In this paper we consider sequential fixed-width confidence interval estimation for the percentiles of a normal distribution with unknown mean and variance. We construct two kinds of confidence intervals by using a stopping rule and show their asymptotic consistency. We also try to compare the performance of these confidence intervals by the simulation results.

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This paper deals with the situation in which a current experiment is given and although a future design matrix has been prepared, the corresponding observation matrix is not available. To predict the future observation matrix, we consider selecting an appropriate design matrix by proposing a predictive Akaike Information Criteria (PAIC). The PAIC is derived as an exact unbiased estimator for the risk function and is based on the expected Kullback-Leibler divergence and the future design matrix. A simulation study illustrated that model selection with PAIC performs well for some extrapolation cases.

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We propose nonparametric time domain statistics to test time series nonlinearity. We show the asymptotic properties of our statistics for an autoregressive process and also discuss the asymptotic results for some kinds of nonlinear processes. Next, we show the power of our statistics for various time series and compare the power of our statistics with that of other well known nonparametric statistics proposed by McLeod and Li [7], Tsay [11] and Hjellvik and Tjøstheim [12] by simulation studies.

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The maximum quasi-likelihood method suggested by Wedderburn (1974) is widely used. The quasi-score equation (QSE) is linear with respect to a random variable and has useful properties in practical analysis. However, for some variance functions, there are no probability models that match the quasi-likelihood in the univariate 1-parameter family. Consequently, QSE can not be derived by differentiating the likelihood by the mean parameter and it loses the interpretation. In this paper, a tilted exponential family is introduced and new interpretation is given to QSE via the tilted exponential family under the above conditions.

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The conditional expectations of minimum logit-x² and minimum discrepancy estimators including the maximum likelihood estimator given the maximum likelihood estimator are discussed. It is shown that the n^-2 order mean squared errors of all the bias-adjusted conditional expectations of minimum discrepancy and minimum logit-x² estimators are of equal value. Further, their n^-3 order mean squared errors are evaluated, and in a special case, the bias-adjusted maximum likelihood estimator is numerically compared with the others.

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In this paper, we will investigate the consistency of a frequency estimate of real-valued signal with varying amplitude. The wavelet based estimation procedure has already been investigated by Shibata and Takagiwa (1997) for the case of complex-valued signals. Whether the signal is complex-valued or real-valued does not seem to make any significant difference, but in fact it does. We will propose a new wavelet based estimation procedure which is different from the procedure previously proposed for complex-valued signals. The sampling scheme employed in this paper is that of a dense observation on a fixed time interval or on the neighborhood of a specified time point. We will demonstrate that our estimation procedure is consistent under the smoothness condition of the amplitude, but that the conventional Fourier based estimation procedure is rarely consistent.

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This paper estimated the parameter values of several functional forms for income distributions and the Gini coefficients, using individual (ungrouped) observations by maximum likelihood estimator. An emphasis was placed upon comparing them with results based on grouped data estimated by minimum chi-square or MLE. It is preferable, in principle, to use individual observations based on a theoretical ground. When zero figures, however, of incomes are included, some functional forms cannot describe individual data properly. It is possible to obtain reasonable and robust estimates of parameters and Gini coefficients for these functional forms by using grouped data. Finally, some observations about the performances of the estimated functions and the Gini coefficients were discussed.

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