A Bootstrap Test for Positive Definiteness of Income Effect Matrices
研究了用自助法检验收入效应矩阵正定性的理论，该正定性是需求定律成立的充分条件，并利用英国家庭支出调查数据进行了实证。
Positive definiteness of income effect matrices provides a sufficient condition for the law of demand to hold. Given cross section household expenditure data, empirical evidence for the law of demand can be obtained by estimating such matrices. Härdle, Hildenbrand, and Jerison used the bootstrap method to simulate the distribution of the smallest eigenvalue of random matrices and to test their positive definiteness. Here, theoretical aspects of this bootstrap test of positive definiteness are considered. The asymptotic distribution of the smallest eigenvalue , of the matrix estimate is obtained. This theory applies generally to symmetric, asymptotically normal random matrices. A bootstrap approximation to the distribution of is shown to converge in probability to the asymptotic distribution of . The bootstrap test is illustrated using British family expenditure survey data.