20 (1) ◽  
pp. 1 ◽  
Author(s):  
Terry M Mayhew
Keyword(s):  
Surface Area ◽  
Test Point ◽  
Systematic Sampling ◽  
Vascular Perfusion ◽  
Correlation And Regression Analysis ◽  
Intervillous Space ◽  
Terminal Villi ◽  
Villous Surface ◽  
Normal Gestation

Stereological methods were used to examine fibrin-type fibrinoid deposition in the intervillous spaces of human placentas collected during gestation (12-41 weeks) and from term pregnancies at low (400 m) and high (3.6 km) altitude. The main aim was to test predictions about the relationships between fibrinoid deposits and either the volume of intervillous space or the surface area of (intermediate + terminal) villi. Fields of view on Masson trichrome-stained paraffin sections were selected as part of a systematic sampling design which randomised section location and orientation. Relative and absolute volumes were estimated by test point counting and surfaces by intersection counting. Apparent differences were tested by analyses of variance and relationships by correlation and regression analysis. Fibrinoid volume increased during gestation and correlated positively with intervillous volume and villous surface area. However, relative to intervillous volume, the main increase in fibrinoid occurred towards term (36-41 weeks). At high altitude, placentas contained more intervillous space but less fibrinoid. At both altitudes, there were significant correlations between fibrinoid volume and villous surface area. In all cases, changes in fibrinoid volume were commensurate with changes in villous surface area. Whilst findings lend support to the notion that fibrinoid deposition during normal gestation is influenced by the quality of vascular perfusion, they also emphasise that the extent of the villous surface is a more generally important factor. The villous surface may influence the steady state between coagulation and fibrinolysis since some pro-coagulatory events operate at the trophoblastic epithelium. They occur notably at sites of trophoblast de-epithelialisation and these arise following trauma or during the extrusion phase of normal epithelial turnover.

ASYMPTOTIC THEORY FOR A FACTOR GARCH MODEL

2009 ◽  
Vol 25 (2) ◽  
pp. 336-363 ◽  
Author(s):  
Christian M. Hafner ◽  
Arie Preminger
Keyword(s):  
Strong Consistency ◽  
Asymptotic Theory ◽  
Sufficient Conditions ◽  
Order Moment ◽  
Model Parameters ◽  
Conditional Heteroskedasticity ◽  
Volatility Spillover ◽  
Likelihood Estimator ◽  
Consistency And Asymptotic Normality ◽  
Quasi Maximum Likelihood

This paper investigates the asymptotic theory for a factor GARCH (generalized autoregressive conditional heteroskedasticity) model. Sufficient conditions for asymptotic stability and existence of moments are established. These conditions allow for volatility spillover and integrated GARCH. We then show the strong consistency and asymptotic normality of the quasi–maximum likelihood estimator (QMLE) of the model parameters. The results are obtained under the finiteness of the fourth-order moment of the innovations.

scholarly journals Nonparametric estimation of boundary measures and related functionals: asymptotic results

2009 ◽  
Vol 41 (2) ◽  
pp. 311-322 ◽  
Author(s):  
Inés Armendáriz ◽  
Antonio Cuevas ◽  
Ricardo Fraiman
Keyword(s):  
Asymptotic Normality ◽  
Surface Area ◽  
Nonparametric Estimation ◽  
Strong Consistency ◽  
Nonparametric Method ◽  
Asymptotic Results ◽  
Minkowski Content ◽  
Compact Body ◽  
Consistency And Asymptotic Normality ◽  
The One

We study a nonparametric method for estimating the boundary measure of a compact body G ⊂ ℝd (the boundary length when d = 2 and the surface area for d = 3) in the case when this measure agrees with the corresponding Minkowski content. The estimator we consider is closely related to the one proposed in Cuevas, Fraiman and Rodríguez-Casal (2007). Our method relies on two sets of random points, drawn inside and outside the set G, with different sampling intensities. Strong consistency and asymptotic normality are obtained under some shape hypotheses on the set G. Some applications and practical aspects are briefly discussed.

Systematic sampling on the circle and on the sphere

2000 ◽  
Vol 32 (3) ◽  
pp. 628-647 ◽  
Author(s):  
Ximo Gual-Arnau ◽  
Luis M. Cruz-Orive
Keyword(s):  
Historical Perspective ◽  
Sampling Design ◽  
Systematic Sampling ◽  
Periodic Functions ◽  
Unbiased Estimators ◽  
Bounded Support ◽  
Measurable Functions ◽  
Curve Length ◽  
First Time

Useful approximations have been developed along the years to predict the precision of systematic sampling for measurable functions of a bounded support in ℝd. Recently, the theory of systematic sampling on ℝ has received a thrust. In geometric sampling, design based unbiased estimators exist, however, which imply systematic sampling on the circle (𝕊1) and the semicircle (ℍ1); the planimeter estimator of an area, or the Buffon-Steinhaus estimator of curve length in the plane constitute popular examples. Over the last two decades, many other estimators of geometric measures have been obtained which imply systematic sampling also on the sphere (𝕊2). In this paper we adapt the theory available for non-periodic functions of bounded support on ℝ to periodic functions, and thereby to 𝕊1 and ℍ1, and we obtain new estimators of the corresponding variance approximations. Further we consider - we believe for the first time - the problem of predicting the precision of systematic sampling in 𝕊2. The paper starts with a historical perspective, and ends with suggestions for further research.

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