A Unified Way to Represent and Compute the Cumulative Distribution Function for Noncentral t,F, and χ2

This short article shows an unified approach to representing and computing the cumulative distribution function for noncentral t, F, and χ². Unlike the existing algorithms, which involve different expansion and/or recurrence, the new approach consistently represents all the three noncentral cumulative distribution functions as the integral of the normal cumulative distribution function and χ² density function.     

Inference of non-centrality parameter of a truncated non-central chi-squared distribution

Non-central chi-squared distribution plays a vital role in statistical testing procedures. Estimation of the non-centrality parameter provides valuable information for the power calculation of the associated test. We are interested in the statistical inference property of the non-centrality parameter estimate based on one observation (usually a summary statistic) from a truncated chi-squared distribution. This work is motivated by the application of the flexible two-stage design in case–control studies, where the sample size needed for the second stage of a two-stage study can be determined adaptively by the results of the first stage. We first study the moment estimate for the truncated distribution and prove its existence, uniqueness, and inadmissibility and convergence properties. We then define a new class of estimates that includes the moment estimate as a special case. Among this class of estimates, we recommend to use one member that outperforms the moment estimate in a wide range of scenarios. We also present two methods for constructing confidence intervals. Simulation studies are conducted to evaluate the performance of the proposed point and interval estimates.     

麦克仑南论一妻多夫制

古典进化论学派学者麦克伦南（John· Fergus· McLennan）曾在其著作《原始婚姻》中对一妻多夫这种婚姻家庭形态进行了论述。麦克仑南对一妻多夫的基本看法是,这种婚姻家庭形态并不是一种例外和反常形态,而认为一妻多夫是人类社会发展的一个重要和普遍阶段。麦克仑南的这个论点是基于他对人类早期社会基本图景的推论和分析。本文试图在说明麦克伦南关于人类早期社会与婚姻发展脉络的基础上,来讨论一妻多夫制在其中的序列与价值。     

THE DEMAND FOR LIQUID ASSETS,CORPORATE SAVING,AND INTERNATIONAL CAPITAL FLOWS

The recent period of capital outflows from emerging economies has coincided with an increase in their corporate saving. In this paper, we model corporate saving as a demand for liquid assets by credit‐constrained firms in a dynamic open‐economy macroeconomic model. We find that the implications of this model are very different from standard models, because the demand for foreign bonds is a complement to domestic investment rather than a substitute. We show that this complementarity is at work when an emerging economy is on its convergence path or when it has a higher TFP growth rate. This framework is consistent with a number of stylized facts found in high‐growth, high‐investment emerging economies.     

基于单片机的无线遥控小车研究与实现

本文介绍了一种由STC12C5A60S2单片机控制的无线遥控小车,采用控传和图传独立设计的思想,即数据收发模块进行控制和温度数据的传输,图传模块负责作业环境的图像传输.控传部分以STC12C5A60S2单片机为核心,利用NRF24L01+模块数据收发,L298N电机驱动两路直流电机,使小车完成相应动作;DS18B20负责检测温度,由小车收发模块发射,LCD1602液晶模块显示.系统采用模块化设计,结构紧凑,便于优化,且可靠性能高.     

Mr.J.F.McLennan's Study of Polyandry

John F.McLennan is well known for introducing the terms of “exogamy” and “en-dogamy” in Primitive Marriage:An Inquiry into the Origins of the Form of Capture in Marriage Ceremo-nies(1865) .In this book...     

Noninformative priors for linear combinations of normal means with unequal variances

For normal populations with unequal variances, we develop matching priors and reference priors for a linear combination of the means. Here, we find three second-order matching priors: a highest posterior density (HPD) matching prior, a cumulative distribution function (CDF) matching prior, and a likelihood ratio (LR) matching prior. Furthermore, we show that the reference priors are all first-order matching priors, but that they do not satisfy the second-order matching criterion that establishes the symmetry and the unimodality of the posterior under the developed priors. The results of a simulation indicate that the second-order matching prior outperforms the reference priors in terms of matching the target coverage probabilities, in a frequentist sense. Finally, we compare the Bayesian credible intervals based on the developed priors with the confidence intervals derived from real data.     

Threshold Estimation for Stochastic Processes with Small Noise

Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent but numerically unstable in the sense of large standard deviations under finite samples when the noise process has jumps. We propose a filter to cut large shocks from data and construct the same LSE from data selected by the filter. The proposed estimator can be asymptotically equivalent to the usual LSE, whose asymptotic distribution strongly depends on the noise process. However, in numerical study, it looked asymptotically normal in an example where filter was chosen suitably, and the noise was a Lévy process. We will try to justify this phenomenon mathematically, under certain restricted assumptions.     

Deletion residuals in the detection of heterogeneity of variances in linear regression

The heterogeneity of error variance often causes a huge interpretive problem in linear regression analysis. Before taking any remedial measures we first need to detect this problem. A large number of diagnostic plots are now available in the literature for detecting heteroscedasticity of error variances. Among them the ‘residuals’ and ‘fits’ (R–F) plot is very popular and commonly used. In the R–F plot residuals are plotted against the fitted responses, where both these components are obtained using the ordinary least squares (OLS) method. It is now evident that the OLS fits and residuals suffer a huge setback in the presence of unusual observations and hence the R–F plot may not exhibit the real scenario. The deletion residuals based on a data set free from all unusual cases should estimate the true errors in a better way than the OLS residuals. In this paper we propose ‘deletion residuals’ and the ‘deletion fits’ (DR–DF) plot for the detection of the heterogeneity of error variances in a linear regression model to get a more convincing and reliable graphical display. Examples show that this plot locates unusual observations more clearly than the R–F plot. The advantage of using deletion residuals in the detection of heteroscedasticity of error variance is investigated through Monte Carlo simulations under a variety of situations.