A non-local perspective on the power properties of the CUSUM and CUSUM of squares tests for structural change

We consider the power properties of the CUSUM and CUSUM of squares (CUSQ) tests in the presence of a one-time change in the parameters of a linear regression model. A result due to Ploberger and Krämer [1990. The local power of the cusum and cusum of squares tests. Econometric Theory 6, 335–347.] is that the CUSQ test has only trivial asymptotic local power in this case, while the CUSUM test has non-trivial local asymptotic power unless the change is orthogonal to the mean regressor. The main theme of the paper is that such conclusions obtained from a local asymptotic framework are not reliable guides to what happens in finite samples. The approach we take is to derive expansions of the test statistics that retain terms related to the magnitude of the change under the alternative hypothesis. This enables us to analyze what happens for non-local to zero breaks. Our theoretical results are able to explain how the power function of the tests can be drastically different depending on whether one deals with a static regression with uncorrelated errors, a static regression with correlated errors, a dynamic regression with lagged dependent variables, or whether a correction for non-normality is applied in the case of the CUSQ. We discuss in which cases the tests are subject to a non-monotonic power function that goes to zero as the magnitude of the change increases, and uncover some curious properties. All theoretical results are verified to yield good guides to the finite sample power through simulation experiments. We finally highlight the practical importance of our results.     

Minimax optimality of CUSUM for an autoregressive model

Different change point models for AR(1) processes are reviewed. For some models, the change is in the distribution conditional on earlier observations. For others, the change is in the unconditional distribution. Some models include an observation before the first possible change time – others not. Earlier and new CUSUM type methods are given, and minimax optimality is examined. For the conditional model with an observation before the possible change, there are sharp results of optimality in the literature. The unconditional model with possible change at (or before) the first observation is of interest for applications. We examined this case and derived new variants of four earlier suggestions. By numerical methods and Monte Carlo simulations, it was demonstrated that the new variants dominate the original ones. However, none of the methods is uniformly minimax optimal.     

A Panel CUSUM Test of the Null of Cointegration*

This paper proposes a simple residual‐based panel CUSUM test of the null hypothesis of cointegration. The test has a limiting normal distribution that is free of nuisance parameters, it is robust to heteroskedasticity and it allows for mixtures of cointegrated and spurious alternatives. Our Monte Carlo results suggest that the test has small‐size distortions and reasonable power. In our empirical application to international R&D spillovers, we present evidence suggesting that total factor productivity is heterogeneously cointegrated with foreign and domestic R&D capital stocks.     

Combination schemes for turning point predictions

We propose new forecast combination schemes for predicting turning points of business cycles. The proposed combination schemes are based on the forecasting performances of a given set of models with the aim to provide better turning point predictions. In particular, we consider predictions generated by autoregressive (AR) and Markov-switching AR models, which are commonly used for business cycle analysis. In order to account for parameter uncertainty we consider a Bayesian approach for both estimation and prediction and compare, in terms of statistical accuracy, the individual models and the combined turning point predictions for the United States and the Euro area business cycles.     

A self-balancing CUSUM approach for the efficient allocation of resources during post-disaster debris disposal operations

Hurricane Katrina and other recent disasters have underscored the challenges related to disaster-generated debris disposal. During Katrina, extraordinary amounts of debris, far exceeding typical annual amounts of solid waste, were almost instantaneously deposited across a three-state area. Collection and disposal of disaster debris is an enormous task. Although the locations and amounts of debris can be easily summarized after recovery activities have been completed, they are uncertain and difficult to estimate in real time. Inaccurate estimates can result in inequitable allocation of disposal resources, increased costs, prolonged recovery, and increased social, political, and economic unrest. This paper uses prospective statistical process control methods to achieve equity in allocating debris disposal resources. These methods enable the detection of emerging debris collection patterns in real time as debris information becomes available during disposal operations. Using the self-starting CUSUM method proposed by Hawkins (Statistician 36:299?C315, 1987) as a foundation, we develop a self-balancing approach for debris cleanup operations and evaluate its performance using data from a 2003 Atlantic hurricane.     

爱尔朗排队模型在配送中心车辆调度中的应用研究

利用随机过程和排队论的相关知识,通过对爱尔朗排队模型进行性能分析以及参数求解,给出其在配送中心中的具体应用,并通过实例求解.通过求解系统空闲的概率、系统平均队长、排队等候平均队长、车辆在配送中心中的逗留时间、平均排队时间,比较单路排队和多路排队的区别,以此判断配送中心的车辆调度系统建设是否合理.     

爱尔朗排队模型在配送中心车辆调度中的应用研究

利用随机过程和排队论的相关知识,通过对爱尔朗排队模型进行性能分析以及参数求解,给出其在配送中心中的具体应用,并通过实例求解。通过求解系统空闲的概率、系统平均队长、排队等候平均队长、车辆在配送中心中的逗留时间、平均排队时间,比较单路排队和多路排队的区别,以此判断配送中心的车辆调度系统建设是否合理。     

Incentive compatible reward schemes for labour-managed firms

We consider a simple case of team production, where a set of workers have to contribute a single input (say labour) and then share the joint output amongst themselves. Different incentive issues arise when the skills as well as the levels of effort expended by workers are not publicly observable. We study one of these issues in terms of a very simple model in which two types of workers, skilled and unskilled, supply effort inelastically. Thus, we assume away the problem of moral hazard in order to focus on that of adverse selection. We also consider a hierarchical structure of production in which the workers need to be organised in two tiers. We look for reward schemes which specify higher payments to workers who have been assigned to the top-level jobs when the principal detects no lies, distribute the entire output in all circumstances, and induce workers to revel their true abilities. We contemplate two scenarios. In the first one, each individual worker knows only her own type, while in the second scenario each worker also knows the abilities of all other workers. Our general conclusion is that the adverse selection problem can be solved in our context. However, the range of satisfactory reward schemes depends on the informational framework.     

