Repeat Exercise 11.4, assuming spatial independence (i.e., setting all cross-covariances between Ithaca and Canandaigua variables to zero). Exercise 11.4 a. Compute the 1-sample T 2 testing the linear...

Repeat Exercise 11.4, assuming spatial independence (i.e., setting all cross-covariances between Ithaca and Canandaigua variables to zero).

Exercise 11.4

a. Compute the 1-sample T²
testing the linear combinations [B]
^T
x with respect to H₀:

₀
= 0, where x and [B]^T
are defined as in Exercise 11.2. Ignoring the serial correlation, evaluate the plausibility of H₀, assuming that the w²
distribution is an adequate approximation to the sampling distribution of the test statistic.

b. Compute the most significant linear combination for this test.

Exercise 11.2

Assume that the four temperature variables in Table A.1 are MVN-distributed, with the ordering of the variables in x being [MaxIth, MinIth, MaxCan, MinCan] T . The respective means are also given in Table A.1, and the covariance matrix [S] is given in the answer to Exercise 10.7a. Assuming the true mean and covariance are the same as the sample values,

a. Specify the conditional distribution of [MaxIth, MinIth]^T, given that [Max_Can, Min_Can]
^T
= [31.77, 20.23]^T
(i.e., the average values for Canandaigua).

b. Consider the linear combinations b₁
= [1, 0, –1, 0], expressing the difference between the maximum temperatures, and b₂
= [1, –1 –1, 1], expressing the difference between the diurnal ranges, as rows of a transformation matrix [B] T . Specify the distribution of the transformed variables [B]
^T
x.