Die Robustheit der Schätzer wurde überprüft durch

You will mostly use this in a professional or academic setting. It usually starts a sentence that describes a method. You follow the word durch with a noun or a specific test name. For example, durch eine Sensitivitätsanalyse. It sounds very sophisticated. It shows you are a serious researcher or analyst. You are proving that your findings aren't sensitive to small changes.

Use this when presenting a thesis or a business report. It is perfect for the 'Methodology' section of a paper. If a boss asks how sure you are about a sales forecast, use this. It adds immediate authority to your work. It is also common in engineering and data science circles. Basically, use it whenever you need to sound like the smartest person in the room.

Do not use this at a casual dinner party. If you say this while explaining why you like a certain wine, people will stare. It is too heavy for everyday life. Avoid it in casual texts unless you are being sarcastic. It is strictly for 'serious' data talk. Don't use it for simple physical objects either. You wouldn't say this about a sturdy pair of boots.

Germans value Gründlichkeit (thoroughness) above almost everything else. This phrase is a linguistic manifestation of that value. In German academia, showing your work is just as important as the result. The word überprüft carries a sense of official verification. It reflects a culture that loves 'DIN' standards and 'TÜV' certifications. Everything must be checked, double-checked, and then documented.

You might hear Die Validität der Ergebnisse wurde geprüft. This focuses more on validity than robustness. Another version is Die Zuverlässigkeit wurde mittels... sichergestellt. This sounds even more formal because of the word mittels. If you want to be slightly less formal, you could say Wir haben die Schätzer getestet. But for a C1 level, stick to the original phrase for maximum impact.