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.     

Testing Wagner's Law in India: A cointegration and causality analysis

The present study empirically analyzes the validity of Wagner's Law for Indian economy. With the use of annual time series data from 1970–71 to 2013–14, all the six versions of Wagner's Law have been analyzed to test the relationship between government expenditure and gross domestic product. Wagner's Law states that the economic growth is the causative factor of the growth of the public expenditure. The study applied the unit root test and cointegration test to find the long-run relationship between government expenditure and gross domestic product. The present study employed the various econometric techniques such as unit root test, cointegration, and causality analysis for empirical analysis. The empirical analysis under study inferred mixed results of Wagner's Law for Indian economy, where four versions, namely Peacock, Gupta, Guffman, and Musgrave, found valid for Indian economy. The study concluded that the Wagner's Law is valid for the Indian economy except the Pryor and Mann Versions of the Wagner's Law.     

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.     

基于熵理论的河北省可持续发展水平评价研究

根据2000—2009年国家统计年鉴中河北省的有关数据，选取有代表性的指标，构造评价可持续发展水平的指标体系，并采用熵理论确定各指标的权重，以观察近10年来河北省经济社会可持续发展的具体情况。实证研究结果表明：河北省正逐渐迈向可持续发展的道路,但任重道远。根据省际具体情况，在实证研究的基础上，就河北省经济社会的长期可持续发展提出了若干建议。     

长三角创新资源的空间错配与调整政策——基于次级和县级区域的实证研究

依据对长江三角洲次级和县级区域资源配置现状的实证研究发现：一是长江三角洲区域在经历高速重化工业化的同时，开始跨入了内生增长模式的门槛，人力资本的贡献日益显现；二是越来越多的次级区域工业生产能力和技术创新能力正在超越北京、上海以及省会城市，由此国家的科技资源和高等教育资源也应当流向这些区域，使产业、科技、教育资源能够融合在同一个空间，以大大提高整个国家技术创新投入的收益；三是转变经济发展方式和实施创新型国家建设战略的真正落脚点是支持和推动更多的次级和县级区域建立高等教育体系，创造更多的人力资本，开展更多的技术创新活动，使更多的区域采取基于技术进步的增长战略。充足的证据表明，现在到了需要采取一个重视创新资源效率的区域增长战略的时候了。     

Multivariate normal estimation: the case (n < p)

Estimation in the multivariate context when the number of observations available is less than the number of variables is a classical theoretical problem. In order to ensure estimability, one has to assume certain constraints on the parameters. A method for maximum likelihood estimation under constraints is proposed to solve this problem. Even in the extreme case where only a single multivariate observation is available, this may provide a feasible solution. It simultaneously provides a simple, straightforward methodology to allow for specific structures within and between covariance matrices of several populations. This methodology yields exact maximum likelihood estimates.     

Testing variance components in balanced linear growth curve models

It is well known that the testing of zero variance components is a non-standard problem since the null hypothesis is on the boundary of the parameter space. The usual asymptotic chi-square distribution of the likelihood ratio and score statistics under the null does not necessarily hold because of this null hypothesis. To circumvent this difficulty in balanced linear growth curve models, we introduce an appropriate test statistic and suggest a permutation procedure to approximate its finite-sample distribution. The proposed test alleviates the necessity of any distributional assumptions for the random effects and errors and can easily be applied for testing multiple variance components. Our simulation studies show that the proposed test has Type I error rate close to the nominal level. The power of the proposed test is also compared with the likelihood ratio test in the simulations. An application on data from an orthodontic study is presented and discussed.