Estimation of bias and standard error of an improved estimator of normal mean

This paper considers an improved estimator of normal mean which is obtained by considering a feasible version of minimum mean squared error estimator. The exact expression for the bias and the mean squared error are fairly complicated and do not provide any guidelines as how to estimate the standard error of improved estimator. As is well known that any estimator without a formula for standard error has little practical utility. We therefore derive unbiased estimators for the bias and mean squared error of the improved estimator. Incidently, they turn out to be minimum variance unbiased estimators. Further, this exercise yields a simple formula for estimating the standard error. Based on the criterion of estimated standard error, the efficiency of the improved estimator with respect to the traditional unbiased estimator (i.e., sample mean) is examined numerically. The relationship with asymptotic standard error is also studied.     

Testing for Linearity

The problem of testing for linearity and the number of regimes in the context of self‐exciting threshold autoregressive (SETAR) models is reviewed. We describe least‐squares methods of estimation and inference. The primary complication is that the testing problem is non‐standard, due to the presence of parameters which are only defined under the alternative, so the asymptotic distribution of the test statistics is non‐standard. Simulation methods to calculate asymptotic and bootstrap distributions are presented. As the sampling distributions are quite sensitive to conditional heteroskedasticity in the error, careful modeling of the conditional variance is necessary for accurate inference on the conditional mean. We illustrate these methods with two applications — annual sunspot means and monthly U.S. industrial production. We find that annual sunspots and monthly industrial production are SETAR(2) processes.     

Identification of simultaneous equation models with measurement error: a computerized evaluation

Rank conditions for identification in structural models are often difficult evaluate. Here we consider simultaneous equation models with measurement error and we show that previously published rank conditions for identification are not well-suited for evaluation. An alternative rank condition is derived and a computer algebra program is presented that takes care of both the construction and the computation of the rank of the relevant Jacobian matrix. It uses the parameter restrictions as input in order to characterize the identification situation of the individual parameters in the output.     

Statistical Proofs of Some Matrix Theorems *

Books on linear models and multivariate analysis generally include a chapter on matrix algebra, quite rightly so, as matrix results are used in the discussion of statistical methods in these areas. During recent years a number of papers have appeared where statistical results derived without the use of matrix theorems have been used to prove some matrix results which are used to generate other statistical results. This may have some pedagogical value. It is not, however, suggested that prior knowledge of matrix theory is not necessary for studying statistics. It is intended to show that a judicious use of statistical and matrix results might be of help in providing elegant proofs of problems both in statistics and matrix algebra and make the study of both the subjects somewhat interesting. Some basic notions of vector spaces and matrices are, however, necessary and these are outlined in the introduction to this paper.     

Probability of multiple crossings and pricing of double barrier options

This paper derives pricing formulas of standard double barrier option, generalized window double barrier option and chained option. Our method is based on probabilitic approach. We derive the probability of multiple crossings of curved barriers for Brownian motion with drift, by repeatedly applying the Girsanov theorem and the reflection principle. The price of a standard double barrier option is presented as an infinite sum that converges very rapidly. Although the price formula of standard double barrier option is the same with Kunitomo and Ikeda (1992), our method gives an intuitive interpretation for each term in the infinite series. From the intuitive interpretation we present the way how to approximate the infinite sum in the pricing formula and an error bound for the given approximation. Guillaume (2003) and Jun and Ku (2013) assumed that barriers are constant to price barrier options. We extend constant barriers of window double barrier option and chained option to curved barriers. By employing multiple crossing probabilities and previous skills we derive closed formula for prices of 16 types of the generalized chained option. Based on our analytic formulas we compute Greeks of chained options directly.     

De invloed van de keuze der gewichten op de hoogte van een gewogen indexcijfer

The influence of the choice of the weights on the value of an indexnumber.
Price and quantity indexnumbers are weighted averages of groups of price and quantity ratios and they are convenient instruments to indicate the general tendency of such groups, especially if the number of basic ratios is considerable. The frequent use of indexnumbers is due to the fact that they can often be applied to problems for which, strictly speaking, an indexnumber had to be used derived from the same group of ratios but based on a different set of weights.
Two typical examples of such problems are given.
The use of a set of weights differing from the appropriate one is only justified, however, when the indexnumber is rather insensitive to changes in the set of weights. A simple formula is derived showing that the relative change of an index-number due to a change in the set of weights is equal to the product of the (weighted) coefficient of variation of the basic ratios, the (weighted) standard deviation of the relative changes of the weights and the (weighted) coefficient of correlation of the ratios and of the relative changes. The system of weights used in the calculation of these three factors is the same and is equal to the set of true weights belonging to the problem under consideration.
The practical use of the formula is demonstrated at the problem of index-numbers of costs frequently encountered in the practice of cost accounting.     

