Localization of growth estimates using non-parametric imputation methods

The purpose of this study was to examine different non-parametric imputation methods to reduce regional biases in growth estimates. Growth estimates were obtained using non-parametric k-nearest neighbour imputation (k-NN) to predict future 5-year diameter increment over bark at breast height for Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies). The Mahalanobis distance function was chosen as the most suitable measure of similarity, and then it was modified using weights provided by linear regression analysis. The use of weights from linear regression facilitated the examination of the correlation structure of the variables and allowed for transformations of the independent variables. Localization of the non-parametric estimates was obtained through a variety of methods, in particular, by using spatial coordinates as independent variables, by restricting the selection of neighbours to a circular area around the target tree, and by restriction the selection of neighbours to a local database. The localized estimates using spatial measures were then compared with non-spatial imputation and also with estimates from a parametric growth model. Results were then compared by vegetation zones in Finland. The differences between the non-spatial k-NN estimates and the localized spatial estimates were negligible when summarized to the stand level, and localization did not reduce the regional biases relative to the non-spatial k-NN estimates. Regional biases in northern Finland and in south-western Finland were reduced substantially using the non-parametric estimates rather than the parametric growth models, however, and the mean biases in all of the regions were quite similar, while the mean biases of the growth estimates obtained with the parametric model varied notably between the regions.

[1]  Timothy G. Gregorie,et al.  Generalized Error Structure for Forestry Yield Models , 1987, Forest Science.

[2]  W. Cleveland,et al.  Smoothing by Local Regression: Principles and Methods , 1996 .

[3]  Rafael Calama,et al.  Multilevel linear mixed model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach , 2005 .

[4]  Hans Gustav Gustavsen,et al.  Kivennäismaiden talousmetsien pysyvät (INKA ja TINKA) kokeet: suunnitelmat, mittausmenetelmät ja aineistojen rakenteet . , 1988 .

[5]  Nicholas C. Coops,et al.  Estimating stand structural details using nearest neighbor analyses to link ground data, forest cover maps, and Landsat imagery , 2008 .

[6]  P. Mahalanobis.  On the generalized distance in statistics , 1936 .

[7]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[8]  Hannu Hökkä,et al.  Models for predicting stand development in MELA System , 2002 .

[9]  Annika Kangas,et al.  Application of nearest-neighbour regression for generalizing sample tree information , 1997 .

[10]  Andrew W. Moore,et al.  Locally Weighted Learning , 1997, Artificial Intelligence Review.

[11]  K. Korhonen,et al.  Generalizing sample tree information with semiparametric and parametric models. , 1995 .

[12]  Annika Kangas,et al.  SIMO – SIMulointi ja Optimointi uuteen metsäsuunnitteluun , 1970 .

[13]  M. Maltamo,et al.  The k-MSN method for the prediction of species-specific stand attributes using airborne laser scanning and aerial photographs , 2007 .

[14]  Albert R. Stage,et al.  Most Similar Neighbor: An Improved Sampling Inference Procedure for Natural Resource Planning , 1995, Forest Science.

[15]  Annika Kangas,et al.  Estimating Individual Tree Growth with the k-Nearest Neighbour and k-Most Similar Neighbour Methods , 2001 .

[16]  Antti Mäkinen,et al.  SIMO: An adaptable simulation framework for multiscale forest resource data , 2009 .

[17]  K. Lowell,et al.  Spatial Accuracy Assessment : Land Information Uncertainty in Natural Resources , 1999 .

[18]  Ronald E. McRoberts,et al.  Stratified estimation of forest area using satellite imagery, inventory data, and the k-Nearest Neighbors technique , 2002 .

[19]  Annika Kangas,et al.  Estimating individual tree growth with nonparametric methods , 2003 .

[20]  S. R. Searle,et al.  Linear Models For Unbalanced Data , 1988 .

[21]  Annika Kangas,et al.  Methods based on k-nearest neighbor regression in the prediction of basal area diameter distribution , 1998 .

[22]  Jouko Laasasenaho.  Taper curve and volume functions for pine, spruce and birch [Pinus sylvestris, Picea abies, Betula pendula, Betula pubescens] , 1982 .

[23]  N. Altman.  An Introduction to Kernel and Nearest-Neighbor Nonparametric Regression , 1992 .

[24]  W. Härdle.  Applied Nonparametric Regression , 1991 .

[25]  J. Lappi.  Calibration of Height and Volume Equations with Random Parameters , 1991, Forest Science.

[26]  David A. Ratkowsky,et al.  Problems of hypothesis testing of regressions with multiple measurements from individual sampling units , 1984 .

[27]  Annika Kangas,et al.  Most similar neighbour‐based stand variable estimation for use in inventory by compartments in Finland , 2003 .

[28]  Göran Ståhl,et al.  Simultaneous Estimations of Forest Parameters using Aerial Photograph Interpreted Data and the k Nearest Neighbour Method , 2001 .