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Volume 35 (2006)
- Issue 3 Pages 139-
- Issue 2 Pages 79-
- Issue 1 Pages 1-
Volume 35, Issue 1
Displaying 1-3 of 3 articles from this issue
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Mitsunori Kayano, Sadanori Konishi, Hideki Hirakawa, Satoru Kuhara2006 Volume 35 Issue 1 Pages 1-16
Published: July 30, 2006
Released on J-STAGE: June 12, 2009
JOURNAL FREE ACCESSRecently, functional data analysis (FDA) has received considerable attention in various fields and a number of successful applications have been reported (see, e.g., Ramsay and Silverman (2005)). The basic idea behind FDA is the expression of discrete observations in the form of a function and the drawing of information from a collection of functional data by applying concepts from multivariate data analysis.
There are some reports discussing principal component analysis for functional data. We introduce the regularized functional principal component analysis for multi-dimensional functional data set, using Gaussian radial basis functions.
The use of the proposed method is illustrated through the analysis of the three-dimensional (3D) protein structural data by converting the 3D protein data to the 3-dimensional functional data set. The visual inspection showed that the PC (principal component) plot mostly coincided with the biological classification.View full abstractDownload PDF (2538K) -
Masaaki Sibuya2006 Volume 35 Issue 1 Pages 17-47
Published: July 30, 2006
Released on J-STAGE: June 12, 2009
JOURNAL FREE ACCESSThe hyperbolic secant distribution (HpSc) is one of six subfamilies of the natural exponential family with quadratic variance functions, NEF-QVF. The others are normal, gamma, Poisson, binomial and negative binomial distributions. It is, however, little-known and rarely used in applied statistics. In this paper, its properties are surveyed and graphically visualized; new facts on the moments, mode, and conjugate prior distribution are shown; ML estimation, generalized linear model and generalized additive model are explored. HpSc models are fitted to some data sets, and the results are preferable to the conventional ones. Some numerical procedures are to be developed, and further research will be promising.View full abstractDownload PDF (997K) -
Manabu Iwasaki, Takayuki Abe2006 Volume 35 Issue 1 Pages 49-60
Published: July 30, 2006
Released on J-STAGE: June 12, 2009
JOURNAL FREE ACCESSCensoring and truncation are two main sources of incomplete data. For such cases, the actual values of a measurement x are observed if x satisfies a certain condition such as x≤c, where c is a pre-specified cut-off point. For censoring, the number of unobserved values is known, whereas such number is not reported for truncation. Comparisons of the accuracy of estimates of population parameter θ under censoring and truncation have been performed by calculating asymptotic variances or by inspection of the figures of log-likelihood functions.
In this paper, a different approach is proposed in assessing the stability of the estimates under censoring and truncation. We perturb the cut-off point c and examine the effect of the perturbation that influences the estimates. Specifically, we examine implicit functions θ=g(c) given by likelihood equations. It is observed that the function g(c) is increasing in c under censoring, but is decreasing under truncation. It is also observed that for censoring, the effect of c becomes small if the number of observed data, m, is large, but that for truncation, the number m does not contribute to make estimates stable. Two important cases, exponential and normal distributions will be examined in detail. Two numerical examples are also given to illustrate the situation. One of the inferences obtained from this paper is that the estimate under truncation is quite unstable even for large values of m.View full abstractDownload PDF (542K)
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