Evaluating estimation methods for ordinal data in structural equation modeling

This study examined the performance of two alternative estimation approaches in structural equation modeling for ordinal data under different levels of model misspecification, score skewness, sample size, and model size. Both approaches involve analyzing a polychoric correlation matrix as well as adjusting standard error estimates and model chi-squared, but one estimates model parameters with maximum likelihood and the other with robust weighted least-squared. Relative bias in parameter estimates and standard error estimates, Type I error rate, and empirical power of the model test, where appropriate, were evaluated through Monte Carlo simulations. These alternative approaches generally provided unbiased parameter estimates when the model was correctly specified. They also provided unbiased standard error estimates and adequate Type I error control in general unless sample size was small and the measured variables were moderately skewed. Differences between the methods in convergence problems and the evaluation criteria, especially under small sample and skewed variable conditions, were discussed.     

Over de spreiding bij het droge-stofonderzoek van brood

The accuracy of the determination of the amount of solids in bread.
Of a loaf with a nominal weight of 800 grams only about 480 grams remains after complete drying. This so-called 'amount of solids in bread' is regularly checked by samples. From a batch of loaves a group of at least 5. but usually more, are taken at random and weighed. From this group one is selected with a weight as nearly as possible equalling the average weight of the whole group; for two slices of this sample loaf the decrease in weight upon drying is determined in the laboratory, and is considered as representative for the entire batch.
The accuracy of these determinations is analysed on the basis of 35 samples which were investigated in 3 different laboratories. The standard error is estimated at 5 grams per loaf. The influence of various factors, such as the method of sampling which may be altered in many ways, is briefly considered, while in a final section the results obtained are discussed from a practical point of view.     

基于蚁群算法的双线铁路列车运行调整研究

将列车运行调整问题归并为大规模job shop调度问题,借助引入的列车路径矩阵、列车通过顺序矩阵,构建了双线铁路列车运行调整的优化模型。针对模型解空间大、约束条件复杂的特点,提出了先利用蚁群算法优化列车铺画顺序,后运用极大代数法安排列车到发时刻的求解方法。仿真试验表明,算法的效率和稳定性可以很好的满足行车调度指挥的要求。     

Testing for random effects in panel models with spatially correlated disturbances

In the empirical analysis of panel data the Breusch–Pagan (BP) statistic has become a standard tool to infer on unobserved heterogeneity over the cross-section. Put differently, the test statistic is central to discriminate between the pooled regression and the random effects model. Conditional versions of the test statistic have been provided to immunize inference on unobserved heterogeneity against random time effects or patterns of spatial error correlation. Panel data models with spatially correlated error terms are typically set out under the presumption of some known adjacency matrix parameterizing the correlation structure up to a scaling factor. This paper delivers a bootstrap scheme to generate critical values for the BP statistic allowing robust inference under misspecification of the adjacency matrix. Moreover, asymptotic results are derived for the case of a finite cross-section and infinite time dimension. Finite sample simulations show that misspecification of spatial covariance features could lead to large size distortions, while the robust bootstrap procedure retains asymptotic validity.     

Least absolute deviations estimation for the censored regression model

This paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression (or censored ‘Tobit’) model. The proposed estimator is a generalization of least absolute deviations estimation for the standard linear model, and, unlike estimation methods based on the assumption of normally distributed error terms, the estimator is consistent and asymptotically normal for a wide class of error distributions, and is also robust to heteroscedasticity. The paper gives the regularity conditions and proofs of these large-sample results, and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances.     

Matlab软件在矩阵运算教学中的应用

文章以实例说明如何将Matlab软件融入到矩阵运算的教学中,解决矩阵计算中的冗繁性,增强学生应用数学软件和数学知识解决实际问题的能力,为线性代数的教学改革提供了一种新的模式。     

基于SimMechanics模块的转盘轴承实验台模型的建立

转盘轴承实验台是一种根据转盘轴承工作特点设计的专用实验设备。本文采用Simulink软件中的SimMechanics模块搭建实验台机械结构的仿真模型。仿真模型是在有限元计算的基础上,将实验台结构简化为线性弹簧。仿真模型中的转盘轴承采用Zupan等提供的解析法简化。通过滚珠最大应力验证仿真模型结果的正确性,参照标准是美国国家可再生能源实验室提供的经验公式。SimMechanics仿真结果与经验公式、有限元模型结果比较,误差在10%以内,误差可以接受。SimMechanics仿真模型的精度不及有限元模型,但仿真模型实现了机械系统与控制系统在同一仿真环境中搭建,并且仿真模型的计算成本远小于有限元模型。     

