Optimum linear unbiased estimation of the scale parameter by absolute values of order statistics in the double exponential and the double weibull distributions

The first two moments and product moments of absolute values of order statistics are obtained for the double exponential and the double Weibull distributions. In both of the distributions an optimum linear unbiased estimator of the scale parameter, by absolute values of the order statistics, is obtained from complete and censored samples of size n=3(1)10. It is found that the new estimator is generally more efficient than the best linear unbiased estimator (BLUE) of the scale parameter by order statistcs in both of the distributions.     

On Least Absolute Value Estimators for Poisson Processes

We consider the problem of parameter estimation for an inhomogeneous Poisson process observed on the time interval [0, τ]. We introduce the minimum L ₁-norm estimator of the unknown parameter and study the asymptotical behaviors of the estimates when the number of observations increases. It is established that this estimator is consistent and we show that the corresponding differences converge to certain variables. These limit variables are asymptotically normal as τ tends to infinity.     

Graphical Demonstration of an Optimality Property of the Median

The property that the mean absolute deviation is a minimum when measured from a median is demonstrated with graphs. Deficiencies of the usual proof of the property are pointed out, and a new, general proof is suggested.     

Least absolute value regression: a special case of piecewise linear minimization

The Barrodale and Roberts algorithm for least absolute value (LAV) regression and the algorithm proposed by Bartels and Conn both have the advantage that they are often able to skip across points at which the conventional simplex-method algorithms for LAV regression would be required to carry out an (expensive) pivot operation.

We indicate here that this advantage holds in the Bartels-Conn approach for a wider class of problems: the minimization of piecewise linear functions. We show how LAV regression, restricted LAV regression, general linear programming and least maximum absolute value regression can all be easily expressed as piecewise linear minimization problems.     

后小康时代的相对贫困治理

后小康时代中国扶贫战略将由绝对贫困治理转向相对贫困治理,相对贫困治理的任务会更加艰巨。与绝对贫困治理相比,相对贫困治理具有分散性、多维性、艰巨性、长期性、系统性五大特征,同时也面临脱贫攻坚成效不稳定、脱贫内生动力不足、政策有效性和文化贫困四大治理难点。对此,必须构建转型衔接机制、内生动力机制、多重保障机制、人文发展机制四大相对贫困长效治理机制,以顺利实现贫困治理体系和治理能力现代化。     

热力学第二定律的表述和绝对熵的定义

给出了热力学第二律的一种新表述．并在此基础上．定义了封闭热力学系统的绝对熵；证明了在绝热过程中Δs≥0，在准静态过程中存在ds≥δQ／T定义了温度；给出了熵的物理意义；讨论了新表述与经典热力学的关系，得出了新表述与经典力学一样可靠的结论．     

Robust analogs to the coefficient of variation

The coefficient of variation (CV) is commonly used to measure relative dispersion. However, since it is based on the sample mean and standard deviation, outliers can adversely affect it. Additionally, for skewed distributions the mean and standard deviation may be difficult to interpret and, consequently, that may also be the case for the CV. Here we investigate the extent to which quantile-based measures of relative dispersion can provide appropriate summary information as an alternative to the CV. In particular, we investigate two measures, the first being the interquartile range (in lieu of the standard deviation), divided by the median (in lieu of the mean), and the second being the median absolute deviation, divided by the median, as robust estimators of relative dispersion. In addition to comparing the influence functions of the competing estimators and their asymptotic biases and variances, we compare interval estimators using simulation studies to assess coverage.