Ritei Shibata

Selection of the number of regression variables; A minimax choice of generalized FPE

SummaryA generalized Final Prediction Error (FPEα)_ criterion is considered. Based onn observations, the numberk of regression variables is selected from a given range 0≦k≦K, so as to minimize

Weak Stationarity of a Time Series with Wavelet Representation

FPE_\alpha (k) = n\hat \sigma ^2 (k) + \alpha k\{ n\hat \sigma ^2 (k)/(n - K)\}

Consistency of Frequency Estimates Based on the Wavelet Transform

. It is shown that if α tends to infinity withn, the selection is consistent but the maximum of the mean squared error of estimates of parameters diverges to infinity with the same order of divergence as that of α. A meaningful minimax choice of α exists for a regret type mean squared error, while for simple mean squared error it is trivially 0. The minimax regret choice of α converges to a constant, approximately 3.5 forK≧8 ifn−K increases simultaneously withn, otherwise it diverges to infinity withn.

Exploration of the disease locus by a careful evaluation of the likelihood polynomial for pedigree data.

The textile plot is a parallel coordinate plot in which the ordering, locations and scales of the axes are simultaneously chosen so that the connecting lines, each of which represents a case, are aligned as horizontally as possible. Plots of this type can accommodate numerical data as well as ordered or unordered categorical data, or a mixture of these different data types. Knots and parallel wefts are features of the textile plot which greatly aid the interpretation of the data. Several practical examples are presented which illustrate the potential usefulness of the textile plot as an aid to the interpretation of multivariate data.

Interdatabase and DandD

Weak stationarity of a time series, which has a Karhunen-Loève representation with a wavelet function, is investigated. Under the assumption that orthogonal incrementdZ(a, b) of the Karhunen-Loève representation with the dilation and translation parametersa andb, can be written as productdZ1(a) dZ2 (b) of two orthogonal increment processesZ1 (a) andZ2(b), it is shown that a necessary and sufficient condition for the weak stationarity of the given processX(t) is that the power ‖dZ2(b)‖2 is uniform in terms ofb and has no jumps. This holds true irrespective ofZ1(a).

PARTIAL CORRELATION AND CONDITIONAL CORRELATION AS MEASURES OF CONDITIONAL INDEPENDENCE

Seven different Japanese Yen interest rates recorded on a daily basis for the period from 1986 to 1992 are simultaneously analyzed. By introducing a new concept of ‘short term trend’, we decompose each interest rate series into three components, ‘long termtrend’, ‘short term trend’ and ‘irregular’. It is obtained by a two step lowess smoothing technique. After that, a multivariate autoregressive model (MAR) is fitted to the vector valued time series obtained by combining those seven irregular components. The decomposition and MAR model fitting were quite satisfactory. It enables us to understand well various aspects of interest rate series from the trends, the MAR (2) coefficients and its residuals. The result is compared with the decomposition through sabl and the advantages of our procedure will be demonstrated in relations to other parametric model fitting like ARCH or GARCH. Based on the decomposition we can have better daily prediction and more stable long term forecasting.

Characteristic features of Japanese women's hair with aging and with progressing hair loss

The consistency of the least squares estimate of frequencies modulated in amplitude is investiga ted. It is proved that the estimate based on the wavelet transform is consistent when dilation and translation parameters of the wavelet transform as well as the sampling points are carefully chosen in order to preserve consistency. Our theorem shows that an intuitive method proposed by P. Guillemain et al. (Estimation of spectral lines with the help of the wavelet transform: application in NMR spectroscopy. In Wavelets and Applications (ed. Y. Meyer). New York: Springer, 1992, pp. 38–68) works well for the non-noisy case but does not work well for the noisy case. A key to the consistency is the use of the localization property of the wavelet transform

Effectiveness of Stochastic Neural Network for Prediction of Fall or Rise of TOPIX

It is demonstrated through two case studies that a careful evaluation of the likelihood polynomial results in a more accurate localization of disease locus. The evaluation of the likelihood function as a polynomial enables more flexible exploration of the disease locus. Visualization by a contour plot of the function on a unit square of paternal and maternal recombination fractions along with a superimposed ellipsoid of the Fisher information matrix helps us to find a more accurate localization of the disease locus.