Random sampling method

依照同样的方法写出其他规则，可以得到模糊控制规则表，如表1所示。表中LH1、LH2、RH1、RH2分别表示anglelh1、anglerh1、anglelh2、anglerh2。

沈湖与河渠连接方案：规划扩挖沈湖处大治河、柴米河与蛇家坝干渠平行走向，三河共用两堤。大治河、柴米河与沈湖相连通，过沈湖后两条河道变为一条向下游排水，在沈湖上游蛇家坝干渠处新建一节制闸，向沈湖补水。该方案基本不打乱原有灌排体系，实施矛盾小，且随着雨污分流工程的实施，沈湖水质将得到保证。

Introduction

The Monte Carlo method is also known as a random or statistical experimental method. It is assumed that the sample data conform to a certain random process and generated by computer simulation.Simulation of random problem is the basic feature of Monte Carlo method.

Bootstrap method is a non-parametric statistical inference method based on computer. It does not need to make any assumptions about the unknown population, but generates “pseudo” random Numbers by randomly sampling the given original sample, so as to judge the statistical characteristics of the population. Common Bootstrap methods include residual Bootstrap, parameter Bootstrap, Wild Bootstrap, Pairs Bootstrap and Block Bootstrap.

The Bootstrap method has a lot in common with the Monte Carlo method. For example, both methods are random sampling methods. The parameter Bootstrap method in the Bootstrap method is also a Monte Carlo method. The difference between these two methods is mainly reflected in: first, the sampling data sources are different. The Bootstrap method generates data from the original sample, while the Monte Carlo method generates data based on the given random process. Second,the applicable conditions are different. The Monte Carlo method requires that the data generation process be known, while Bootstrap replicates observations or adds new sample information based on the given original sample. Therefore, Bootstrap method is more suitable for solving real economic problems. Monte Carlo simulation method is mainly from the perspective of simulation, which provides the basis from laboratory for studying actual problems, and is the basis for effectively solving real economic problems.

Currently, Bootstrap and Monte Carlo methods in the study are usually used interactively and complement each other. Monte Carlo method is often used to investigate the finite sample properties of statistics through simulation experiments, and Bootstrap method is often used for interval estimation, hypothesis testing and parameter estimation, etc.

(5): The third and fourth steps were repeated for a total of B times,and a group of Bootstrap samples were obtained, so as to conduct hypothesis testing or solve confidence interval by using Bootstrap samples.

Based on the linear regression model:

超声-超声图像叠加融合成像是近几年发展起来的新技术。消融前首先嘱患者屏住呼吸，通过手动扫描的方式获取肝脏的三维超声容积图像，扫描区域包括肿瘤和肿瘤旁的肝内管系，这个三维超声容积数据被储存在超声机器中。将消融后和消融前超声图像叠加，肿瘤的影像可以被实时投射到白色的消融区域内，即可以在消融过程中清晰显示消融边界，早期评价消融效果，为及时补充消融提供了可能。三维容积图像与二维超声相比，能更全面、更直观地显示病灶情况及与周围组织的关系。Minami Y等研究发现，以多层螺旋CT为金标准，超声-超声图像叠加融合成像对射频消融术后早期评价的准确率约92.6%[16]。

There are many statistical tests for spatial econometric studies,most of which, such as Wald statistics, LR and LM statistics, are based on the asymptotic theory in large samples. However, empirical studies in reality are often carried out only on the basis of a limited sample,and the asymptotic test statistics obtained in a limited sample tend to cause higher levels of distortion and weaker efficacy. Therefore, it is necessary to build test statistics that are still valid under limited samples. Monte Carlo method and Bootstrap method based on a large amount of experimental data can precisely solve this problem.

交互式教学是在宏观教学情景下，教师的教与学生的学围绕某一个问题进行平等交流和自主互动的一种教学方法。它是基于支架式教学的理论，通常包含几个步骤：一是确定主题；二是导入问题；三是学生独立探索；四是协作学习；五是学习效果评价。很多老师在备课上课时也会采用交互式教学法，但是在很多方面不能取得良好的效果，例如在讲解某一景点时，学生对旅游景点的不熟悉而导致缺乏代入感，搭建的框架不清晰，独立探索的功能不强，再就是对于学生学习的效果评价的方法单一等。

There are two representative studies on the properties of finite sample of parameter estimation.

First. Use Monte Carlo method to study the finite sample properties of the estimator, and the finite sample properties of the estimation of two or more comparison, the following main steps: first,by using Monte Carlo method to generate satisfy the data of the model set, using different estimation methods to estimate the model, compare different estimation the bias and mean square error of the model estimator on behalf of the estimator of the nature of indexes such as;Secondly, generate new sample data again and repeat the above steps to analyze the limited sample properties of a single estimator or compare the limited sample properties of different estimators under different sample data.

Second, using Monte Carlo method to study the finite sample properties of the test statistics, as well as to two or more than two to compare the finite sample properties test statistics, the main steps for:using Monte Carlo method to generate satisfy the data of the model set conditions, and then estimate the model, based on the model to estimate the results calculated the sample under test statistics; Repeat the above steps to study the limited sample properties of single or multiple test statistics.

the estimators of parameters and are and respectively,and the residual vector .

How is the standard residual Bootstrap method used for spatial correlation test.

