Limit theorems for dependent Bernoulli variables with statistical inference

We consider a class of dependent Bernoulli variables where the conditional success probability is a linear combination of the last few trials and the original success probability. We obtain its limit theorems including the strong law of large numbers, weak invariance principle, and law of the iterated logarithm. We also derive some statistical inference results which make the model applicable. Simulation results are exhibited as well to show that with small sample size the convergence rate is satisfying and the proposed estimators behave well.     

Model Checks in Inverse Regression Models with Convolution‐Type Operators

Abstract. We consider the problem of testing parametric assumptions in an inverse regression model with a convolution‐type operator. An L ₂ ‐type goodness‐of‐fit test is proposed which compares the distance between a parametric and a non‐parametric estimate of the regression function. Asymptotic normality of the corresponding test statistic is shown under the null hypothesis and under a general non‐parametric alternative with different rates of convergence in both cases. The feasibility of the proposed test is demonstrated by means of a small simulation study. In particular, the power of the test against certain types of alternative is investigated. Finally, an empirical example is provided, in which the proposed methods are applied to the determination of the shape of the luminosity profile of the elliptical galaxy NGC 5017.     

Optimal hedging through limit orders

This article applies the methods of stochastic dynamic programming to a risk management problem, where an agent hedges her derivative position by submitting limit orders. Therefore, this model is the first, in the literature on optimal trading with limit orders, to handle a problem of hedging options or other derivatives. A hedging strategy is developed where both the size and the limit price of each order is optimally set.     

Composite Estimation for Single‐Index Models with Responses Subject to Detection Limits

We propose a semiparametric estimator for single‐index models with censored responses due to detection limits. In the presence of left censoring, the mean function cannot be identified without any parametric distributional assumptions, but the quantile function is still identifiable at upper quantile levels. To avoid parametric distributional assumption, we propose to fit censored quantile regression and combine information across quantile levels to estimate the unknown smooth link function and the index parameter. Under some regularity conditions, we show that the estimated link function achieves the non‐parametric optimal convergence rate, and the estimated index parameter is asymptotically normal. The simulation study shows that the proposed estimator is competitive with the omniscient least squares estimator based on the latent uncensored responses for data with normal errors but much more efficient for heavy‐tailed data under light and moderate censoring. The practical value of the proposed method is demonstrated through the analysis of a human immunodeficiency virus antibody data set.     

未焊透缺陷安全尺寸的评价研究

未焊透是压力管道焊接接头常见缺陷之一,严重时会导致管道的承载能力明显降低,进而引发严重的安全事故。 目前我国的《在用工业管道定期检验规程》中对未焊透管道的定级是很保守的,为了减少对未焊透缺陷的返修,文章采 用非线性有限元分析的方法,通过简化未焊透管道的影响因素,并研究在不同载荷工况下管道失效模式与缺陷尺寸的关 系,获得了未焊透管道的极限载荷曲线簇;再运用塑性力学分析方法对有限元分析结果进行筛选,得到了焊接缺陷的安 全尺寸;最终通过试验验证极限载荷数值分析结果的合理性。研究结果表明含有超标焊接缺陷（如未焊透）的管道不通 过复杂应力计算和安全评定即可在保证安全前提下最大限度地使用。     

On asymptotic distribution of prediction in functional linear regression

There has been substantial recent attention on problems involving a functional linear regression model with scalar response. Among them, there have been few works dealing with asymptotic distribution of prediction in functional linear regression models. In recent literature, the centeral limit theorem for prediction has been discussed, but the proof and conditions under which the random bias terms for a fixed predictor converge to zero have been ignored so that the impact of these terms on the convergence of the prediction has not been well understood. Clarifying the proof and conditions under which the bias terms converge to zero, we show that the asymptotic distribution of the prediction is normal. Furthermore, we have derived those results related to other terms that already obtained by others, under milder conditions. Finally, we conduct a simulation study to investigate performance of the asymptotic distribution under various parameter settings.     

理性极限及其突破断想

思维具有历史的特征.而理性思维只是人类思维的一个阶段.因此,理性思维及与之相对应的理性哲学都无法超越自身的历史局限.理性哲学缺失与当下生活的对应的根本原因就在于理性极限.而理性的偏见与虚妄的悲剧价值预设正是这种极限的表现.打破理性极限的前提是将理性还原于历史中并具体列出突破理性哲学的叙述方案.     

A probabilistic approach to Wallis’ formula

We present an alternative proof of Wallis’ formula from the probabilistic point of view. Based on the classical central limit theorem, some discrete distributions with additive property, such as binomial, negative binomial, Poisson and multinomial distributions, are considered to derive π/2.