You are trying to create an associative array (hash). Try out the following
sequence of commands
$arr=@{}
$arr["david"] = @{}
$arr["david"]["TSHIRTS"] = @{}
$arr["david"]["TSHIRTS"]["SIZE"] ="M"
$arr.david.tshirts.size
Note the difference between hashes and arrays
$a = @{} # hash
$a = @() # array
Arrays can only have non-negative integers as indexes