The article develops new tests for checking relationships in a type of regression model with weak evidence. It shows that a specific method, JIVE, can estimate parameters accurately even when the data is messy. Other common methods don't work well in this situation. The authors also create new ways to calculate the reliability of JIVE estimates. These calculations can be used to make sure the results are correct. The tests built on these calculations give results that can be trusted. This new approach is useful because it allows for testing a wider range of ideas than before, even when the data is not perfect.