日本統計学会誌

私の中の統計学

山本純恭

1978 年 8 巻 1 号 p. 1-7
発行日: 1978年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.8.1

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A NEW DEVELOPMENT IN MULTIVARIATE STATISTICAL ANALYSIS

T. W. Anderson

1978 年 8 巻 1 号 p. 9-13
発行日: 1978年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.8.9

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MINIMAX REGRET CRITICAL VALUES FOR A PRELIMINARY TEST IN POOLING VARIANCES

Kazuhiro Ohtani, Toshihisa Toyoda

1978 年 8 巻 1 号 p. 15-20
発行日: 1978年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.8.15

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Suppose we have independent random samples from two normal populations N (μ_i, σ_??_) where the means and the variances are unknown except for the fact that σ_??__??_σ_??_. We wish to estimate the variance of the first population, σ_??_. Then, whether to pool or not to pool two samples is decided via a preliminary F test for equality between the two variances. In this note we discuss the pre-test estimator and seek the optimal critical values for the pre-test, based on a minimax regret criterion. It is shown that the optimal critical values depend on the degrees of freedom and are about 1.7_??_2.8. Also we see that the ordinary (never-pool) estimator of variances is dominated by the pre-test estimator for λ=1.

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THE MAXIMUM LIKELIHOOD ESTIMATES BASED ON THE INCOMPLETE QUANTAL RESPONSE DATA

Taichi Kariya, Tadashi Nakamura

1978 年 8 巻 1 号 p. 21-28
発行日: 1978年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.8.21

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In this paper we present statistical techniques appropriate to one exceedingly important type of response, that known as all-or-nothing or quantal.
With incomplete quantal response data, the estimation of parameters has usually been solved approximately as the estimation problems based on grouped data, which is not always practicable or adequate [1]. We therefore propose a new method of maximum likelihood for estimating parameters based on ‘individual incomplete quantal response data’ without grouping. The existence theorems of its maximum likelihood estimates (its optimal solutions) are proved in the appendix.

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A UNIFORM TWO-ARMED BANDIT PROBLEM: THE PARAMETER OF ONE DISTRIBUTION IS KNOWN

Toshio Hamada

1978 年 8 巻 1 号 p. 29-35
発行日: 1978年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.8.29

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The sequential design procedure which selects one of two experiments e₀ and e₁ at each stage in order to maximize the sum of n observations is considered, where the distributions of e₀ and e₁ are uniform distributions on the intervals (0, u) and (0, 1) respectively. The value of u is unknown and is assumed to have a Pareto distribution with parameters w and α as a prior distribution. This problem is formulated by the dynamic programming and is solved recursively. The expected sum of n observations is given as function of w, α and n, and the optimal strategy is to perform e₀ if and only if w_??_w_n (α). w_n (α) is strictly increasing in α and non-decreasing in n, and the value of w_n (α) is calculated for several values of w and α and tabulated.

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A CONDITION FOR THE EXISTENCE OF CERTAIN RESOLVABLE 2-DESIGNS

Sanpei Kageyama

1978 年 8 巻 1 号 p. 37-38
発行日: 1978年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.8.37

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A resolvable 2-(v=2k, k, λ₂) design (i.e., a resolvable BIB design with parameters v=2k, b, r, k, λ₂) is characterized as follows: A necessary condition for the existence of a resolvable 2-(v=2k, k, λ₂) design is that r-λ₂ is even. This necessary condition is also sufficient for the practical range of values of k. That design is also a 3-design (i.e., a doubly BIB design).

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エラータ

1978 年 8 巻 1 号 p. 53
発行日: 1978年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.8.1_53

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