Some classes of multivariate distributions, which have the same partial and conditional correlation coefficients, are obtained. In one class, the sum of components is fixed and all the components have negative correlation coefficients. Another class is constructed as mixtures of independent samples from the NEF-QVF mixed by conjugate prior, and all the components are positively correlated. Implications of the equivalence of partial and conditional covariances, and simple covariance structures are briefly discussed.
The problem of estimating the inverse matrix of scale parameters of an elliptically contoured distribution is considered with respect to Stein’s loss function. It is shown that improvement of the estimators obtained under the normality assumption remains robust under an elliptically contoured distribution. A numerical study is also conducted to evaluate the risk performances of the improved estimators.
We propose a simple estimation procedure of the number of components of the fundamental frequency model when all the adjacent harmonics are present. The proposed method is based on the penalty function approach like other Information Theoretic Criteria. The new method is shown to be consistent. We compute the probability of wrong estimates of a particular penalty function and propose a re-sampling technique to estimate the probability of wrong estimates. It is observed that the probability of wrong estimates can be used to choose the best possible penalty function from a particular class of penalty functions. The effectiveness of the proposed method is verified using computer simulations. Two speech data are analyzed using our proposed technique and the performances are quite satisfactory. Finally, we extend our results when all the adjacent harmonics may not be present in the model.
Skewed symmetric distributions have attracted a great deal of attention in the last few years. One of them, the skewed Pearson type VII distribution suffers from limited applicability because it is well known that the Pearson type VII distribution does not have finite moments of all orders. This note proposes an alternative referred to as skewed truncated Pearson type VII distribution and defined by the pdf f(x) = 2g(x)G(λx), where g(·) and G(·) are taken, respectively, to be the pdf and the cdf of a truncated Pearson type VII distribution. This distribution possesses finite moments of all orders and could therefore be a better model for certain practical situations. Two such situations are discussed. The note also derives various properties of the distribution, including its moments.
Some statistics in common use take a form of a ratio of two statistics such as sample correlation coefficient, Pearson’s coefficient of variation and so on. In this paper, obtaining an asymptotic representation of the ratio statistic until the third order term, we will discuss asymptotic mean squared errors of the ratio statistics. We will also discuss bias correction of the sample correlation coefficient and the sample coefficient of variation. Mean squared errors of the corrected estimators are also obtained.
This note gives a statistical description of the Hodrick-Prescott Filter (1997), originally proposed by Leser (1961). A maximum-likelihood estimator is derived and a related moments estimator is proposed that has a straightforward intuitive interpretation and coincides with the maximum-likelihood estimator for long time series. The method is illustrated by an application and several simulations. The statistical treatment in the state-space tradition implies some scepticism regarding the interpretation in terms of low-frequency filtering.
The Patient Survey is a designated statistical survey conducted every three years with the objective of obtaining basic data on the current status of patients in medical institutions in Japan. One of the most important items in the report of this survey is the estimated number of patients with various diseases in each prefecture or secondary medical area. This paper shows that the amount of missing data has increased recently and has reduced the precision in the estimation of patient numbers. We propose to adopt variable weighting for ratio estimation dependent on the differences in the institutional sampling rate instead of the currently used constant weighting, as the proposed method can be adapted to take account of the increases in missing data. The proposed method can improve the precision in the estimation of patient numbers in most diseases, based on quantitative assessment conducted using the actual data from the 1996 and the 1999 Patient Survey.
The Patient Survey is a designated statistical survey conducted every three years with the objective of obtaining basic data on the current status of patients in medical institutions in Japan. Since stratified sampling is used in this survey, suitable construction of strata is essential for achieving low error rates in the estimation of the number of patients having various diseases. We investigated the performance of the current stratification through a correspondence analysis between disease categories and clinic categories and found that patients having diseases related to mental or behavioural disorders were not well sampled by the current stratification method. Therefore, we proposed to create a clinic category, “psychiatry,” as a new stratum for sampling and examined the effect of this stratification on the precision in the estimation through a Monte Carlo simulation. The simulation results indicate that the new stratification achieved a decrease of approximately seven points in the standard error rate of the estimated number of patients with “mental and behavioural disorders.”