Detection and attribution (D&A) analysis for climate extremes plays an important role in understanding the human influence on the observed change in climate extremes. In recent methodologies, signals are estimated from climate model simulation under external forcing and then used as the true signal in the following statistical analysis. The estimated signal, however, contains measurement error inherited from the climate model simulation, and may lead to bias in the analysis. In this study, we propose a method which combines the signal estimation and D&A analyis where the signal is estimated jointly from both the simulated and the observed extremes. We show that this method can reduce the bias effectively in the estimation compared to the previous method using a simulation study. We also apply the new method to the extreme temperature indices in East Asia area.