# 2011Nx

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### 10jZ~i[ (Lm_E͊wnZ~i[ƍZ~i[)

F2012N 3 9 16:00` (ƎԂႤƂɒ)

Fw C816

uF Prof. Mohsen Pourahmadi (Texas A&M University, Department of Statistics)

uF Prediction and Estimation of Random Fields on Quarter Planes

uv|F (ȂǂĂꍇAȂꍇR`PDFĂ)

We present solutions of several prediction problems for random fields (2-D processes) which extend some nonstandard prediction problems for a stationary time series (1-D process) based on the modified pasts. The solutions lead to informative and explicit expressions involving the AR and MA parameters (Nakazi, 1984; Pourahmadi, Inoue and Kasahara, 2006) as summarized in the following:
Theorem: Let be a nondeterministic stationary process with the innovation process , innovation variance , MA and AR parameters and , respectively. Then, an integer the prediction error variance of based on

(a) , having only one additional observation at time , is

(b) , having@ additional observations at times is

(c) , missing only one observation at time@ is

These expressions involving and are reminiscent of the -step ahead predistion error variance , and reveal the eect (worth) of observations in prediction. Using the Wold decomposition of stationary random fields, their multi-step ahead prediction errors and variances, solutions are provided for various nonstandard prediction problems when a number of observations are either added to or deleted from the quarter-plane past. Unlike the time series situation, the prediction error variances for random fields seems to be expressible only in terms of the MA parameters, attempts to express them in terms of the AR parameters runs into a mysterious projection operator which captures the nature of the "edge-effects" encountered in estimation of random fields. These prediction problems provide useful information for assessing worth of observations in the spatial setting, and are closely related to the design issue or network site selection in the environmental, geostatistical and engineering applications (Zimmerman, 2006). For a given data, a prediction methodology is implemented by fitting exponential models (Bloomfield, 1973; Solo, 1986) to the spectrum and then using recursive formulas expressing the AR, MA and predictor coefficients in terms of the cepstral coefficients of the random field. The procedure is illustrated using a simulation study and application to real data.

## ȑŐjZ~i[

### 9jZ~i[

F2011N 12 16 15:10`

Fw C816

uF R q iLEj

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### 8jZ~i[

F2011N 11 18 15:10`

Fw C816

uF iDyȑj

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### 7jZ~i[

F2011N 11 11 15:10`

Fw C816

uF (LEw)

uFʊƂ̐

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### 6jZ~i[

F2011N 10 28 15:10`

Fw C816

uF匴 Ga(LEw)

uF An Explicit Solution to Minimization Problem for GCV in Generalized Ridge Regression

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### 5jZ~i[

F2011N 10 14 15:10`

Fw C816

uF q (LEw)

uFςƕUUsɍ\̋ÂƂł̌蓝vʂ̕z̑QߓWJ

uv|F Kz̕ςƕUUsɈʓIȍ\lD Wakaki & Eguchi & Fujikoshi(1990)ł͕UUŝ݂ɈʓIȍ\lCޓx䌟܂ނ悤Ȍ蓝vʂĂCÂƂł̑QߓWJ𓱏oD Shimizu(2011)ł͓ľƌ蓝vʂlCǏΗ̂Ƃł̑QߓWJ𓱏oD {񍐂ł́@Wakaki & Eguchi & Fujikoshi(1990)ŒĂꂽ蓝vʂ̊gƂȂVȌ蓝vʂĂCÂƂł̑QߓWJ𓱏oD

### 4jZ~i[

F2011N 7 29 15:10`

Fw C816

uFRc G (LEoρj)

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### 3jZ~i[

F2011N 6 10 15:10`

Fw C816

uFi E (LEw)

uFmpgbNȐfƂ̐@

uFe̂ɑ΂, ԖɊϑꂽf[^͌of[^ƌĂ΂. of[^Ɋւ͂ɂ, oϓ̐肪Â猤Ă (ႦGoldstein (1979)Q). ܂, of[^, SĂ̌̂̑莞_łȂɂ, oX^f[^ƃAoX^f[^ɕ. oX^f[^ɑ΂Ă, Pottoff & Roy (1964)ŒEEĂꂽʉϗʕU (GMANOVA) fp, oϓ𐄒肷邱Ƃł. ܂,AoX^f[^ɑ΂Ă, Vonesh & Cater (1987) ɂĂꂽ_WȐf (RCGCM) p, oϓ𐄒肷邱Ƃł. ̃fp]̌oϓ̐ł, (q-1)pĐsĂ. , oϓGȏꍇ͑ł͂܂肷邱ƂłȂ. Nagai (2011)ɂ, GMANOVA fɂ, ֐pămpgbNɌoϓ𐄒肷邱ƂĂꂽ. {\ł, RCGCM ɂČoϓmpgbNɐ肷邱ƂĂ.

### 2jZ~i[

F2011N 5 13 15:10`

Fw C816

uFR S (LEw)

uF̃f^̃f܂܂Ȃꍇł̐֕͂ɂϐÎ߂̏ʋK

uv|F֕͂Ƃ́AQ̑ϗʃxNg̐`ɂ鍇ϗʂ̑ւ𕪐͂鑽ϗʉ͂̎@łB͂ɂėLȕϐI邱Ƃ͏dvȖłA֕͂ɂϐIւ̃Av[`Ƃď璷f̑IƂ݂Ȃ@B 璷f͋U\fƂĒ莮ł, fI̕@̂ЂƂƂAICp@BU\f̑Iɑ΂āAf[^ɐK肵łAIĆA^̕zm̔񐳋KzłꍇA^̕z̐xɈˑoCAXB {\ł́ATICWbNiCt@p邱ƂɂA^̕z̔񐳋K̉eȂ悤ȑI@ĂAV~[Vɂ肻̗Lpm߂B

### 1jZ~i[

F2011N 4 5 15:10`()

Fw C816

uFɐX W (LEw)

uFʉ`fɂoCAX␳AIC

uv|F fI͎f[^͂ɂďdvȁEłB fI̕@̂ЂƂAIC̍ŏɂčœK@A ̉pv̏ʂŗLpł邱ƂmĂB AIC̓TvƂɃXNɑ΂oCAXłȂȂ邱ƂB f̓XNɂđ邽߁AoCAX̏Ȑʂ̕]܂ƍlB ̂߁AoCAX␳AICp邱Ƃ͌ʓIłA ̃fɑ΂AIC̃oCAXn-2̃I[_[܂ŊSɕ␳AIC (CAIC)ĂĂ邪A CAIC̓o̓fɈˑĂÃfœo邱Ƃ͊ȒPł͂ȂB ŁA{\ł͈ʉ`fƂLNXɂCAIC̈ʌЉB

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