Journal of the Japan Statistical Society, Japanese Issue

SEARCH FOR GD DESIGNS WITH SMALL VALUES OF CHARACTERISTICS

Sanpei Kageyama, Rahul Mukerjee

1987 Volume 17 Issue 1 Pages 1-10
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.1

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Consider a group divisible (GD) design with parameters v, b, r, k, λ₁, λ₂. From apractical point of view on optimality, GD designs with λ₂=λ₁-1 are partly characterized. Furthermore, all the GD designs satisfying rk-λ₂v_??_4 and r-λ₁_??_4 aresearched, where rk-λ₂v and r-λ₁ are eigenvalues ofNN' other than rk for the incidente matrix N of the design. These produce more efficient GD designs.

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DETECTION OF AN INFLUENTIAL OBSERVATION ON A SUBSET OF REGRESSION PARAMETERS IN MULTIPLE REGRESSION

Sung H. Park, Kazumasa Wakimoto

1987 Volume 17 Issue 1 Pages 11-19
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.11

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The partial regression plots can be used to examine an influential observation for a single parameter in multiple regression. However, it is often desirable to detect an influential observation for a subset of regression parameters when interest centers on a selected subset of independent variables. Cook and Weisberg (1980) suggest a statistic which can be used for this purpose.
In this paper, first, the partial regression is redefined to include more than a single parameter and its properties are discussed. Next, using the partial regression model, two statistics are suggested to detect an influential observation on a subset of regression parameters. An example is illustrated to compare the proposed statistics with the statistic of Cook and Weisberg.

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A TWO-ARMED BANDIT PROBLEM WITH ONE ARM KNOWN INCLUDING SWITCHING COSTS AND TERMINAL REWARDS

Toshio Hamada

1987 Volume 17 Issue 1 Pages 21-30
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.21

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Suppose that the trial to select and perform one of two experiments e₀ and e₁ has to be made sequentially n times. By performing e_i (i=0, 1), a continuous random sample Z_i is obtained from the distribution with parameter u_i and then the reward aZ_i is obtained, where a=(E[Z₁])^-1. The value of u₁ is known a priori, but that of u₀ is unknown and there is a natural conjugate prior distribution of u₀. The change of experiments at the subsequent two trials causes the switching cost. Also, the final reward is incurred at the end of the final trial. The objective is to maximize the total expected reward. This problem is formulated by the principle of optimality of dynamic programming and the optimal strategy is derived by using a critical value function. Several properties of this function are also derived.

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THE ASYMPTOTIC BEHAVIOUR OF THE SAMPLE AUTOCOVARIANCE FUNCTION FOR AN AUTOREGRESSIVE INTEGRATED MOVING AVERAGE PROCESS

Junji Nakano, Shigemi Tagami

1987 Volume 17 Issue 1 Pages 31-38
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.31

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We derive the first two asymptotic moments of the sample autocovariance function of a time series generated from an autoregressive d-th integrated moving average process for any positive integer d. The obtained results show that the sample autocovariance function is a random variable of order N^2d-1, where N is the observed length of data.

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RANK ORDER TESTS FOR ORDERED CATEGORICAL RESPONSES ASSUMING LATENT CONTINUOUS VARIABLES

Hiroyuki Uesaka

1987 Volume 17 Issue 1 Pages 39-53
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.39

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The ordered categorical response is assumed to be a manifestation of a latent continuous response or trait. The observed category is assumed to indicate the latent class interval in which the latent continuous variable falls. Nonparametric tests for homogeneity of several populations against regression alternatives are discussed. In univariate case, rank order tests are defined by an extension of Rao's criterion and in a similar manner multivariate rank order tests are defined. Large sample distributions and several power properties as well as properties of rank order scores are discussed. It is shown that Rao's criterion gives an asymptotically most powerful test in the class of rank order tests for univariate distributions.

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MAXIMUM LIKELIHOOD ESTIMATES FOR BEHRENS-FISHER PROBLEM

Nariaki Sugiura, Arjun K. Gupta

1987 Volume 17 Issue 1 Pages 55-60
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.55

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It is shown that likelihood equation for estimating common mean and different variances of two normal distributions has either one real solution or three real solutions. Necessary and sufficient conditions for the solution to be maximum likelihood estimates are given. An extension to multivariate problem is discussed.

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ON THE ESTIMATION ERROR OF THE KALMAN FILTER WITH UNKNOWN PARAMETERS

Norio Watanabe

1987 Volume 17 Issue 1 Pages 61-73
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.61

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State estimation and prediction problems are discussed for stationary and nonstationary processes represented by state space forms, which include unknown parameters. First we calculate the variance of the difference between the state variable and its estimate constructed by the Kalman filter in which unknown parameters are replaced by any fixed values. Second we consider a special case when the process is purely explosive and show that the prediction error, which is obtained by substituting least squares estimates of parameters into unknown parameters, has a limit distribution with a bounded variance, though the variance of the process diverges to infinity.

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ESTIMATION OF A COMMON MEAN WITH SYMMETRICAL LOSS

Tatsuya Kubokawa

1987 Volume 17 Issue 1 Pages 75-79
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.75

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Consider the problem of estimating common mean μ of several normal populations with possibly different unknown variances. When the loss is a nondecreasing concave function of |_??_-μ|^r for r>0, the paper gives sufficient conditions under which a combined estimator has a smaller risk than each sample mean.

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SOME SMALL SAMPLE PROPERTIES OF A PRE-TEST ESTIMATOR OF THE DISTURBANCE VARIANCE IN A MISSPECIFIED LINEAR REGRESSION

Kazuhiro Ohtani

1987 Volume 17 Issue 1 Pages 81-89
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.81

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In this paper, we examine small sample properties of a pre-test estimator of the disturbance variance when we have extraneous information on the disturbance variance and when there is a possible specification error in a specified model. It is shown that the pre-test estimator dominates the usual (OLS) estimator if the level of the pre-test is chosen appropriately, when the alternative hypothesis in the pre-test is one-sided.

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A Rank Test Using Special Score

Yasushi Kawara

1987 Volume 17 Issue 1 Pages 91-100
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.91

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In this paper, the rank test using special score [=2^i-1(i=rank)] is described.
This test has the advantage in that we can calculate the value of probability of significance exactly, even though the size of sample is large, and we can select the level of significance more freely than any other test.
The power of this test is examined by computer, and is compared with the power of Wilcoxon test, Siegel-Tukey test, and Savage test. Consequently it is proved that this test is effective for location and scale tests.

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