diff --git a/inst/Regression/robustfit.m b/inst/Regression/robustfit.m
index 43d4d8d96..849e29f90 100644
--- a/inst/Regression/robustfit.m
+++ b/inst/Regression/robustfit.m
@@ -70,7 +70,7 @@
   if (! (isnumeric (X) && isreal (X) && ismatrix (X)))
     error ("robustfit: X must be a real matrix.");
   endif
-  if (! (isnumeric (y) && isreal (y) && isvector (y)))
+  if (! (isnumeric (y) && isreal (y) && (isvector (y) || isempty (y))))
     error ("robustfit: Y must be a real vector.");
   endif
   y = y(:);
@@ -114,7 +114,7 @@
   endif
   [n, p] = size (X);
   if (n <= p)
-    error ("robustfit: not enough observations for the number of parameters.");
+    error ("robustfit: Not enough points to perform robust estimation.");
   endif
 
   ## Ordinary least squares start, leverages, and the OLS scale.
@@ -322,3 +322,10 @@
 %! robustfit (X, y, "huber", -1)
 %!error <robustfit: CONST must be 'on' or 'off'.> ...
 %! robustfit (X, y, "huber", 1.345, "maybe")
+
+%!test
+%! ## Edge cases with empty arrays
+%!error<robustfit: Not enough points to perform robust estimation.> ...
+%! robustfit ([], [])
+%!error<robustfit: Not enough points to perform robust estimation.> ...
+%! robustfit (zeros(0,3), zeros(0,1))