scholarly journals An Approximate Point-based Alternative for the Estimation of Variance under Big BAF Sampling

2020 ◽  
Author(s):  
Thomas B. Lynch ◽  
Jeffrey H Gove ◽  
Timothy G Gregoire ◽  
Mark J Ducey
Keyword(s):  
Forest Inventory ◽  
Variance Estimation ◽  
Basal Area ◽  
Simulation Studies ◽  
Variance Estimator ◽  
Forest Types ◽  
Variance Estimators ◽  
Computer Simulation Studies ◽  
New Formula ◽  
Estimation Of Variance

Abstract BackgroundA new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including \dbh s and heights needed for volume estimation.MethodsThe new estimator is derived using the \Dm\ from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce's formula.ResultsSeveral computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas.ConclusionsA possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the \dbh-height relationship can be affected substantially by density perhaps through competition. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1/n where n is the number of sample points.

scholarly journals An approximate point-based alternative for the estimation of variance under big BAF sampling

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Thomas B. Lynch ◽  
Jeffrey H. Gove ◽  
Timothy G. Gregoire ◽  
Mark J. Ducey
Keyword(s):  
Forest Inventory ◽  
Variance Estimation ◽  
Basal Area ◽  
Volume Estimation ◽  
Delta Method ◽  
Sampling Point ◽  
Variance Estimator ◽  
Computer Simulation Studies ◽  
New Formula ◽  
Estimation Of Variance

Abstract Background A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. Methods The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula. Results Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas. Conclusions A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of $\frac {1}{n}$ 1 n where n is the number of sample points.

scholarly journals A note on the estimation of variance for big BAF sampling

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Jeffrey H. Gove ◽  
Timothy G. Gregoire ◽  
Mark J. Ducey ◽  
Thomas B. Lynch
Keyword(s):  
Variance Estimation ◽  
Basal Area ◽  
Estimation Procedure ◽  
Delta Method ◽  
Sampling Effort ◽  
Individual Tree ◽  
Variance Estimators ◽  
Taylor Series Approximation ◽  
The Mean ◽  
Estimation Of Variance

Abstract Background The double sampling method known as “big BAF sampling” has been advocated as a way to reduce sampling effort while still maintaining a reasonably precise estimate of volume. A well-known method for variance determination, Bruce’s method, is customarily used because the volume estimator takes the form of a product of random variables. However, the genesis of Bruce’s method is not known to most foresters who use the method in practice. Methods We establish that the Taylor series approximation known as the Delta method provides a plausible explanation for the origins of Bruce’s method. Simulations were conducted on two different tree populations to ascertain the similarities of the Delta method to the exact variance of a product. Additionally, two alternative estimators for the variance of individual tree volume-basal area ratios, which are part of the estimation process, were compared within the overall variance estimation procedure. Results The simulation results demonstrate that Bruce’s method provides a robust method for estimating the variance of inventories conducted with the big BAF method. The simulations also demonstrate that the variance of the mean volume-basal area ratios can be computed using either the usual sample variance of the mean or the ratio variance estimators with equal accuracy, which had not been shown previously for Big BAF sampling. Conclusions A plausible explanation for the origins of Bruce’s method has been set forth both historically and mathematically in the Delta Method. In most settings, there is evidently no practical difference between applying the exact variance of a product or the Delta method—either can be used. A caution is articulated concerning the aggregation of tree-wise attributes into point-wise summaries in order to test the correlation between the two as a possible indicator of the need for further covariance augmentation.

