Construct a multivariate version of the estimate in Problem 10.6 and show that it is strongly universally consistent. Hint: Use functions which are equal to a multivariate polynomial of degree M (or...

Construct a multivariate version of the estimate in Problem 10.6 and show that it is strongly universally consistent.

Hint: Use functions which are equal to a multivariate polynomial of degree M (or less, in each coordinate) with respect to suitable partitions.