Before revision:  Thus, while traditional asymptotic analysis in RDD requires a growing number of observations local to the cut-off as n grows, our framework allows for the number q of observations local to the cut-off to be fixed as n grows. The new test is easy to implement, asymptotically valid under weaker conditions than those used by competing methods,  exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity , and has favorable power properties against certain alternatives .
After revision:  Thus, while traditional asymptotic analysis in RDD requires a growing number of observations local to the cut-off as n grows, our framework allows for the number q of observations local to the second framework q diverges to infinity slowly as n diverges to infinity. Under both of these frameworks, we show that the test we propose is asymptotically valid in the sense that it has limiting rejection probability under the null hypothesis not exceeding the nominal level. More importantly, the test is easy to implement, asymptotically valid under weaker conditions than those used by competing methods, exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity , and has favorable power properties against certain alternatives .