The laws of large numbers for Pareto-type random variables with infinite means

In this paper, we consider the laws of large numbers for NSD random variables satisfying Pareto-type distributions with infinite means. Based on the Pareto-Zipf distributions, some weak laws of large numbers for weighted sums of NSD random variables are obtained. Meanwhile, we show that a weak law for Pareto-Zipf distributions cannot be extended to a strong law. Furthermore, based on the two tailed Pareto distribution, a strong law of large numbers for weighed NSD random variables is presented. Our results extend the corresponding earlier ones.     

The effect of small sample on optimal designs for logistic regression models

Asymptotic methods are commonly used in statistical inference for unknown parameters in binary data models. These methods are based on large sample theory, a condition which may be in conflict with small sample size and hence leads to poor results in the optimal designs theory. In this paper, we apply the second order expansions of the maximum likelihood estimator and derive a matrix formula for the mean square error (MSE) to obtain more precise optimal designs based on the MSE. Numerical results indicate the new optimal designs are more efficient than the optimal designs based on the information matrix.     

MSE performance of the weighted average estimators consisting of shrinkage estimators when each individual regression coefficient is estimated

In this paper, we analytically derive the exact formula for the mean squared error (MSE) of two weighted average (WA) estimators for each individual regression coefficient. Further, we execute numerical evaluations to investigate small sample properties of the WA estimators, and compare the MSE performance of the WA estimators with the other shrinkage estimators and the usual OLS estimator. Our numerical results show that (1) the WA estimators have smaller MSE than the other shrinkage estimators and the OLS estimator over a wide region of parameter space; (2) the range where the relative MSE of the WA estimator is smaller than that of the OLS estimator gets narrower as the number of explanatory variables k increases.     

变动均值和方差资产配置模型的应用研究

本文在均值-方差模型的基础上,以改善估计误差为主线,选取了10种变动均值-方差的资产配置模型,以等权重策略为基准,运用了确定性等价收益和Alpha值为判断准则,同时考虑了允许卖空限制和非允许卖空的情况,实证研究结果表明：虽然在资本市场中配置模型并不能显著战胜等权重策略,但随着投资范围的扩大,模型开始显现配置效果,尤其在Alpha准则下,变动均值-方差资产配置显著。同时本文还将实证结果和目前我国投资者的实际资产配置情况进行了比较,发现了现实配置结构中的不合理之处,并提出了相应的改善建议。最后对4类常用资产进行了模拟研究,其结果也进一步证实了本文的结论。     

CO-OFDM系统中基于线性预处理的新相位噪声抑制算法

针对相干光正交频分复用（coherent optical orthogonal frequency division multiplexing,CO-OFDM）系统中相位噪声引起的载波间干扰（inter-carrier interference,ICI）问题,提出了一种基于线性预处理的新判决反馈相位噪声抑制算法。该新算法改进了线性预处理部分,利用循环前缀与OFDM符号固有的相关性,在时域进行简单的线性组合运算,充分利用了OFDM符号中冗余信息。仿真分析表明,在激光器线宽为200 kHz且误码率（bit error rate, BER）为10－4时,与判决反馈相位噪声抑制算法和一次迭代的判决反馈相位噪声抑制算法相比,该新算法BER曲线的信噪比（signal to noise ratio,SNR）分别改善了3 dB和1 dB,有效地降低由ICI引起的错误平层。     

论"中"

“中”的思想在中国历史渊源流长,成为中华民族人文精神的核心,也是中国哲学的精髓。《周易》倡导“中和”精神,儒家践行中庸之道,佛家崇尚以中观法,道家提倡守中致道,都从不同角度深刻地阐发了“中”的思想。万物皆有中,中是一切存在的根本属性,“中律”是宇宙万物运行的根本法则,中和是创新的灵魂。     

Random errors in egocentric networks

The systematic errors that are induced by a combination of human memory limitations and common survey design and implementation have long been studied in the context of egocentric networks. Despite this, little if any work exists in the area of random error analysis on these same networks; this paper offers a perspective on the effects of random errors on egonet analysis, as well as the effects of using egonet measures as independent predictors in linear models. We explore the effects of false-positive and false-negative error in egocentric networks on both standard network measures and on linear models through simulation analysis on a ground truth egocentric network sample based on facebook-friendships. Results show that 5–20% error rates, which are consistent with error rates known to occur in ego network data, can cause serious misestimation of network properties and regression parameters.     

Optimal Dynamic Order Scheduling under Capacity Constraints Given Demand‐Forecast Evolution

We consider a manufacturer without any frozen periods in production schedules so that it can dynamically update the schedules as the demand forecast evolves over time until the realization of actual demand. The manufacturer has a fixed production capacity in each production period, which impacts the time to start production as well as the production schedules. We develop a dynamic optimization model to analyze the optimal production schedules under capacity constraint and demand‐forecast updating. To model the evolution of demand forecasts, we use both additive and multiplicative versions of the martingale model of forecast evolution. We first derive expressions for the optimal base stock levels for a single‐product model. We find that manufacturers located near their market bases can realize most of their potential profits (i.e., profit made when the capacity is unlimited) by building a very limited amount of capacity. For moderate demand uncertainty, we also show that it is almost impossible for manufacturers to compensate for the increase in supply–demand mismatches resulting from long delivery lead times by increasing capacity, making lead‐time reduction a better alternative than capacity expansion. We then extend the model to a multi‐product case and derive expressions for the optimal production quantities for each product given a shared capacity constraint. Using a two‐product model, we show that the manufacturer should utilize its capacity more in earlier periods when the demand for both products is more positively correlated.     

Statistical analysis of error for fourth-order ordinary differential equation solvers

We develop an autoregressive integrated moving average (ARIMA) model to study the statistical behavior of the numerical error generated from three fourth-order ordinary differential equation solvers: Milne's method, Adams–Bashforth method and a new method that randomly switches between the Milne and Adams–Bashforth methods. With the actual error data based on three differential equations, we desire to identify an ARIMA model for each data series. Results show that some of the data series can be described by ARIMA models but others cannot. Based on the mathematical form of the numerical error, other statistical models should be investigated in the future. Finally, we assess the multivariate normality of the sample mean error generated by the switching method.     

Forecast mean squared error reductionin the VAR(1) process

When VAR models are used to predict future outcomes, the forecast error can be substantial. Through imposition of restrictions on the off-diagonal elements of the parameter matrix, however, the information in the process may be condensed to the marginal processes. In particular, if the cross-autocorrelations in the system are small and only a small sample is available, then such a restriction may reduce the forecast mean squared error considerably.

In this paper, we propose three different techniques to decide whether to use the restricted or unrestricted model, i.e. the full VAR(1) model or only marginal AR(1) models. In a Monte Carlo simulation study, all three proposed tests have been found to behave quite differently depending on the parameter setting. One of the proposed tests stands out, however, as the preferred one and is shown to outperform other estimators for a wide range of parameter settings.