In 1981 it will be fifty years since The Japan Statistical Society was organized. We have reached a very important phase in the development of the statistical science in Japan. I would like to give a few impressions in this address.
Recently serious problems about environments of statistics have been recognized by many specialists of various countries. The word, environment or milieu, was originally considered as a part of the contents of statistics. For what contents of statistics obtainable through statistical survey are closely related to the situations of the society. The environments surrounding the statistical survey are recently deteriorating due to the democratization of the society because it has stimulated the people's desire to protect their privacy especially from the political power.
Thus we face the anatagonism of our desire to get the statistics about the people and their desire to protect their privacy. Special researches which have been carried out by some members of our society are to be reported at this meeting. I expect the fruitfulness of these reports to clarify our difficult situations.
I would like to appeal you to recall the extremely deteriorated environments of statistical science due to no publication of statistical survey results under the military pressure during the World War II in Japan. Compared with it, the present situation around us is like a heaven but we must not be satisfied with this situation because we may again face difficulty to access the statistics, this time, due to the difficulty of getting a cooperation from the people surveyed.
Finally it must be stressed that statistics and statistical science are closely related to other fields of sciences. Therefore the advancement and development of statistical science will surely contribute to all other sciences.

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A graphical method is developed for fitting a straight line to a set of data consisting of two-dimensional points in such a way as to minimize the sum of the absolute deviations of the points from the line.
In this paper, the uniqueness of the solution, which is the line of least absolute deviations, is discussed.

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In a 1974 paper, T. Matsui studied a selection procedure based on rank sums, the ranks being generated within N blocks of observations, and postulated that the slippage configuration is the least favorable configuration for a procedure _??_ he studied. It is demonstrated by a counterexample constructed for specific cases (k=3; n=1, 2) that this postulation is not always true; further, sometimes the slippage configuration maximizes the probability of correct selection.

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Applying the algorithm of selecting r variables out of k variables, we present three computational schemes for determining the formula of the likelihood of populations, the constant term and the coefficient of the linear term in the pairwise linear discriminant function and the Mahalanobis distance for each pair of populations. The second one of the three schemes discussed is found to be adequate and is recommended.

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Stabilizing constants of a distribution function which belongs to the domain of attraction of exp (-e^-x) are given by inverse function of the distribution function. But with some distributions their exact values can not be expressed by sample size n in simple forms. For instance in the case of normal distribution, inadequate sequences based on an approximation of the inverse function are used sometimes as stabilizing constants. In this paper, we shall show some properties of stabilizing constants in particular simple necessary and sufficient condition, and then apply the results obtained to some examples.

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This paper deals with obtaining the shortest invariant prediction interval for the largest observation X_n in an ordered sample of size n from the exponential distribution where the first m observations X₁<X₂<…<X_m, 1≤-m<n, have been observed. The interval is based on the statistics Z=(X_n-X_m)/S, where S=_??_X_i+(n-m)X_m.

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A general connection between a balanced fractional 2^m factorial (2^m-BFF) design of resolution 2l+1 and a balanced array (B-array) of strength 2l has been established by Yamamoto, Shirakura and Kuwada [11]. Recently, Kuwada [6] has obtained a connection between a 3^m-BFF design of resolution V and a B-array of strength 4.
As a generalization of a multidimensional partially balanced association scheme, a multidimensional relationship is considered here. By utilizing the property of a multidimensional relationship and its algebra, it can be proved that a necessary and sufficient condition for a fractional s^m factorial design T of resolution 2l+1 to be balanced is that T is a B-array of strength 2l with index set {λ_i0i1…_is-1}, provided the information matrix M_T is non-singular.

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In this paper we study bivariate life distribution functions for the two units subject to sequences of shocks. The following three stochastically independent shock processes are considered: a shock from source 1 is to the unit 1 only, a shock from source 2 is to the unit 2 only and a shock from source 3 is to both units simultaneously. A shock from source i (i=1, 2, 3) occurs randomly in time as events in a Poisson process. If unit i does not fail till it receives k_i shocks (i=1, 2), bivariate life distribution functions for two units is called bivariate Erlang distribution functions (BVEr). Throughout the paper monotonic dependency and some properties of BVEr are discussed. It is shown that BVEr has not bivariate increasing failure rate property.

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This article is concerned with the preliminary test estimator for the regression coefficients of a (p+1)-dimensional normal distribution. It is shown that when p≥3, the preliminary test estimator is dominated by a modified version of the estimator given by Baranchik.

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