I suspect it's probably wrong to set BMR as the minimum. According to
this site describes BMR as
the number of calories you'd burn if you stayed in bed all day. Wikipedia says much the same thing in a more verbose way.
Take for example the scenario where I do 8 hours of light exercise and spend the rest of the day resting. That requires 5288 calories. My BMR is 2362. That's almost 3,000 calories below maintenance! That seems potentially unsafe.
A rule of thumb for healthy weight loss is to reduce your calories 15-20% below maintenance but never below 1800 for men or 1200 for women, and to a total drop of no more than 1,000 calories.
In this case, my range for the day in question would be 4288 to 5288.