We attempt to estimate a state space model of investment and borrowing in a Bayesian framework, and to extract the unobservable agency costs of Japanese firms, which we differentiate by firm size. Our estimates suggest that agency cost exhibited a declining trend in the late 1980s, which changed to an increasing trend in the 1990s. We pinned down the driving force of fluctuations in agency cost as the market value of land. Furthermore, we found that the investment and borrowing behavior of small firms was very much affected by their agency costs in the late 1980s and early 1990s. Our evidence suggests that imperfections in the capital market were important for small firms in Japan.

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An estimator of the number of components of a finite mixture of k-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of a k-dimensional independent random sample. Some properties of the estimator are given. Some simulation results also are given for the case of finite mixtures of two-dimensional normal distributions.

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In the inference for jump-diffusion processes, we often need to get the information of the jump part and of the continuous part separately from the data. Although some asymptotic theories have been studied on this issue, a practical interest is the inference from finitely many discrete samples. In this paper we propose a numerical procedure to construct a filter to judge whether or not a jump occurred from finite samples. The paper includes a discussion about the validity of the procedure.

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The (arbitrary) higher order asymptotic expansion for posterior distributions of a single parameter is derived by using posterior modes, and its validity is shown. An asymptotic expansion for the Bayes risk with squared error loss of a posterior mode is derived.

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We consider the variable selection problem in the nonlinear discriminant procedure using local likelihood. The local likelihood method is an effective technique for analyzing data with complex structure, and various bandwidth selection methods have been suggested in recent years. Variable selection in a nonlinear model, however, is more complex than bandwidth selection, since the optimal bandwidth depends on the combination of the variables. We propose a technique for variable selection using generalized information criteria in logistic discrimination based on local likelihood. We derive the logistic discrimination method with a sample covariance matrix to account for the correlation of the variables. Real data examples are given to examine the effectiveness of our technique.

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In canonical correlation analysis, canonical vectors are used in the interpretation of the canonical variables. We are interested in the asymptotic representation of the expectation, the variance and the distribution of the canonical vector. In this study, we derive the asymptotic distribution of the canonical vector under nonnormality. To obtain the asymptotic expansion of the canonical vector, we use a perturbation method. In addition, as an example, we show the asymptotic distribution with an elliptical population.

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We will consider the central limit theorem for the smoothed version of statistical functionals in a finite population. For the infinite population, Reeds (1976) and Fernholz (1983) discuss the problem under the conditions of Hadamard differentiability of the statistical functionals and derive Taylor type expansions. Lindeberg-Feller's central limit theorem is applied to the leading term, and controlling the remainder terms, the central limit theorem for the statistical functionals are proved. We will modify Fernholz's method and apply it to the finite population with smoothed empirical distribution functions, and we will also obtain Taylor type expansions. We then apply the Erdös-Rényi central limit theorem to the leading linear term to obtain the central limit theorem. We will also obtain sufficient conditions for the central limit theorem, both for the smoothed influence function, and the original non-smoothed versions. Some Monte Carlo simulation results are also included.

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In the Kolmogorov-Smirnov theorem, the underlying distribution is assumed to be a continuous distribution. On the other hand, real data in practice is always given in a discretized (rounded) form. In this paper we establish a Donsker type theorem in the fashion of the modern empirical process theory to obtain a (right) Kolmogorov-Smirnov test for discretized data.

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