HW1Sol - STA 6934 Spatial Statistics HW 1 HW 1 Problem No 1...

STA 6934 - Spatial Statistics: HW 1
HW 1 - Problem No. 1
a) Both the contour and perspective plots show a trend toward higher values in
the northeast, or upper right, of LA. Thee are some lower ”peaks” towards the
southeast.
b) Your eye estimates should be similar with your answer in c).
c) We choose spherical model because it relates more points than the exponential
one. The still is (0.0253+0.1546=0.1799), range is 121.5, nugget is 0.0253 from R
output.
(see ozone.pdf)
HW 1 - Problem No. 2
The Still = Co + (Cr*Ar)
The Nugget = Co regardless of Cr or Ar
The Range = Ar/2
(see Routput-hw1.2.pdf)
1

HW 1 - Problem No. 3
Cov ( Z ( S
i
, Z ( S
j
)) = C ( S
i
- Sj )
V ar ( Z ) = V ar (
N
i =1
Z ( S
i
) /N )
= 1 /N
2
[
N
i =1
V ar ( Z ( S
i
)) +
i = j
Cov ( Z ( S
i
, Z ( S
j
))]
= 1 /N
2
[
N
i =1
C (0) +
i = j
C (0) ρ ( S
i
- Sj )]
= C (0)(1 /N + 1 /N
2
i = j
ρ ( S
i
- Sj ))
If the data are independent, V ar ( Z ) = 1 /N 2
∑
N
i =1
V ar ( Z ( S
i
)) = 1 /NC (0)
Since for spatial data, observations closer together tend to be more alike than
observations farther apart, ρ ( S
i
- Sj ) decreases as | S
i
- Sj | becomes larger. So we
can obtain the data from the region as scattered as possible.