Robust trend inference with series variance estimator and testing-optimal smoothing parameter

The paper develops a novel testing procedure for hypotheses on deterministic trends in a multivariate trend stationary model. The trends are estimated by the OLS estimator and the long run variance (LRV) matrix is estimated by a series type estimator with carefully selected basis functions. Regardless of whether the number of basis functions K is fixed or grows with the sample size, the Wald statistic converges to a standard distribution. It is shown that critical values from the fixed-K asymptotics are second-order correct under the large-K asymptotics. A new practical approach is proposed to select K that addresses the central concern of hypothesis testing: the selected smoothing parameter is testing-optimal in that it minimizes the type II error while controlling for the type I error. Simulations indicate that the new test is as accurate in size as the nonstandard test of Vogelsang and Franses (2005) and as powerful as the corresponding Wald test based on the large-K asymptotics. The new test therefore combines the advantages of the nonstandard test and the standard Wald test while avoiding their main disadvantages (power loss and size distortion, respectively).     

The Impact of Shocks on the UK Economy in and Out of EMU

Entry to EMU at an inappropriate exchange rate could trigger a full-blown business cycle in the UK. Once inside EMU, the UK's response to a number of different economic shocks would change — partly because of the fixed exchange rate, and partly because of the common monetary policy. In particular, when an asymmetric shock occurs — one that hits the UK harder than other Eurozone economies — the UK response is generally likely to be more pronounced inside EMU than outside. We find that that result still applies even in a reformed EMU — one in which the ECB and the labour market are reformed to bring them closer to the Anglo–Saxon model.     

关于费用分配代数法的辨析

论文针对辅助生产费用分配代数法的差错,通过列示原文、差错分析、差错纠正,富有新意地提出了对费用分配数学模型的理论解释,最后提出研究建议。     

The omega matrix

This paper uses certain fundamental theorems of matrix algebra to describe a square upper triangular matrix with special properties that make it useful in applications to financial economics. We call this the Omega Matrix.     

The standard error of moving average smoothed equipercentile equating

A very important aspect of virtually any kind of systematic investigation is to be able to identify whether two entities are different, and, almost equivalently, whether they are the same. We need to be sure that measurements made at different time in different places by different experimenters are equivalent. To do this in the social sciences, the procedure of equating is necessary to be able to compare measurements made using different instruments. Small sample sizes can lead to apparent jaggedness in the formulae for equating two quantities, and some kind of smoothing procedure is frequently necessary when dealing with relatively small samples. A large-sample formula is developed for the standard error of moving average smoothed equipercentile equating on a single sample. An example is given of the application in equating two versions of a reading test, and the results are verified using a bootstrap procedure. The large sample formula gives a result that is close to the bootstrap procedure, except at very sparse frequencies.     

From the Arena Into the Streets: Hockey Violence, Economic Incentives and Public Policy

A bstract . The hypothesis that there is a positive relationship between violence and game attendance in the National Hockey League is tested; and the implications of the results for policies aimed at rectifying the violence considered. The empirical analysis, which is based principally on game by game data for the 1989/90 season, confirms the positive relationship, although it occurs mainly in American, not Canadian, cities. Since there is an incentive for teams to promote violence and because the legal system normally only prosecutes players not teams, the standard methods used to control violence—self regulation and the judicial process —are unlikely to work. Consideration should, therefore, be given to more direct control of violence.     

Fiscal Policy in the Eurozone: Stimulus or Consolidation?

Fiscal policy is one of the three pillars of what Dr. Ottmar Issing (2002) has called the Maastricht Assignment. For the Eurozone as a whole, the Central Bank is responsible for area-wide price stability. The twelve national fiscal authorities are responsible for fiscal policy — country by country — subject to the provisions of the Stability and Growth Pact (SGP). The third pillar involves supply-side issues and wage/price developments and is the responsibility of "national governments and the social partners". Issing has argued that this assignment provides a clear division of roles and responsibilities — and that no further macroeconomic coordination is necessary or desirable¹. In this article, Christopher Allsopp² assesses the framework for fiscal policy in the Eurozone, arguing for a system that is more decentralised; ensures 'sustainability' as a primary objective; and, subject to that, allows for activist stabilisation policy against country-specific shocks.