Comparison of estimators of variance for forest inventories with systematic sampling - results from artificial populations
Abstract Background Large area forest inventories often use regular grids (with a single random start) of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations. A design-unbiased estimator of variance does not exist for this design. Oftentimes, a quasi-...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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KeAi Communications Co., Ltd.
2020-03-01
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| Series: | Forest Ecosystems |
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| Online Access: | http://link.springer.com/article/10.1186/s40663-020-00223-6 |
| _version_ | 1797966040849711104 |
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| author | Steen Magnussen Ronald E. McRoberts Johannes Breidenbach Thomas Nord-Larsen Göran Ståhl Lutz Fehrmann Sebastian Schnell |
| author_facet | Steen Magnussen Ronald E. McRoberts Johannes Breidenbach Thomas Nord-Larsen Göran Ståhl Lutz Fehrmann Sebastian Schnell |
| author_sort | Steen Magnussen |
| collection | DOAJ |
| description | Abstract Background Large area forest inventories often use regular grids (with a single random start) of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations. A design-unbiased estimator of variance does not exist for this design. Oftentimes, a quasi-default estimator applicable to simple random sampling (SRS) is used, even if it carries with it the likely risk of overestimating the variance by a practically important margin. To better exploit the precision of systematic sampling we assess the performance of five estimators of variance, including the quasi default. In this study, simulated systematic sampling was applied to artificial populations with contrasting covariance structures and with or without linear trends. We compared the results obtained with the SRS, Matérn’s, successive difference replication, Ripley’s, and D’Orazio’s variance estimators. Results The variances obtained with the four alternatives to the SRS estimator of variance were strongly correlated, and in all study settings consistently closer to the target design variance than the estimator for SRS. The latter always produced the greatest overestimation. In populations with a near zero spatial autocorrelation, all estimators, performed equally, and delivered estimates close to the actual design variance. Conclusion Without a linear trend, the SDR and DOR estimators were best with variance estimates more narrowly distributed around the benchmark; yet in terms of the least average absolute deviation, Matérn’s estimator held a narrow lead. With a strong or moderate linear trend, Matérn’s estimator is choice. In large populations, and a low sampling intensity, the performance of the investigated estimators becomes more similar. |
| first_indexed | 2024-04-11T02:09:35Z |
| format | Article |
| id | doaj.art-6be2d54b3a884640a5c9d62e1362f418 |
| institution | Directory Open Access Journal |
| issn | 2197-5620 |
| language | English |
| last_indexed | 2024-04-11T02:09:35Z |
| publishDate | 2020-03-01 |
| publisher | KeAi Communications Co., Ltd. |
| record_format | Article |
| series | Forest Ecosystems |
| spelling | doaj.art-6be2d54b3a884640a5c9d62e1362f4182023-01-03T02:27:07ZengKeAi Communications Co., Ltd.Forest Ecosystems2197-56202020-03-017111910.1186/s40663-020-00223-6Comparison of estimators of variance for forest inventories with systematic sampling - results from artificial populationsSteen Magnussen0Ronald E. McRoberts1Johannes Breidenbach2Thomas Nord-Larsen3Göran Ståhl4Lutz Fehrmann5Sebastian Schnell6506 West Burnside RoadRaspberry Ridge AnalyticsNorwegian Institute of Bioeconomy ResearchDepartment of Geosciences and Natural Resource Management, University of CopenhagenDepartment of Forest Resource Management, Swedish University of Agricultural SciencesForest Inventory and Remote Sensing, Faculty of Forest Sciences, University of GöttingenAlfred-Möller-Straße 1Abstract Background Large area forest inventories often use regular grids (with a single random start) of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations. A design-unbiased estimator of variance does not exist for this design. Oftentimes, a quasi-default estimator applicable to simple random sampling (SRS) is used, even if it carries with it the likely risk of overestimating the variance by a practically important margin. To better exploit the precision of systematic sampling we assess the performance of five estimators of variance, including the quasi default. In this study, simulated systematic sampling was applied to artificial populations with contrasting covariance structures and with or without linear trends. We compared the results obtained with the SRS, Matérn’s, successive difference replication, Ripley’s, and D’Orazio’s variance estimators. Results The variances obtained with the four alternatives to the SRS estimator of variance were strongly correlated, and in all study settings consistently closer to the target design variance than the estimator for SRS. The latter always produced the greatest overestimation. In populations with a near zero spatial autocorrelation, all estimators, performed equally, and delivered estimates close to the actual design variance. Conclusion Without a linear trend, the SDR and DOR estimators were best with variance estimates more narrowly distributed around the benchmark; yet in terms of the least average absolute deviation, Matérn’s estimator held a narrow lead. With a strong or moderate linear trend, Matérn’s estimator is choice. In large populations, and a low sampling intensity, the performance of the investigated estimators becomes more similar.http://link.springer.com/article/10.1186/s40663-020-00223-6Spatial autocorrelationLinear trendModel basedDesign biasedMatérn varianceSuccessive difference replication variance |
| spellingShingle | Steen Magnussen Ronald E. McRoberts Johannes Breidenbach Thomas Nord-Larsen Göran Ståhl Lutz Fehrmann Sebastian Schnell Comparison of estimators of variance for forest inventories with systematic sampling - results from artificial populations Forest Ecosystems Spatial autocorrelation Linear trend Model based Design biased Matérn variance Successive difference replication variance |
| title | Comparison of estimators of variance for forest inventories with systematic sampling - results from artificial populations |
| title_full | Comparison of estimators of variance for forest inventories with systematic sampling - results from artificial populations |
| title_fullStr | Comparison of estimators of variance for forest inventories with systematic sampling - results from artificial populations |
| title_full_unstemmed | Comparison of estimators of variance for forest inventories with systematic sampling - results from artificial populations |
| title_short | Comparison of estimators of variance for forest inventories with systematic sampling - results from artificial populations |
| title_sort | comparison of estimators of variance for forest inventories with systematic sampling results from artificial populations |
| topic | Spatial autocorrelation Linear trend Model based Design biased Matérn variance Successive difference replication variance |
| url | http://link.springer.com/article/10.1186/s40663-020-00223-6 |
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