Estimation of the Parameters of a Normal Distribution When the Mean Is Restricted to an Interval1

Abstract

Summary Suppose it is known that the mean of a normal distribution is non‐negative. Naturally one will use the sample mean truncated at zero as an estimator of the distribution mean. In this paper the properties of such an estimator are investigated.

Simple linear regression estimation with inequality constraints on the parameters

“…The "cruder" version of Bartholomew (1971) is given by a^(0) = 0 02(9) -ct when ®i~®i''"^ aj^(e) = 012(0) = ^ a when -0^+c<8<8^-c (1.29) a^(0) = a ^2(8) = a when 0^-c_^0^0^ for some suitably chosen value of c < ^ » As before, we note that choosing c=0 will yield the Malinvaud (1966) solution. Also, Heiny and Siddiqui (1970) consider the solution (1.29) with c=0 and ^ _ -0^ when X < -0^ s = > X when -0^ i ^ ^ (1=30) 0 ^ when X > 0 ^ and approximate the variance of s by the variance of X.…”