Readme file
SERIES
B
 Statistical
Methodology
Ordering and selecting components in multivariate or functional data linear prediction, by . Hall and Y.-J. Yang, pages 93-110
JRSSB_B7337.txt contains two parts: the Australian rainfall and temperature data and the main program.
Four measurements of 206 cities are recorded each month for each city in the Australian rainfall and temperature data, which are available at http://www.worldweather.org. The sub-part "cities" is 206 city names and the other sub-part "measurements" is the four measurements of each of the 206 cities as follows:
Month Mean Temperature Daily Min,
Month Mean Temperature Daily Max,
Mean Total Rainfall (mm),
Mean Number of Rain Days.
For example, the first 12 rows in the file of measurements are
Jan 15.7 27.9 17.8 4.7
Feb 16.0 28.1 19.0 3.8
Mar 14.3 25.3 21.8 5.7
Apr 11.6 22.0 36.1 8.9
May 9.5 18.4 56.1 13.3
Jun 7.6 15.9 55.7 13.6
Jul 6.9 14.9 62.2 16.0
Aug 7.6 15.8 50.9 16.0
Sep 8.8 18.0 47.9 13.3
Oct 10.6 20.8 40.4 11.2
Nov 12.5 23.5 25.1 7.8
Dec 14.3 25.5 24.0 6.9
These give the Month Mean Temperature Daily Min, Month Mean Temperature Daily Max, Mean Total Rainfall (mm) and Mean Number of Rain Days, for the first-named city, Adelaide. The next 12 rows, i.e.
Jan 13.6 25.0 24.8 8.3
Feb 14.3 25.0 23.1 8.0
Mar 13.4 24.0 32.7 10.8
Apr 11.6 21.9 55.4 13.8
May 9.8 18.8 97.8 17.5
Jun 8.2 16.6 102.8 19.1
Jul 7.5 15.8 122.7 20.5
Aug 7.5 16.0 108.3 20.7
Sep 8.0 17.3 85.8 18.3
Oct 9.0 18.7 74.4 15.6
Nov 10.6 20.8 45.7 12.9
Dec 12.4 23.2 27.2 9.5
give the measurements for the second-named city, Albany; and so on.
The software R is used in our numerical study. The main program is included in file "JRSSB.txt". You can use oriMethod function, weightMethod function and rankMethod function to obtain the predictor proposed in equation (2.5) and "weighted" predictor and "rank" predictor proposed in equation (3.15).
The input "X" is a matrix of explanatory variables (multivariate or functional), and each row should corresponds to each individaul. The input "Y" is a column vector of dependent variables. The input "ppseq" and "rrseq" are sequences of candidates of tuning parameters. The output "pp" and "rr" are the cross-validation estimate of the tuning parameters. The output "Error" is a vector of prediction errors. The output "pred" is a vector of prediction values of each individual. The output "rank" is the estimated order of the eigenvectors, where the number j in this sequence indicates that the eigenvector corresponding to the jth largest eigenvalue would appear there.
Peter Hall
Department of Mathematics and Statistics
University of Melbourne
Melbourne
VIC 3010
Australia
E-mail: halpstat@ms.unimelb.edu.au
You-Jun Yang
Department of Mathematics
National Taiwan University
Taipei
Taiwan
E-mail: d93221006@ntu.edu.tw
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