Marco Riani1, Anthony C. Atkinson2, Aldo Corbellini1 , Paolo Di Lazzaro3
1 Department of Economics and Management and Interdepartmental Research Centre for Robust Statistics
2 London School of Economics
3 ENEA Research Centre
The paper describes statistical methods for the regression analysis of spatial data when some spatial information is missing. Our numerical example comes from the results of the 1988 carbon dating of the Shroud of Turin (TS). The statistical problem is that the dating was performed at three laboratories, which each received a sample from the Shroud. The physical location on the TS of these samples is known. However, the data consist of readings on several subsamples, the locations of which within the samples are not known. This is then a problem of spatial regression with partially labelled regressors. In 2019 the laboratory data (the ‘raw’ data) from which the original dating was derived became available. We analyse the raw data by considering all 165,888 permutations of observations to subsamples. We first use modern graphical methods to interpret the output from these permutations, with a focus on the age of the TS. Further exploration of the data requires the selection of a single fitted model. We select a model by reference to the distribution of R2, the selected model being used, via robust regression, to screen the data for outliers. Simpler versions of this problem occur in commercial ovens in food and antibiotic preparation, when records on shelf location are not available.
Computer-intensive methods; clustering; data display; missing information.
In the table below you can find the original source (MATLAB live script): .mlx file and the corresponding .ipynb file.
MATLAB live script files
The .mlx file contain both the code and the output that the code produces.
👀 To view the .mlx files click on the "File Exchange button"
The Jupiter notebook version of the files is also given in the last column of the table below. Similarly to the .mlx files the Jupiter notebook files also contain both the code and the output produced by the code.
Jupiter notebook files
To view the .ipynb files click on the corresponding link.
To run the .ipynb files inside the agnostic environment jupiter notebook follow the instructions in the file ipynbRunInstructions.md.
Note: in order to run the files below you need to have FSDA toolbox installed.
The following section contains a table with the source code that enables the reproduction of the Figures of the paper and the simulation study.
| FileName | View 👀 | Run |
Jupiter notebook | m format |
|---|---|---|---|---|
RACDtable2.mlx: This code generates Table 2 of the paper. |
 |
 |
RACDtable2.ipynb | RACDtable2.m |
RACDfigures.mlx: This code generates all Figures. |
|
|
RACDfigures.ipynb | RACDfigures.m |
