Davidson
Russell Davidson
Publications
In practice, bootstrap tests must use a finite number of bootstrap samples. This means that the outcome of the test will depend on the sequence of random numbers used to generate the bootstrap samples, and it necessarily results in some loss of power. We examine the extent of this power loss and propose a simple pretest procedure for choosing the number of bootstrap samples so as to minimize experimental randomness. Simulation experiments suggest that this procedure will work very well in practice.
We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality or social welfare is greater in one distribution than in another for general classes of indices. We also derive the sampling distribution of the maximal poverty lines (or income censoring thresholds) up to which we may confidently assert that poverty or social welfare is greater in one distribution than in another. The sampling distribution of convenient estimators for dual approaches to the measurement of poverty is also established. The statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes. Our results are briefly illustrated using data for 6 countries drawn from the Luxembourg Income Study data bases. On étudie les propriétés asymptotiques de plusieurs estimateurs fréquemment utilisés pour ordonner les répartitions de revenus en termes de pauvreté, bien-être social, et inégalité. Ces estimateurs incluent les estimateurs de la plupart des indices de pauvreté couramment en usage ainsi que les estimateurs des courbes utiles pour l'inférence de la dominance stochastique de n'importe quel ordre. Ces courbes nous permettent de déterminer si la pauvreté, l'inégalité ou le bien-être social sont plus élevés dans une répartition que dans une autre pour des classes générales d'indices. On étudie aussi la distribution échantillonnale des seuils maximum de pauvreté ou de censure des revenus jusqu'auxquels on peut affirmer sans ambiguïté que la pauvreté ou le bien-être social sont plus élevés dans une répartition de revenus que dans une autre. La distribution échantillonnale d'estimateurs po
This paper examines the properties of stationary-state general equilibrium in a monocentric city with durable housing. On the demand side, identical households choose location, housing quality and quantity, and other goods. On the supply side, developers choose the structural density and time path of building quality. Under a certain set of assumptions, existence and uniqueness of equilibrium are proved, and its comparative static/dynamic properties determined.
We provide a theoretical framework in which to study the accuracy of bootstrap P values, which may be based on a parametric or nonparametric bootstrap. In the parametric case, the accuracy of a bootstrap test will depend on the shape of what we call the critical value function. We show that, in many circumstances, the error in rejection probability of a bootstrap test will be one whole order of magnitude smaller than that of the corresponding asymptotic test. We also propose a simulation method for estimating this error that requires the calculation of only two test statistics per replication.
Bootstrap testing of nonlinear models normally requires at least one nonlinear estimation for every bootstrap sample. We show how to reduce computational costs by performing only a fixed, small number of Newton or quasi-Newton steps for each bootstrap sample. The number of steps is smaller for likelihood ratio tests than for other types of classical tests and smaller for Newton's method than for quasi-Newton methods. The suggested procedures are applied to tests of slope coefficients in the Tobit model and to tests of common factor restrictions. In both cases, bootstrap tests work well, and very few steps are needed. Copyright 1999 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.
Much progress has been made in recent years in understanding the mechanistic details of atomistic processes in the early stages of thin-film growth. We present in this paper a “shorthand” theoretical method for assessing the statistical consequences of different assumptions on the mechanism of island growth, and we illustrate the generality of the method using several examples. The method is based on constructing transformations of the fundamental matrix of the theory of finite Markov processes.
We draw upon the theoretical methods developed in the preceding contribution to explore different mechanisms of island growth in the initial stages of the development of a thin film. In particular, we study the entropic consequences of assuming different sequences for generating a final nucleation pattern or island morphology on a finite, planar array. Our calculations lead to the conclusion that the most entropically favorable process for island growth is one in which the morphology is generated by a ?row-filling? mechanism on a lattice with triangular geometry.
We propose a form of semi-nonparametric regression based on wavelet analysis. Traditional time series methods usually involve either the time or the frequency domain, but wavelets can combine the information from both of these. While wavelet transforms are typically restricted to equally spaced observations an integer power of 2 in number, we show how to go beyond these constraints. We use our methods to construct "patios" for twenty-one important international commodity price series. These graph the magnitude of the variations in the series at different time scales for various subperiods of the full sample. Citation Copyright 1998 by Kluwer Academic Publishers.
Simple techniques for the graphical display of simulation evidence concerning the size and power of hypothesis tests are developed and illustrated. Three types of figures–called P value plots, P value discrepancy plots, and size-power curves–are discussed. Some Monte Carlo experiments on the properties of alternative forms of the information matrix test for linear regression models and probit models are used to illustrate these figures. Tests based on the outer-product-of-the-gradient regression generally perform much worse in terms of both size and power than efficient score tests. Copyright 1998 by Blackwell Publishers Ltd and The Victoria University of Manchester
We establish the asymptotic sampling distribution of general functions of quantile-based estimators computed from samples that are not necessarily independent. The results provide the statistical framework within which to assess the progressivity of taxes and benefits, their horizontal inequity, and the change in the inequality of income which they cause. By the same token, these findings characterise the sampling distribution of a number of popular indices of progressivity, horizontal inequity, and redistribution. They can also be used to assess welfare and inequality changes using panel data, and to assess poverty when it depends on estimated population quantiles. We illustrate these results using micro data on the incidence of taxes and benefits in Canada.
