The article introduces new tests for checking if a statistical model fits data well. These tests are better than older ones because they are more accurate and powerful. They can also give more useful information if the model doesn't fit. The tests use a method called nonparametric density estimation, which helps estimate the shape of the data without assuming a specific form. This method is shown to work well in different testing situations. If the model doesn't fit, the method can still provide good estimates of important values in the data.