Quadratic hedging schemes for non-Gaussian GARCH models

We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended Girsanov principle that generalizes Duan׳s (1995) delta hedge. Since the minimal martingale measure fails to produce a probability measure in this setting, we construct local risk minimization hedging strategies with respect to a pricing kernel. These approaches are investigated in the context of non-Gaussian driven models. Furthermore, we analyze these methods for non-Gaussian GARCH diffusion limit processes and link them to the corresponding discrete time counterparts. A detailed numerical analysis based on S&P 500 European call options is provided to assess the empirical performance of the proposed schemes. We also test the sensitivity of the hedging strategies with respect to the risk neutral measure used by recomputing some of our results with an exponential affine pricing kernel.     

Limit theorems for multivariate discrete distributions

According to the usual law of small numbers a multivariate Poisson distribution is derived by defining an appropriate model for multivariate Binomial distributions and examining their behaviour for large numbers of trials and small probabilities of marginal and simultaneous successes. The weak limit law is a generalization of Poisson's distribution to larger finite dimensions with arbitrary dependence structure. Compounding this multivariate Poisson distribution by a Gamma distribution results in a multivariate Pascal distribution which is again asymptotically multivariate Poisson. These Pascal distributions contain a class of multivariate geometric distributions. Finally the bivariate Binomial distribution is shown to be the limit law of appropriate bivariate hypergeometric distributions. Proving the limit theorems mentioned here as well as understanding the corresponding limit distributions becomes feasible by using probability generating functions.     

Estimators of distance distributions for spatial patterns

Baddeley and Gill (1994, 1996) have introduced an edge-corrected Kaplan–Meier type estimator of the empty space function, which is very important in point process statistics. The present paper suggests a further estimator of this function, which is based on a method used by Hanisch (1984) for unbiased edge-corrected estimation of the nearest neighbour distance distribution function. Moreover, it turns out that the Kaplan–Meier and the new estimator are closely related, since their densities are border method or minus-sampling type estimators.     

Generalized gauss-chebyshev inequalities for unimodal distributions

Letg be an even function on ℝ which is nondecreasing in |x|. Letk be a positive constant. Sharp inequalities relatingP(|X|≥k) toEg(X) are obtained for random variablesX which are unimodal with mode 0, and for random variablesX which are unimodal with unspecified mode. The bounds in the mode 0 case generalize an inequality due to Gauss (1823), whereg(x)=x ². The bounds in the second case generalize inequalities of Vysochanskiĭ and Petunin (1980, 1983) and Dharmadhikari and Joag-dev (1985).     

Incentive schemes for executive officers when forecasts matter

This paper develops a new perspective on results‐based incentive schemes for non‐CEO managers. It shows that it is possible to establish incentive schemes that take into account both the actual output obtained and the forecast figure previously established as a target, without the negative consequences derived from the perverse loop of hiding‐ratchet effects. A general linear two‐staged scheme is proposed. In addition, relevant properties of this incentive system are stated that show how principals (corporate management) may determine the expected forecasting behavior of agents (executive officers) by suitably choosing the scheme parameters according to a simple set of rules. Copyright © 2009 John Wiley & Sons, Ltd.     

Three dual regression schemes for the Lukacs theorem

In the paper we study regressional versions of Lukacs' characterization of the gamma law. We consider constancy of regression instead of Lukacs' independence condition in three new schemes. Up to now the constancy of regressions of U=X/(X + Y) given V=X + Y for independent X and Y has been considered in the literature. Here we are concerned with constancy of regressions for X and Y while independence of U and V is assumed instead.     

Characterizations of negative multinomial distributions based on conditional distributions

In this paper characterizations of negative multinomial distributions based on conditional distributions have been studied.     

A test for equality of two exponential distributions

Abstract Let X ₁., X _n1 and Y ₁., Y _n1, be two independent random samples from exponential populations. The statistical problem is to test whether or not two exponential populations are the same, based on the order statistics X _[1],. X _[r1] and Y [₁],. Y _[rs] where 1 r₁ n ₁ and 1 r₂ n ₂. A new test is given and an asymptotic optimum property of the test is proved.     

Berry-Esseen-type inequality for a special class of distributions

LetQ be the distribution of the suitably normalized sum of i. i. d.k-dimensional random vectors (k2) and letf be a measurable real valued function of the formf(z ₁,...,z _k )=z ₁+r(z ₂,...,z _k ), where the measurable functionr fulfills certain regularity conditions. A Berry-Esseen-type inequality is derived for the one-dimensional distributionP=Qf ^–1.     

Quasi goodness of fit tests for lifetime distributions

In this paper we propose a general method for the construction of tests that can be used for testing goodness of fit of lifetime distributions. The method is the following: first find an identity which holds for the survival function or the cumulative hazard function of the null distribution. Then replace the function by a consistent estimate. The resulting statistic is asymptotically normal. Estimating its asymptotic variance then gives a test statistic which is underH ₀ asymptotically chi². The method can be used for randomly (right) censored and single type-I (right) censored data. We apply this method to the following distributions: Weibull, Log-logistic, Log-normal, Half-normal, Rayleigh, Gompertz, Pareto.