Pitfalls of testing non-nested hypotheses by the lagrange multiplier method

The paper considers the problem of testing non-nested hypotheses by the application of the Lagrange Multiplier (LM) method to an exponentially combined likelihood function. It shows that the general test statistic derived by Atkinson (1970) and later by Breusch and Pagan (1980) can be regarded as an LM statistic only if it can be assumed that the parameters of the alternative model are known. When none of the parameters are known, the paper shows that a straightforward application of the LM method to testing non-nested hypotheses breaks down and it discusses the reasons for this failure.     

Some aspects of testing non-nested hypotheses

This paper examines some aspects of testing non-nested hypotheses. An inequality between the Cox and Atkinson statistics is noted, and the necessary and sufficient condition for the Atkinson test to be consistent is derived. A new test procedure is also outlined. The rest of the paper illustrates the various test statistics, their properties, and relationships for competing linear regression models.     

On the comprehensive method of testing non-nested regression models

The paper derives the specific form of the exponentially combined likelihood function of two competing multivariate non-linear regression models and shows that the application of the comprehensive approach to testing non-nested regression models will, in general, be indeterminate. It establishes that in the univariate case there exists a large number of tests of non-nested regression models which are consistent in addition to having the same asymptotic distribution under the null hypothesis. The paper then derives a set of conditions under which all these consistent tests are asymptotically equivalent not only under the null hypothesis but also under local alternatives. As an application of this latter result the paper establishes the asymptotic equivalence of the tests recently proposed by Davidson and MacKinnon, and Fisher and McAleer under local alternatives, and shows that within the class of tests considered in the paper these proposed tests possess maximum local power. The latter test has this property only when the number of explanatory variables of the ‘true’ model is not more than that of the ‘false’ model.     

A lagrange multiplier interpretation of disturbance estimators with an application to testing for nonlinearity

This paper describes a Lagrange multiplier interpretation of LUF disturbance estimators and an associated means of constructing residuals and procedures for testing for certain kinds of misspecification. Together with a recent technique for partially ordering multivariate data, the methods are used to devise an F test for nonlinearity in some or all of the explanatory variables in multiple regression. Unlike several alternatives, the proposed test does not require all misspecified variables to be positively correlated. Power computations, and comparisons with other procedures, yield encouraging results.     

The behaviour of the Lagrangian multiplier test in testing the orders of an ARMA-model

Summary The Lagrange multiplier test for testing the order of an ARMA-model is investigated. It is shown that it exhibits some pathologies stemming from the special properties of parameter spaces of ARMA-models. As a consequence one has to be careful in using the LM-test in this context. Furthermore results of this paper are used in a subsequent paper [Pötscher, 1983], to show the consistency of an order estimation procedure based on Lagrange multiplier tests, described there.     

Approximations and time-discretization in testing one-sided hypotheses for the mean of a gaussian process

Summary In addition to the considerations of Luschgy, approximate locally most powerful tests of a computational form based on continuous sampling are derived and the asymptotic effect of discrete sampling is discussed.     

Multiple and pairwise non-nested tests of the influence of taxes on money demand

The minimal computational requirements of the linear embedding techniques initiated by Davidson and MacKinnon (1981) accommodate multiple and binary tests of autoregressive, non-nested regression models with different dependent variables. The small sample adjustments of Fisher and McAleer (1981) effectively reduce the size of the P-tests for our models. Our application to transactions demand for money models supports the Holmes and Smyth (1972) hypothesis that pre-tax variables are preferred to GNP in M1 money equations.     

Generalized method of moments specification testing

This paper analyzes the asymptotic power properties of specification tests which are based on a finite set of moment conditions. It shows that any such test may fail against general misspecification that causes estimator inconsistency. The mutual asymptotic equivalence of maximal degree of freedom tests is shown and the form of optimal tests against specific forms of misspecification is derived. Applications to testing for exogeneity of a set of instrumental variables are presented.     

沥青低温性能评价试验方法讨论

沥青是一种温度敏感性材料,在温度较低时呈现脆性,影响了沥青路面低温抗裂性能。文章对沥青低温性能评价方法及评价指标进行了介绍,并根据伯格斯模型认为沥青低温粘度测试方法是表征沥青低温性能的最佳测试方法。     

Realization of closed,convex, and symmetric subsets of the unit square as regions of risk for testing simple hypotheses

It is well-known that the region of risk for testing simple hypotheses is some closed, convex, and (1/2, 1/2)-symmetric subset of the unit square, which contains the points (0, 0) and (1, 1). It is shown that for any such subsetR of the unit square and any atomless probability measureP on some -algebra there exists some probability measureQ on the same -algebra such thatR is the corresponding region of risk for testingP againstQ. This generalizes a result of [4] and is as a first step derived here for the special case, whereP is equal to the uniform distribution on the unit interval. The corresponding distributionQ is given explicitly in this case and the general case is treated by some well-known measure-isomorphism. This method of proof shows thatQ might be chosen to be of typeQ=Q ₁+(1–)Q ₂ for some satisfying 01, whereQ ₁ is a probability measure, which is absolutely continuous with respect toP andQ ₂ is a one-point mass.     

浅析钢结构建筑的无损检测方法

文章介绍了钢结构建筑目前无损检测的主要技术.并分析了钢结构无损检测技术的应用的策略.     

浅析钢结构建筑的无损检测方法

文章介绍了钢结构建筑目前无损检测的主要技术,并分析了钢结构无损检测技术的应用的策略。     

热工仪表输出信号的测试新方法

文章针对电测试验专业人员在进行热工仪表校验时,校验仪表输出信号过程中可能会出现电压、电流值计算错误,拆接二次线后造成误接线,而且工作量大、耗时等问题进行了论述,并提出了新的方法。     

稀土元素的化验测试方法研究

文章研究了电感耦合等离子体发射光谱法同时测定15稀土元素的化验测试方法,确定了合适的谱线和仪器工作条件,探讨了上柱溶液酸度、洗脱液酸度和洗脱液用量对稀土元素测定值影响,确定了最佳的上柱溶液酸度为0.677 mol/L;最佳的洗脱液酸度为3.5 mol/L;最佳的洗脱液用量为150～200 mL。并进行了稀土标准样品的定值试验和样品的外检比对试验,均取得满意的结果,该方法结果准确,能够满足稀土样品的检测要求。     

低应变反射波法测桩的局限性探讨

文章根据低应变反射波法测桩工作原理,对桩基低应变反射波法适用性进行探讨,并对波形判读中的有关问题进行分析,为合理利用低应变法进行桩基检测提供参考。     

On the optimality of differentiated SPR tests of composite hypotheses

Summary It is shown that differentiated SPR tests, which are limiting cases of ordinary SPR tests, are asymptotically optimal in a decision-theoretic formulation for composite hypotheses in one-parameter problems. It is also given some results connected with comparisons of different tests in this case.