给水泵运行时，当泵内任意一点的压力小于当地饱和压力时，该处的水就会发生汽化，形成小的蒸汽泡，当蒸汽泡被带入高压区，受压破裂，使泵产生汽蚀，引起泵的噪音、振动，甚至破坏。因此泵不发生汽蚀的条件是必须保证泵内最低压力处的压力大于水的饱和压力值。泵内流体最低点不是发生在泵的入口，当给水由泵的入口流至叶轮入口过程中，由于流道收缩，流速增加，流体动能增加，在叶片进口边位置处，压力降至最低值，之后叶片对流体做功，压力逐渐升高。泵入口至叶轮进口最低压力点处的压力将称为泵的汽蚀余量，用 NPSHr表示。该值与管路系统无关，仅与泵吸入室的结构、叶轮的吸入口形状以及叶片进口处的流速有关。

Test the spatial econometric model of a finite sample

 

The steps for the standard residual Bootstrap are as follows:

AHEADTM将综合汽车胶粘剂、高性能弹性体、工程热塑性塑料、制动液/特种润滑剂、电子材料、高性能纤维及安全材料，为以下应用提供创新解决方案：

(3): We take N random samples of the formula (2-2) that we put back, and we get N

(2): Scale transformation and centralization are carried out for residual e,

 

Where, when the OLS method is used to estimate the formula (2-1), is the k (l) element on the diagonal of matrix .

(1): The OLS method was used to estimate the expression (2-1), and the estimator of parameter and the residual vector e were obtained. In.

(4): A Bootstrap sample () can be obtained above,where

语言中的绝大多数词都拥有多个意义。传统的语义研究没有认识到多义词各个义项之间的内在联系，没有对语义扩展的机制做出合理的解释。认知语言学揭示了多义现象的本质，认为词的多个意义中除了基本义之外，其他意义是通过隐喻和转喻的方式由基本义扩展而来的。雷可夫指出，一词多义起源于不同认知域之间以及同一认知域中不同元素之间的关系。词的基本义与扩展义之间有直接的认知性关系。词的各义项之间存在着理据性关系是因为词义的扩展从主观上来说主要是通过隐喻和转喻思维来实现的。词义扩展的方式主要有两种:基于与中心义的相似性关系派生新义为词义的隐喻性扩展，基于与中心义的邻近关系派生新义为词义的转喻性扩展。

3. Estimation of spatial econometric models for limited samples

Monte Carlo method is usually used to study the finite sample properties of parameter estimators or test statistics in space econometric studies

Under the condition of limited samples, the commonly used estimation method have good asymptotic properties no longer, for this kind of situation, the researchers usually use the Bootstrap method to have back to the original data of repeated sampling, while ensuring the data distribution form, do not change under the condition of data capacity, and then using the maximum likelihood method, generalized moment method to estimate the model, in order to get parameters of robust estimation.

In the empirical study of limited samples, the model estimation based on Bootstrap method mainly has two forms, namely the residual Bootstrap method and the Pairs Bootstrap method.However, as the data in the spatial econometric model has spatial structure characteristics, if the sampling method of Pairs Bootstrap is adopted, the spatial structure characteristics of the data may change, so the Pairs Bootstrap method is not suitable for the estimation of spatial econometric model. The execution steps of the residual Bootstrap method and the residual Bootstrap of the previous test method. Similar. Taking the Bootstrap method of the residual error of the spatial lag model as an example, the estimation of the spatial econometric model of the limited sample is explained. The estimation process of other models is similar.

(1): By using the maximum likelihood method to estimate spatial lag model

 

Bootstrap method is often used for statistical test, including parameter stability test, structural stability test, unit root test, Hausman test in panel data model and spatial correlation test. In addition,Bootstrap method is also used for statistical inference of parameters in spatial econometric model. In the test of spatial autocorrelation,the premise condition for the asymptotic distribution of test statistics such as Moran’s I is that the model error term is subject to normal independent identically distribution or independent identically distribution, but the above conditions are usually not met in the empirical study. Therefore, Lin (2011) et al. applied the residual Bootstrap method to the test of spatial correlation Moran’s I, LM -Error and LM - Lag.

(2): A random sampling of is performed, and N residuals are obtained.

(3): Give X and W, we can find a Y here

(5)单位面积吸能S(Unit area energy absorption)，定义为结构压溃前的总吸能E与承载面积A之比，见式(4)：

 

(4)：The new estimation model (3-1) is based on ,and ,New estimates of parametersand ,and , can be obtained.

式中,τ(k)为根据式(3)计算得到的第k帧语音信号的时延,ρ(k)为第k帧平滑后的时延,α决定平滑的程度,α越大平滑效果越明显,但响应速度会减慢。

(5): Repeat steps 2 through 4 for a total of B times, resulting in estimators ofand , that is and , Finally,the parameter estimators ofand are respectively

 

Compared with the residual Bootstrap method, the sampling method of Pairs Bootstrap is random sampling method that is put back for the observed value of paired samples a. N samples extracted each time are substituted into the model for parameter estimation, and B times are repeated. The final parameter estimation method is the same as formula (3-3).

The estimated results of the residual Bootstrap method and the Pairs Bootstrap method are asymptotically equivalent. However, the two methods differ in the estimation results of limited samples. In general, when the residual term is subject to normal independent and same distribution, the residual Bootstrap method can obtain the same covariance matrix as OLS estimation. When the function form was missed, the estimated results obtained by the Pairs Bootstrap method were more robust.

4.Concllusion

In conclusion, in practical economic studies, the good properties of large sample spatial correlation test statistics are often difficult to satisfy, and the results obtained from Moran’s I and other test statistics based on large sample are no longer valid. At this point,the simulated Monte Carlo method or Bootstrap method may be more suitable for small samples.

Reference

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Allowance for Spatially Correlated Errors[J]. Biometrics,1983,39(2):361-371.

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