Looping with "Table" over two variables

Question

so essentially, I have a table:

table= Table[0, {5}, {30}, {6}];

I have now been trying to loop the functions below over level 2, (30) of the table and then looping it over dimension 3, (6).

I have gotten the loop over dimension 2 to work:

a=Flatten[Position[Transpose[table], 
   Min[Table[Max[Transpose[table][[p]]], {p, 1, 30}]]]][[1]]

This gives me the minimax of dimension 2 of the data. What I am failing at is looping this over dimension 3 also, ultimately producing a list of six different values in a.

Closest in my mind would be something like:

a=Table[Flatten[
   Position[Transpose[teststat], 
    Min[Table[Max[Transpose[teststat][[n]][[i]]], {n, 1, 30}]]]], {i, 
   1, 6}];

but this is clearly wrong.

The first line of input data would be: {2.95095, 0.186768, 0.10373, 0.0430614, 0.13822, 0.0535124}, total data is this x30 x5.

Expected output would be something like: {2,3,7,22,11,44} I suppose my question can be reduced to: where do I have to place the second variable definition [[i]] and {i,1,6}

Context is: the table contains test statistics of 6 different model variations for the top 30 percentiles of data with 5 implicates. Within the percentiles I want to find the position of the value which minimizes the maximum of the test-statistics, for everyone of the six model variations.

Thank you for any and all suggestions. B

Answer 1

I guess you can create a function such as this:

minimax[table_] := 
 Module[{slices, val, pos = {}}, 
  slices = table[[All, All, #]] & /@ Range[Last@Dimensions@table];
  val = Min@Max@slices[[#]] & /@ Range[Last@Dimensions@table];
  pos = Position[slices[[#]], val[[#]]] & /@ 
    Range[Last@Dimensions@table]
  ]

Then just run the

minimax[t] where t where t is your table.

EDIT: This way you will get the positions in the second level of your table.

EDIT2: cleared up the code this will give you pairs of indices, of the first two levels