司马迁“序彖系象说卦文言”新解--兼《易传》经学史节点考析

对司马迁"序彖系象说卦文言"这句话的理解,涉及现存《周易》通行文本的内部层次结构问题。关于《周易》经、传的写作年代,目前,学术界较为通行的说法是《易经》作于殷末周初、《易传》(十翼)作于战国时期。这其实是决定现存《周易》文本结构层次的根本因素。这种两分法,起码在彖传、象传的定位上令人难以信服;而且,如果从文本形成时段角度考察,《文言》的位置也有移至全书最后、与《序卦》《杂卦》配伍的可能。     

A comparative study on a permutation statistic

We studied asymptotic distribution and finite sample properties of a randomly weighted permutation statistic. The asymptotic normality and the finite sample simulations derived from our studies provided theoretical and numerical justifications for distributional assumption of many useful test statistics used in identifying spatial autocorrelations of mapped data. We compared a new method in computing the mean and the approximated variance of the randomly weighted D statistic, a special permutation statistic, with the Walter’s conditional method. In the numerical illustration of the method, we calculated the standardized values of the D statistic by subtracting the mean from the D statistic and dividing the difference by the standard deviation for the standardized mortality ratios (SMRs) and the life expectancies among the 48 states of the continental USA. Spatial autocorrelations of the SMRs and the life expectancies were found to be statistically significant.     

The Covariance Inflation Criterion for Adaptive Model Selection

We propose a new criterion for model selection in prediction problems. The covariance inflation criterion adjusts the training error by the average covariance of the predictions and responses, when the prediction rule is applied to permuted versions of the data set. This criterion can be applied to general prediction problems (e.g. regression or classification) and to general prediction rules (e.g. stepwise regression, tree-based models and neural nets). As a by-product we obtain a measure of the effective number of parameters used by an adaptive procedure. We relate the covariance inflation criterion to other model selection procedures and illustrate its use in some regression and classification problems. We also revisit the conditional bootstrap approach to model selection.     

A Permutation and Combination-Based Solution on the Ranking of Multivariate Populations in the Case of Ordered Categorical Responses with Application to the Evaluation of the Indoor Environment

This article deals with the problem of classifying and ranking several multivariate populations of interests using the permutation and combination approach providing also an inferential validity of the procedure. The need to define an appropriate classification of populations, i.e., products, services, teaching courses, degree programs, and so on, is very common within many areas of applied research. Many times the populations of interest are multivariate in nature meaning that many aspects of that populations can be simultaneously observed on the same unit/subject. From a statistical point of view, when the response variable of interest is multivariate in nature, the problem may become quite difficult to cope with especially in case of ordered categorical responses, due to the large dimensionality of the parametric space. Nonparametric inference based on the NPC methodology however, allows us to overcome these limitations, without the need of referring to assume any specified random distribution.     

Dimension test approach of heteroscedasticity in the linear model

Heteroscedasticity testing has a long history and is still an important matter in the linear model. There exist many types of tests, but they are limited in use to their own specific cases and sensitive to normality. Here, we propose a dimension test approach to heteroscedasticity. The proposed test overcomes the shortcomings of the existing methods, so that it is robust to normality and is unified in sense that it is applicable in the linear model with multi-dimensional response. Numerical studies confirm that the proposed test is favorable over the existing tests with moderate sample sizes, and real data analysis is presented.     

Tabu search for covering arrays using permutation vectors

A covering array  CA(N;t,k,v)$\mathsf{CA}(N;t,k,v)$ is an N×k$N\times k$ array, in which in every N×t$N\times t$ subarray, each of the v^t$v^t$ possible t  -tuples over v$v$ symbols occurs at least once. The parameter t is the strength   of the array. Covering arrays have a wide range of applications for experimental screening designs, particularly for software interaction testing. A compact representation of certain covering arrays employs “permutation vectors” to encode v^t×1$v^t\times 1$ subarrays of the covering array so that a covering perfect hash family whose entries correspond to permutation vectors yields a covering array. We introduce a method for effective search for covering arrays of this type using tabu search. Using this technique, improved covering arrays of strength 3, 4 and 5 have been found, as well as the first arrays of strength 6 and 7 found by computational search.     

Local likelihood smoothing of sample extremes

Trends in sample extremes are of interest in many contexts, an example being environmental statistics. Parametric models are often used to model trends in such data, but they may not be suitable for exploratory data analysis. This paper outlines a semiparametric approach to smoothing sample extremes, based on local polynomial fitting of the generalized extreme value distribution and related models. The uncertainty of fits is assessed by using resampling methods. The methods are applied to data on extreme temperatures and on record times for the women's 3000 m race.     

Randomization tests for small samples: an application for genetic expression data

Summary. An advantage of randomization tests for small samples is that an exact P -value can be computed under an additive model. A disadvantage with very small sample sizes is that the resulting discrete distribution for P -values can make it mathematically impossible for a P -value to attain a particular degree of significance. We investigate a distribution of P -values that arises when several thousand randomization tests are conducted simultaneously using small samples, a situation that arises with microarray gene expression data. We show that the distribution yields valuable information regarding groups of genes that are differentially expressed between two groups: a treatment group and a control group. This distribution helps to categorize genes with varying degrees of overlap of genetic expression values between the two groups, and it helps to quantify the degree of overlap by using the P -value from a randomization test. Moreover, a statistical test is available that compares the actual distribution of P -values with an expected distribution if there are no genes that are differentially expressed. We demonstrate the method and illustrate the results by using a microarray data set involving a cell line for rheumatoid arthritis. A small simulation study evaluates the effect that correlated gene expression levels could have on results from the analysis.     

p-Value for two-Sample Linear Rank Tests Using Permutation Simulations and the Normal Approximation Method

Test statistics from the class of two-sample linear rank tests are commonly used to compare a treatment group with a control group. Two independent random samples of sizes m and n are drawn from two populations. As a result, N = m + n observations in total are obtained. The aim is to test the null hypothesis of identical distributions. The alternative hypothesis is that the populations are of the same form but with a different measure of central tendency. This article examines mid p-values from the null permutation distributions of tests based on the class of two-sample linear rank statistics. The results obtained indicate that normal approximation-based computations are very close to the permutation simulations, and they provide p-values that are close to the exact mid p-values for all practical purposes.