Precision of inventory using different edge overlap methods

2013 ◽  
Vol 43 (11) ◽  
pp. 1081-1083 ◽  
Author(s):  
P.W. West
Keyword(s):  
Forest Inventory ◽  
Stocking Density ◽  
Basal Area ◽  
Radiata Pine ◽  
Forest Edge ◽  
Substantial Effect ◽  
Sampling Procedure ◽  
Simulation Studies ◽  
Forest Types ◽  
Plantation Forest

Bias due to the sampling procedure may occur in estimates from forest inventory when sampled trees are close to the forest edge. The “mirage,” “walkthrough,” and “walk through and fro” methods are three practical measurement methods developed to avoid this problem. However, as an increasing proportion of the sample requires use of these methods, the precision of the population estimates made from the sample is likely to decline. Simulation studies were undertaken of forest inventory, using point sampling, to estimate mean stand basal area and stocking density in both an even-aged, monoculture radiata pine (Pinus radiata D. Don) plantation forest and an uneven-aged, multispecies, complex primary rainforest. In both forest types, bias arising from use of any of the three methods appeared to be negligible. As well, precision of estimates from the inventory was reduced only slightly, even when a high proportion of the samples required use of any one of the three methods. None of the methods appeared appreciably superior in this respect to any of the others. It was concluded that use of any of the three methods was unlikely to have any substantial effect on the overall precision of estimates made from forest inventory.

Variance Estimation by Linearisation for the At Risk of Poverty or Social Exclusion (AROPE) Rate

2020 ◽  
Vol 49 (1) ◽  
pp. 33-44
Author(s):  
Stefan Zins
Keyword(s):  
At Risk ◽  
Social Exclusion ◽  
Variance Estimation ◽  
Simulation Studies ◽  
Important Indicator ◽  
Variance Estimators ◽  
Complex Sampling ◽  
Key Indicator ◽  
Complex Sampling Design ◽  
Data Source

The At Risk of Poverty or Social Exclusion (AROPE) Rate is the key indicator for monitoring the European Commissions 2020 Strategy poverty target. But the variance of the AROPE Rate is not straightforward to estimate. Re-sampling methods can be used, but they are difficult to adapt to complex sampling design, that are often used for the surveys that provide the data source for estimating the AROPER. The presented work fills a methodological gap by providing a linearisation of the AROPE Rate estimator that can be used with well known variance estimators and therefore facilitate the reporting of appropriate inference for this important indicator. The precision of the developed variance estimators based on linearisation is assessed via simulation studies and compared with a bootstrap variance estimator, as an alternative.

scholarly journals Evaluation of mapped-plot variance estimators across a range of partial nonresponse in a post-stratified national forest inventory

2021 ◽  
Author(s):  
James A. Westfall ◽  
Andrew J. Lister ◽  
Charles T. Scott
Keyword(s):  
Forest Inventory ◽  
Variance Estimation ◽  
Phase 1 ◽  
National Forest Inventory ◽  
Forest Area ◽  
Variance Estimator ◽  
Adjustment Factor ◽  
Primary Methods ◽  
Wide Range ◽  
Variance Estimates

When conducting a forest inventory, sometimes portions of plots cannot be measured due to inaccessibility. Two primary methods have been presented to account for partial nonresponse in the estimation phase: 1) use a ratio-to-size estimator, or 2) apply an adjustment factor to all plot observations in proportion to the missing area. Both approaches provide identical estimates of the population mean, but the estimates of variance differ when partial nonresponse is present. Variance estimator performance was examined for a range of population forest area and partial nonresponse proportions in the sample. The ratio-to-size variance estimator performed unbiasedly with respect to simulation results, but the adjustment factor variance estimates were biased with the magnitude and direction dependent upon the forest area proportion and amount of partial nonresponse. The bias is relatively small when the partial nonresponse is small, which is often the case; however, the ratio-to-size method is preferred to ensure accurate variance estimation for a wide range of circumstances.

scholarly journals Multiple-Imputation Variance Estimation in Studies With Missing or Misclassified Inclusion Criteria

2020 ◽  
Vol 189 (12) ◽  
pp. 1628-1632
Author(s):  
Mark J Giganti ◽  
Bryan E Shepherd
Keyword(s):  
Multiple Imputation ◽  
Variance Estimation ◽  
Variance Estimator ◽  
Inclusion Criteria ◽  
Variance Estimators ◽  
Coverage Probabilities ◽  
Log Odds ◽  
Variance Estimate ◽  
High Level ◽  
Analysis Models

