Data tilting for time series

Summary. We develop a general methodology for tilting time series data. Attention is focused on a large class of regression problems, where errors are expressed through autoregressive processes. The class has a range of important applications and in the context of our work may be used to illustrate the application of tilting methods to interval estimation in regression, robust statistical inference and estimation subject to constraints. The method can be viewed as 'empirical likelihood with nuisance parameters'.     

基于机器学习LSTM&US模型的消费者信心指数预测研究

消费者信心指数等宏观经济指标具有时间上的滞后效应和动态变化的多维性,不易精确预测。本文基于机器学习长短时间记忆(Long Short-Term Memory,LSTM)神经网络模型,结合大数据技术挖掘消费者信心指数相关网络搜索数据(User Search,US),进而构建一种LSTM&US预测模型,并将其应用于对我国消费者信心指数的长期、中期与短期的预测研究,同时引入多个基准预测模型进行了对比分析。结果发现:引入网络搜索数据能够提高LSTM神经网络模型的预测性能与预测精度;LSTM&US预测模型具有较好的泛化能力,对不同期限的预测效果均较稳定,其预测性能与预测精度均优于其他六种基准预测模型(LSTM、SVR&US、RFR&US、BP&US、XGB&US和LGB&US);预测结果显示本文提出的LSTM&US预测模型具有一定的实用价值,该预测方法为消费者信心指数的预测与预判提供了一种新的研究思路,丰富了机器学习方法在宏观经济指标预测领域中的理论研究。     

A Primer on Visualizations for Comparing Populations,Including the Issue of Overlapping Confidence Intervals

In comparing a collection of K populations, it is common practice to display in one visualization confidence intervals for the corresponding population parameters θ₁, θ₂, …, θ_K. For a pair of confidence intervals that do (or do not) overlap, viewers of the visualization are cognitively compelled to declare that there is not (or there is) a statistically significant difference between the two corresponding population parameters. It is generally well known that the method of examining overlap of pairs of confidence intervals should not be used for formal hypothesis testing. However, use of a single visualization with overlapping and nonoverlapping confidence intervals leads many to draw such conclusions, despite the best efforts of statisticians toward preventing users from reaching such conclusions. In this article, we summarize some alternative visualizations from the literature that can be used to properly test equality between a pair of population parameters. We recommend that these visualizations be used with caution to avoid incorrect statistical inference. The methods presented require only that we have K sample estimates and their associated standard errors. We also assume that the sample estimators are independent, unbiased, and normally distributed.     

Online interval scheduling: randomized and multiprocessor cases

We consider the problem of scheduling a set of equal-length intervals arriving online, where each interval is associated with a weight and the objective is to maximize the total weight of completed intervals. An optimal 4-competitive algorithm has long been known in the deterministic case, but the randomized case remains open. We give the first randomized algorithm for this problem, achieving a competitive ratio of 3.5822. We also prove a randomized lower bound of 4/3, which is an improvement over the previous 5/4 result. Then we show that the techniques can be carried to the deterministic multiprocessor case, giving a 3.5822-competitive 2-processor algorithm, and a 4/3 lower bound for any number of processors. We also give a lower bound of 2 for the case of two processors. A preliminary version of this paper appeared in the Proceedings of COCOON 2007, LNCS, vol. 4598, pp. 176–186. The work described in this paper was fully supported by a grant from City University of Hong Kong (SRG 7001969), and NSFC Grant No. 70525004 and 70702030.     

Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm

Two new implementations of the EM algorithm are proposed for maximum likelihood fitting of generalized linear mixed models. Both methods use random (independent and identically distributed) sampling to construct Monte Carlo approximations at the E-step. One approach involves generating random samples from the exact conditional distribution of the random effects (given the data) by rejection sampling, using the marginal distribution as a candidate. The second method uses a multivariate t importance sampling approximation. In many applications the two methods are complementary. Rejection sampling is more efficient when sample sizes are small, whereas importance sampling is better with larger sample sizes. Monte Carlo approximation using random samples allows the Monte Carlo error at each iteration to be assessed by using standard central limit theory combined with Taylor series methods. Specifically, we construct a sandwich variance estimate for the maximizer at each approximate E-step. This suggests a rule for automatically increasing the Monte Carlo sample size after iterations in which the true EM step is swamped by Monte Carlo error. In contrast, techniques for assessing Monte Carlo error have not been developed for use with alternative implementations of Monte Carlo EM algorithms utilizing Markov chain Monte Carlo E-step approximations. Three different data sets, including the infamous salamander data of McCullagh and Nelder, are used to illustrate the techniques and to compare them with the alternatives. The results show that the methods proposed can be considerably more efficient than those based on Markov chain Monte Carlo algorithms. However, the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension.     

社会亚稳定制度学成因探析

社会道德滑坡、政府公信力下降、社会矛盾凸显、人们心理安全感下降、各种冲突呈明显增长趋势等构成了当今社会亚稳定主要特征。从制度视角剖析社会亚稳定性状，社会系统内部机制失灵或缺损是引发社会危机的深层原因。完善制度是预防社会危机、拯救民众信心，走出社会亚稳定、实现社会健康可持续发展的重要路径。     

Performance of Interval Estimators for the Inverse Hypergeometric Distribution

The inverse hypergeometric distribution is of interest in applications of inverse sampling without replacement from a finite population where a binary observation is made on each sampling unit. Thus, sampling is performed by randomly choosing units sequentially one at a time until a specified number of one of the two types is selected for the sample. Assuming the total number of units in the population is known but the number of each type is not, we consider the problem of estimating this parameter. We use the Delta method to develop approximations for the variance of three parameter estimators. We then propose three large sample confidence intervals for the parameter. Based on these results, we selected a sampling of parameter values for the inverse hypergeometric distribution to empirically investigate performance of these estimators. We evaluate their performance in terms of expected probability of parameter coverage and confidence interval length calculated as means of possible outcomes weighted by the appropriate outcome probabilities for each parameter value considered. The unbiased estimator of the parameter is the preferred estimator relative to the maximum likelihood estimator and an estimator based on a negative binomial approximation, as evidenced by empirical estimates of closeness to the true parameter value. Confidence intervals based on the unbiased estimator tend to be shorter than the two competitors because of its relatively small variance but at a slight cost in terms of coverage probability.     

Boundary corrected cubic smoothing splines

Smoothing splines are known to exhibit a type of boundary bias that can reduce their estimation efficiency. In this paper, a boundary corrected cubic smoothing spline is developed in a way that produces a uniformly fourth order estimator. The resulting estimator can be calculated efficiently using an O(n) algorithm that is designed for the computation of fitted values and associated smoothing parameter selection criteria. A simulation study shows that use of the boundary corrected estimator can improve estimation efficiency in finite samples. Applications to the construction of asymptotically valid pointwise confidence intervals are also investigated .     

Likelihood ratio test for simultaneous testing of the mean and the variance of a normal distribution

In this paper, we consider the simultaneous testing of the mean and the variance of a normal distribution. The exact distribution of the likelihood ratio test statistic is obtained, which is not available in the literature. The critical points of the exact test are reported. We also consider some of the other exact and asymptotic tests. The powers of these tests are compared using the Monte Carlo simulations.