一类非线性波动方程的新精确解

利用李群对称方法,通过构造变换不变量,将一类1 1维非线性波动方程化为常微分方程,得到了这一类非线性波动方程的一些新的显式精确解,包括孤子解、三角函数解和椭圆函数周期解。     

Race and Population Change: A Longitudinal Look at Cleveland Neighborhoods

This paper investigates the relationship of racial composition to neighborhood population change from 1910 to 1990 in the Cleveland metropolitan area. To better understand the long-term dynamics of urban neighborhood change, we focus our analysis upon the longitudinal relationship of race, socioeconomic status, and life cycle stage to changes in neighborhood population densities. First, we find that the more established neighborhoods of the African-American community have experienced dramatic declines in population since 1950, a pattern that represents a clear change from the earlier part of the twentieth century. Second, population loss is experienced through a variety of mechanisms, including the demolition of dwellings, the increase in housing vacancy, and the decline of household size. Third, much of this population loss should be interpreted within the context of high economic distress, occurring most frequently in older African-American communities. Over time, economic distress appears to be more important than race in and of itself in leading to the loss of neighborhood populations.     

On an adaptive version of the Metropolis–Hastings algorithm with independent proposal distribution

In this paper, we present a general formulation of an algorithm, the adaptive independent chain (AIC), that was introduced in a special context in Gåsemyr et al . [ Methodol. Comput. Appl. Probab. 3 (2001)]. The algorithm aims at producing samples from a specific target distribution Π, and is an adaptive, non-Markovian version of the Metropolis–Hastings independent chain. A certain parametric class of possible proposal distributions is fixed, and the parameters of the proposal distribution are updated periodically on the basis of the recent history of the chain, thereby obtaining proposals that get ever closer to Π. We show that under certain conditions, the algorithm produces an exact sample from Π in a finite number of iterations, and hence that it converges to Π. We also present another adaptive algorithm, the componentwise adaptive independent chain (CAIC), which may be an alternative in particular in high dimensions. The CAIC may be regarded as an adaptive approximation to the Gibbs sampler updating parametric approximations to the conditionals of Π.     

A comparison of maximum likelihood and least squares for the estimation of a cumulative distribution

Monte Carlo methods are used to compare the methods of maximum likelihood and least squares to estimate a cumulative distribution function. When the probabilistic model used is correct or nearly correct, the two methods produce similar results with the MLE usually slightly superior When an incorrect model is used, or when the data is contaminated, the least squares technique often gives substantially superior results.     

The Complete Exact Null Distribution of Spearman's Rho for n = 12(1)18

Spearman's rank correlation coefficient, Rho, is a widely used nonparametric measure of association. Complete, exact tables of the null distribution are calculated and presented for n = 12 to 18.     

A comparison of some conditional and unconditional exact tests for 2x2 contingency tables

In 1935, R.A. Fisher published his well-known “exact” test for 2x2 contingency tables. This test is based on the conditional distribution of a cell entry when the rows and columns marginal totals are held fixed. Tocher (1950) and Lehmann (1959) showed that Fisher s test, when supplemented by randomization, is uniformly most powerful among all the unbiased tests UMPU). However, since all the practical tests for 2x2 tables are nonrandomized - and therefore biased the UMPU test is not necessarily more powerful than other tests of the same or lower size. Inthis work, the two-sided Fisher exact test and the UMPU test are compared with six nonrandomized unconditional exact tests with respect to their power. In both the two-binomial and double dichotomy models, the UMPU test is often less powerful than some of the unconditional tests of the same (or even lower) size. Thus, the assertion that the Tocher-Lehmann modification of Fisher's conditional test is the optimal test for 2x2 tables is unjustified.     

A comparative study of confidence intervals to assess biosimilarity from analytical data

Assessment of analytical similarity of tier 1 quality attributes is based on a set of hypotheses that tests the mean difference of reference and test products against a margin adjusted for standard deviation of the reference product. Thus, proper assessment of the biosimilarity hypothesis requires statistical tests that account for the uncertainty associated with the estimations of the mean differences and the standard deviation of the reference product. Recently, a linear reformulation of the biosimilarity hypothesis has been proposed, which facilitates development and implementation of statistical tests. These statistical tests account for the uncertainty in the estimation process of all the unknown parameters. In this paper, we survey methods for constructing confidence intervals for testing the linearized reformulation of the biosimilarity hypothesis and also compare the performance of the methods. We discuss test procedures using confidence intervals to make possible comparison among recently developed methods as well as other previously developed methods that have not been applied for demonstrating analytical similarity. A computer simulation study was conducted to compare the performance of the methods based on the ability to maintain the test size and power, as well as computational complexity. We demonstrate the methods using two example applications. At the end, we make recommendations concerning the use of the methods.     

偏微分方程的非线性变换和精确解

利用截属的Painlev'e展开式、非线性变换和可积的微分方程，可以求出一类非线性偏微分方程的自Backlund变换和它的精确解，孤立波解。波动方程、Hirota-Satsuma方程组和非线性色散与耗散方程作为例子来说明这一方法。     

Likelihood inference for the component lifetime distribution based on progressively censored parallel systems data

Point and interval estimators for the scale parameter of the component lifetime distribution of a k-component parallel system are obtained when the component lifetimes are assumed to be independently and identically exponentially distributed. We prove that the maximum likelihood estimator of the scale parameter based on progressively Type-II censored system lifetimes is unique and can be obtained by a fixed-point iteration procedure. In particular, we illustrate that the Newton–Raphson method does not converge for any initial value. Furthermore, exact confidence intervals are constructed by a transformation using normalized spacings and other component lifetime distributions including Weibull distribution are discussed.     

一类弹性系统的内部精确能控性

该文考虑的是具有分布控制的Timoshenko梁系统的精确能控性.用谱分解方法建立了保守系统的正反向能量不等式,证明了在通常的能量空间中该系统是精确能控的.