1 2 1 305 8506 16 2 E-mail: murakami.daisuke@nies.go.jp 2 305 8573 1 1 1 E-mail: tsutsumi@sk.tsukuba.ac.jp Key Words: sampling design, geostatistics, officially assessed land price, prefectural land price 1 24 10 25 10 2013 1 1 pp. 27 28 / sampling design Wang et al. 2012 2 i design based approach ii model based approach i simple random sampling systematic sampling stratified random sampling two step sampling Gruijter 1999 3 Ripley 1981 4 design based approach 31
ii ii 1 2004 5 p p median p center space filling design Nychka and Saltzman 1998 6 ii 2 e. g., Silvey 1980 7 e. g., Cressie 1993 8 e. g., Zimmerman 2006 9 Brus and Heuvelink 2007 10 Zidek and Zimmerman 2010 11 Wang et al. 2012 2 ii ii / ii / 4 1 ii 3 2 3 4 5 6 2 1 1 2 1 2 2 2 1 4 2012 12 4 9 1 1 1 4 1 2012 12 9 7 1 4 2013 1 32
3 1 D R s n D n 1, N z s n 1 z=xβ+ε ε~n 0,C 1 z N 1 X N K β K 1 ε N 1 0 N 1 C N N d n, n ' 1 Xβ ε 2 + c d = τ σ if d =0 τ + σ f d if 0<d <r 2 0 otherwise f d = 3d 2r d 2r τ σ r nugget partial sillrange s 0 D z s z s 3 z s = s β+ε s 3 ' s s 0 K 1 ε s s 0 z s Best Linear Unbiased Predictor BLUP 4 z s = s β +c C z Xβ 4 β = X C X X C z c s 0 N 1 z s 5 Ez s z s =σ +τ c C c+ c C X X C X c C X 5 2006 13 2014 14 Cressie 1993 8 Schabenberger and Gotway 2004 15 2 a Zhu and Stein 2005 16 min C S =min w c S 6 i i min C S =min max w c S 7 i i S S i i 1, 2,... I S S i S {S 1, S 2,...S I } m {m 1, m 2,...m M } D R M 1 w m m c S S i Ez s z s w c S S i m 6 7 w c S C S = w c S C S =max w c S 1 Brus and Heuvelink 2007 10 6 7 6 33
1 10 3 10 7 S i S 10 C 7 120 Si* M 30 w m c m S i 67 M w m c m S i 4 S i * 8 S =arg min i g {1, 2} b C S 8 S i * S NP NP hard S * i Simulated Annealing SA : Kirkpatrich et al. 1983 17 SA i S 0 T T 0 iiii a ii b k ii a S i_a 1 S i_b ii b S i_a S i_b S i_a 1 9 S i_a S i_b exp CS _ CS _ T 9 iii T pt ii p 0 p 1 T p 1 SA Kirkpatrich et al. 1983 17 p 1 T 0 10 Brus and Heuvelink 2007 10 T CS C S = 10 M log 0.8 S ii b SA 10 T 0 80% C S S i c m S i Ez s z s 7 D n c n c S 0 S 0 S i_a 1 n c 1 ii D n c n c n c S 0 n c ii 1 SA p 1 Kirkpatrich et al. 1983 17 SA 1 1 SA n c 100 101 1 D 34
D D D' D D' D D' Cressie 1993 8 A A 4 1 D D Brus and Heuvelink 2007 10 T 0 10 k 100 p 0. 95 c S τ σ r τ σ r 4 3 2 1 2 M 1 w m 2 a 1 A B C 2 D C S C S A B B C 2 C 1 C 2 C 3 Zidek and Zimmerman 2010 11 C 3 2 C 3 2 1 1 7 1 C 2 C 2 C 2 35
C 1 D A C 3 C 2 4 B C 1 D D C 1 2 a w m D 1 D 2 D 3 D 1 D 3 D 2 w m w m D 1 D 2D 3 http://www.e-stat.go.jp/sg1/estat/e StatTopPortal.do D 1 w m http://www.land.mlit.go.jp/webland/ 23 3, 557 3, 945 1 Clayton and Kaldor 1987 18 12 m t m 11 t ~Poisson θ t 11 t m m t m m 12 θ ~Gamma a,b 12 a b 11 12 m 13 θ = t +a t +b 13 θ m θ t b t m a θ t Clayton and Kaldor 1987 18 b 36
1 max w c S 7 3 2 b A C 3 b 6 7 D D 1 D 2 D 1 D 2 D 1 D 2 D 1 D 2 7 8 D 3 c 1 w m c S w c S m w c S 6 4 1w m C 1D C 2 B C 3 4 1 5 1 2009 2009 2010 z z z z z z 785 1 10% 79 30% 235 50% 393 3 c S w m 3, 943 c S 1/m 2 km km 1km 2 m 2 3 2 WLS&EGLS Schabenberger and Gotway 2004 15 2 4 VIF Variance Inflation Factor 37
3 2 4 3 2 /m 2 VIF 10 1997 19 1% 10% 1% 1. 15 10 8 1. 84 10 8 62. 51. 15 10 8 / 1. 84 10 8 % 6. 48km 5 4 1 38
4 Mean Percentage Error MPE 14 MPE= 100 N z s z s z s 14 z s n z s MPE 18. 8 81. 2 100 18. 8 % 3 2 a b 0. 309 0. 130 a b 13 a / b 1 5 6 5 fold cross validation 4 3 w c S c S w m c S w m c S w m 5 6 7 w m c S w m c S c S w m I IIIII 9 10 11 8 w c S 39
8 5 7 50% w m c m S i w c S w m c S / 50% 5 I II III 1 III 50% 9 10 11 III I II I II III 12 10% 30% 50% 12 6 40
9 10 11 41
