Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation

Mathematical Proceedings of the Cambridge Philosophical Society - Tập 44 Số 1 - Trang 50-57 - 1948
C. Radhakrishna Rao1
1King's CollegeCambridge

Tóm tắt

If the probability differential of a set of stochastic variates contains k unknown parameters, the statistical hypotheses concerning them may be simple or composite. The hypothesis leading to a complete specification of the values of the k parameters is called a simple hypothesis, and the one leading to a collection of admissible sets a composite hypothesis. In this paper we shall be concerned with the testing of these two types of hypotheses on the basis of a large number of observations from any probability distribution satisfying some mild restrictions and their use in problems of estimation.

Từ khóa


Tài liệu tham khảo

10.1090/S0002-9947-1943-0012401-3

Bernstein, 1925, Zusammenfassende Betrachtungen über die erblichen Blutstrukturen des Menschen, Z. indukt. Abstamm.- u. VererbLehre, 37, 237

10.1017/S0305004100023471

10.1086/281475

10.1111/j.1469-1809.1935.tb02227.x

10.1090/S0002-9947-1934-1501765-1

10.1111/j.1469-1809.1943.tb02321.x

10.1214/aoms/1177731678

Wilks, 1939, Optimum fiducial regions for simultaneous estimation of several population parameters from large samples, Ann. Math. Statist., 10, 85

Fisher, 1945, The logical inversion of the notion of the random variable, Sankhyä, 7, 130

Rao, 1946, On locally most powerful tests when alternatives are one sided, Sankhyä, 7, 439

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Thông tin xuất bản

Mathematical Proceedings of the Cambridge Philosophical Society

Tập 44 Số 1

50-57

Thông tin tác giả