Abstract In observational studies using routinely collected data, a variable with a high level of missingness or misclassification may determine whether an observation is included in the analysis. In settings where inclusion criteria are assessed after imputation, the popular multiple-imputation variance estimator proposed by Rubin (“Rubin’s rules” (RR)) is biased due to incompatibility between imputation and analysis models. While alternative approaches exist, most analysts are not familiar with them. Using partially validated data from a human immunodeficiency virus cohort, we illustrate the calculation of an imputation variance estimator proposed by Robins and Wang (RW) in a scenario where the study exclusion criteria are based on a variable that must be imputed. In this motivating example, the corresponding imputation variance estimate for the log odds was 29% smaller using the RW estimator than using the RR estimator. We further compared these 2 variance estimators with a simulation study which showed that coverage probabilities of 95% confidence intervals based on the RR estimator were too high and became worse as more observations were imputed and more subjects were excluded from the analysis. The RW imputation variance estimator performed much better and should be employed when there is incompatibility between imputation and analysis models. We provide analysis code to aid future analysts in implementing this method.

Point-Poisson, point-pps, and modified point-pps sampling: efficiency and variance estimation

1992 ◽  
Vol 22 (8) ◽  
pp. 1071-1078 ◽  
Author(s):  
H.T. Schreuder ◽  
Z. Ouyang ◽  
M. Williams
Keyword(s):  
Variance Estimation ◽  
Regular Point ◽  
Regression Estimator ◽  
Variance Estimator ◽  
Poisson Sampling ◽  
Variance Estimators ◽  
Sample Tree ◽  
Fixed Sample ◽  
Regression Estimators ◽  
Generalized Regression Estimator

Modified point-pps (probability proportional to size) sampling selects at least one sample tree per point and yields a fixed sample size. Point-Poisson sampling is as efficient as this modified procedure but less efficient than regular point-pps sampling in a simulation study estimating total volume using either the Horvitz–Thompson (ŶHT) or the weighted regression estimator (Ŷwr). Point-pps sampling is somewhat more efficient than point-Poisson sampling for all estimators except ŶHT, and point-Poisson sampling is always somewhat more efficient than modified point-pps sampling across.all estimators. For board foot volume the regression estimators are more efficient than ŶHT for all three procedures. Point-pps sampling is always most efficient, except for ŶHT, and point-Poisson sampling is always more efficient than the modified point-pps procedure. We recommend using Ŷgr (generalized regression estimator), Ŷwr, or ŶHT for total volume and Ŷgr for board foot volume. Three variance estimators estimate the variances of the regression estimates with small bias; we recommend the simple bootstrap variance estimator because it is simple to compute and does as well as its two main competitors. It does well for ŶHT, too, for all three procedures and should be used for ŶHT in point-Ppisson sampling in preference to the Grosenbaugh variance approximation. An unbiased variance estimator is given for ŶHT with the modified point-pps procedure, but the simple bootstrap variance is equally good.

scholarly journals Simulation Studies for Complex Sampling Designs

2016 ◽  
Vol 35 (4) ◽  
Author(s):  
Helga Wagner ◽  
Doris Eckmair
Keyword(s):  
Simulation Study ◽  
Variance Estimation ◽  
Sampling Error ◽  
Estimation Method ◽  
Sampling Plan ◽  
Simulation Studies ◽  
Complex Surveys ◽  
Variance Estimators ◽  
Complex Sampling ◽  
Complex Sampling Designs

Choosing the appropriate variance estimation method in complex surveys is a difficult task since there exist a variety of techniques which usually cannot be compared mathematically. A relatively easy way to accomplish such a comparison is on the basis of simulation studies. Though simulation studies are widely used in statistics, they are not a standard tool for investigating properties of estimators in complex survey sampling designs. In this paper we describe the setup for a simulation study according to the sampling plan of the Austrian Microcensus (AMC), used 1994–2003 which is an example for a very complex sampling plan. To illustrate the proceeding we conducted a simulation study comparing basic variance estimators. Results of the study reveal the extent to which simple variance estimators may underestimate the true sampling error in close to reality situations.

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