12 Fuentes et al. 2007 20 trans gaussian kriging e. g., Cressie 1993 8 geoadditive model Kammann and Wand 2003 21 z z z z z Japan Geoscicence Union Meeting 2012 21 1) 2013 2) Wang, J. F., Stein, A., Gao, B. B. and Ge, Y. : A Review of spatial sampling, Spatial Statistics, Vol.2,pp.1 14, 2012. 3) Gruijter, J. : Spatial sampling schemes for remote sensing, In Stein, A., Meer, F. and Gorte, B. eds., Spatial Statistics for Remote Sensing, pp.211 242, 1999. 4) Ripley, B. D. : Spatial Statistics, JohnWiley& Sons, 1981. 5) Vol. 47 pp. 1 23 2004 6) Nychka, D. and Saltzman, N. : Design of air quality 42
monitoring designs, In Nychka, D., Piegorsch, W. W. and Cox, L. H. eds., Case studies in Environmental Statistics, New York: Springer, pp. 51 76, 1998. 7) Silbey, S. D. : Optimal Design, London: Chapman& Hall, 1980. 8) Cressie, N. : Statistics for Spatial Data. RevisedEdition, John Wiley & Sons, 1993. 9) Zimmerman, D. L. : Optimal network design for spatial prediction, covariance parameter estimation, and empirical prediction, Environmentics, Vol.17,pp.635 652, 2006. 10) Brus, D. J. and Heuvelink, G. B. M. : Optimization of sample patterns for universal kriging of environmental variables, Geoderma, Vol.138,No.1 2, pp. 86 95, 2007. 11) Zidek, J. V. and Zimmerman, D. L. : Monitoring network design, In Gelfand, A. E., Diggle, P. J., Fuentes, M. and Guttorp, P. eds., Handbook of Spatial Statistics,CRCPress, pp. 131 149, 2010. 12) http://tochi.mlit.go.j p/chika/kouji/2012/01.html 2014/ 05/ 01 2012 13) 23 GIS Vol. 17 No. 1 pp. 13 24 2006 14) GIS Vol. 22 No. 2 pp. 1 11 2014 15) Schabenberger, O. and Gotway, C. A. : Statistical Methods for Spatial Data Analysis, ChapmanandHall/CRC,2004. 16) Zhu, Z. and Stein, M. L. : Spatial sampling design for parameter estimation of the covariance function, Journal of Statistical Planning and Inference, Vol.134,No.2,pp. 583 603, 2005. 17) Kirkpatrich, S., Gelatt, C. D. and Vecchi, M. P. : Optimization by simulated annealing, American Association for the Advancement of Science, Vol.220,No.4598,pp. 671 680, 1983. 18) Clayton, D. and Kaldor, J. : Empirical Bayes estimator of age standardized relative risks for use in disease mapping, Biometrics, Vol.43,No.3,pp.671 681, 1987. 19) 1997 20) Fuentes, M., Chaudhuri, A. and Holland, D. M. : Bayesian entropy for spatial sampling design of environmental data, Environmental and Ecological Statistics,Vol.14,No.3,pp. 323 340, 2007. 21) Kammann, E. E. and Wand, M. P. : Geoadditive models, Journal of the Royal Statistical Society: Series C (Applied Statistics), Vol.51,No.1,pp.1 18, 2003. 2014. 5. 13 GEOSTATISTICS FOR THE ASSESSED SITE ALLOCATION PROBLEM IN OFFICIALLY ASSESSED LAND PRICE AND PREFECTURAL LAND PRICE Daisuke MURAKAMI and Morito TSUTSUMI Designing sampling strategy is a major concern in statistics. The same also holds for study fields that discuss spatial data modeling, including geostatistics; and, recently, sample site selection design is intensively discussed in these fields. This study applies geostatistics to the assessed site allocation problem in the officially assessed land price data and prefectural land price data in Japan. Firstly, we explain these land price data, while mainly focusing on basic rules of their assessed site allocation. Then, studies discussing sampling design problems are briefly summarized. Subsequently, points, which we must consider, are clarified, and geostatistical approaches for the land price assessed site allocation problem are developed based on the points. Finally, the developed approaches are used to the assessed site reduction problem in Ibaraki prefecture, and their effectiveness is examined. 43