Journal of the Japan Statistical Society, Japanese Issue

Sampling Surveys from Animal Population

Estimation of Population Size of Animals

Chikio Hayashi

1985 Volume 15 Issue 2 Pages 109-125
Published: 1985
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.15.109

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Several methods on the estimation of population size of animals are discussed. The method of capture-recapture is popular in mathematical statistics. Besidesthis, other methods are introduced. Particulary, the track method and operational method by the author are explained in detail. The contents are as follows; 1) Capture method, 2) Observation method, 3) Capture-recapture method, 4) Method based on home range, 5) Track method, 6) Interval method, 7) Operational method.

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THE VARIABLE SELECTION PROBLEM FOR PREDICTION ON THE PREDICTION AREA DIFFERENT FROM SAMPLE AREA

Takakatsu Inoue

1985 Volume 15 Issue 2 Pages 127-138
Published: 1985
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.15.127

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In the regression model Y_α=x_α'β+ε_α (α=1, 2, …, n), we discuss the variable selection problem for prediction of the future dependent variable Y^* on the future sample point x^*, where x^* is assumed to be a vector of random variables having a known probability density function. As the risk function for variable selection, the expectation with respect to x^* of Prediction Mean Square Error is used. Two criteria for variable selection are proposed and discussed on the basis of numerical examples.

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MEAN EFFICIENCY OF LEAST SQUARES ESTIMATOR OF REGRESSION COEFFICIENTS

Manabu Iwasaki

1985 Volume 15 Issue 2 Pages 139-149
Published: 1985
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.15.139

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The efficiency of the ordinary least squares estimator (OLSE) b of β in the linear regression model y=Xβ+u, where E[u]=0, E[uu']=Σ is considered. The efficiency (EFF) of OLSE is defined by EFF=|var[β]|/|var[b]|, where β is the generalized least squares estimator (GLSE) of β.
Considering 1/EFF instead of EFF, the mean efficiency E[1/EFF] is obtained when the design matrix X is taken arbitrarily, i.e., X has the uniform distribution on the Stiefel manifold. Examples are given to compare E[1/EFF] with the upper bound of 1/EFF.

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DECOMPOSITIONS FOR ODDS-SYMMETRY MODELS IN A SQUARE CONTINGENCY TABLE WITH ORDERED CATEGORIES

Sadao Tomizawa

1985 Volume 15 Issue 2 Pages 151-159
Published: 1985
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.15.151

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For the analysis of square contingency tables with ordered categories, this paper introduces two kinds of odds-symmetry models, which are extensions of McCullagh's [4] conditional symmetry model, and gives their decompositions. This paper also discusses a test theory with an example.

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SERIALLY BALANCED DESIGNS RELATED TO BALANCED INCOMPLETE BLOCK DESIGNS

Masakazu Jimbo

1985 Volume 15 Issue 2 Pages 161-175
Published: 1985
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.15.161

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When a number of treatments are applied, in successive periods, to a single experimental subject or several experimental subjects, there exists the possibility that a treatment may produce not merely a direct effect, in the period in which it is applied, but a residual effect in the following period. In this paper, a few kinds of serially balanced designs which are suitable for the case when residual effects exist are considered and constructions of them are presented. Furthermore, the statistical analysis of designs based on the sequences are given.

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MINIMAXITY AND INADMISSIBILITY OF THE MODEL SELECTION AND ESTIMATION PROCEDURE FOR THE MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION

Yasushi Nagata

1985 Volume 15 Issue 2 Pages 177-182
Published: 1985
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.15.177

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The inference procedure for the mean vector of a p-dimensional normal distribution with known variance-covariance matrix is discussed under a loss function which is based on the Kullback-Leibler information measure and evaluates both an error of model selection and that of estimation. The procedure which selects a model among 2^p competing models by AIC (Akaike's Information Criterion) and then uses the maximum likelihood estimator under the chosen model is shown to be always minimax but inadmissible when p≥3.

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ESTIMATION OF THE AUTOCORRELATION COEFFICIENTS FOR A STATIONARY GAUSSIAN PROCESS BY RANDOM CLIPPING

Minoru Tanaka, Kunio Shimizu

1985 Volume 15 Issue 2 Pages 183-191
Published: 1985
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.15.183

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This paper deals with the problem of estimating the autocorrelation coefficients for a stationary Gaussian process with known mean and variance. Two unbiased estimates using random clipping are proposed. The variances of the proposed estimates are numerically compared against those of competitors.

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FURTHER RESULTS ON A UNIFORM TWO-ARMED BANDIT PROBLEM WITH ONE ARM KNOWN

Toshio Hamada

1985 Volume 15 Issue 2 Pages 193-208
Published: 1985
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.15.193

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Suppose that there are two experiments e₀ and e₁ and by performing e_i (i=0, 1), a random sample X_i is obtained from the uniform distribution on the interval [p_i, q_i]. The values of p₁ and q₁ are known a priori, but at least one of two values p₀ and q₀ are unknown. There is a conjugate prior distribution for the unknown parameters. Experiments are performed sequentially for n times and at each time one of two experiments is selected and performed. The expected value of sum of n observations is maximized. Two cases are considered: First case is that p₀=p₁=0, q₁=1 and the reward is discounted by a discount factor. Another case is that both p₀ and q₀ are unknown. For both cases, the problem is formulated by the principle of optimality of dynamic programming, the optimal strategy is derived and critical values for the strategy are calculated.

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MAXIMUM LIKELIHOOD ESTIMATORS OF THE PARAMETERS IN A MOVING AVERAGE PROCESS WITH TIME VARYING COEFFICIENTS

Gea Hwa Kwoun

1985 Volume 15 Issue 2 Pages 209-220
Published: 1985
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.15.209

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This paper is concerned with a moving average model of order q where the coefficients are allowed to change as functions of time, containing unknown parameters. We derive the exact likelihood function of observations and show under what kinds of functions the maximum likelihood estimators (MLE) have consistency and asymptotic normality for large values of the sample size. Furthermore we consider the asymptotic relationship between the exact MLE and the conditional MLE obtained by letting the starting values be zero.

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Book Review

[in Japanese]

1985 Volume 15 Issue 2 Pages 221-222
Published: 1985
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.15.221

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Summary of Reports Presented at the 53rd Annual Meeting of the Japan Statistical Society, July 1985

1985 Volume 15 Issue 2 Pages 223-242
Published: 1985
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.15.223

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