Exploring the relation between the r* approximation and the Edgeworth expansion

In this paper we study the relation between the r* saddlepoint approximation and the Edgeworth expansion when quite general assumptions for the statistic under consideration are fulfilled. We will show that the two term Edgeworth expansion approximates the r* formula up to an O(n ^?3/2) remainder; this provides a new way of looking at the order of the error of the r* approximation. This finding will be used to inspect the close connection between the r* formula and the Edgeworth B adjustment introduced in Phillips (Biometrika 65:91–98, 1978). We will show that, whenever an Edgeworth expansion exists, this adjustment approximates both the distribution function of the statistic and the r* formula to the same order degree as the Edgeworth expansion. Some numerical examples for the sample mean and U-statistics are given in order to shed light on the theoretical discussion.     

Significance levels of linear rank tests using Edgeworth expansions

We study one aspect of applying Edgeworth expansions to linear rank statistics. Since the use of such expansions is often recommended already for moderate sample sizes we investigate for this case the gain of accuracy for the level of significance of some linear rank tests when their critical values are derived from an Edgeworth expansion instead of from a normal approximation. We verify Does' conditions (1983) for the validity of the expansions for four rank statistics of general interest and show by a numerical study that an Edge-worth expansion does not outperform the normal approximation in all situations. A considerable improvement shows up however for the Klotz test at the 5% level.     

Design-based or Prediction-based Inference? Stratified Random vs Stratified Balanced Sampling

Early survey statisticians faced a puzzling choice between randomized sampling and purposive selection but, by the early 1950s, Neyman's design-based or randomization approach had become generally accepted as standard. It remained virtually unchallenged until the early 1970s, when Royall and his co-authors produced an alternative approach based on statistical modelling. This revived the old idea of purposive selection, under the new name of “balanced sampling”. Suppose that the sampling strategy to be used for a particular survey is required to involve both a stratified sampling design and the classical ratio estimator, but that, within each stratum, a choice is allowed between simple random sampling and simple balanced sampling; then which should the survey statistician choose? The balanced sampling strategy appears preferable in terms of robustness and efficiency, but the randomized design has certain countervailing advantages. These include the simplicity of the selection process and an established public acceptance that randomization is “fair”. It transpires that nearly all the advantages of both schemes can be secured if simple random samples are selected within each stratum and a generalized regression estimator is used instead of the classical ratio estimator.     

Heuristic Approximation to Cramér-von Mises Type Statistics

We derive a formal expansion for a distribution in terms of another distribution. As a particular case we get the formal Edgeworth expansion. The heuristic procedure that we present is used to obtain approximations for distribution functions of the Cramér-von Mises and Watson goodness-of-fit statistics. Finally we compare our results with some obtained in the literature.     

Een noodzakelijke correctie van de overschrijdingsgrenzen voor steekproefgemiddelden bij toepassing van stratified sampling

Summary  (A necessary correction of the control chart limits for averages of samples in the case of stratified sampling).
Application of stratified sampling results in smaller fluctuations of sampling than where the same total number of individuals is drawn at random from the superposed strata.
The proportion of the standard errors of the averages obtained by these two sampling methods may be expressed by a factor φ (o ≤φ≤ 1). The probability limits, between which the random sampling results would be fluctuating normally, should be corrected according to this factor.
A few properties of φ are discussed. This is graphically illustrated. Remarks have been added about the relation between the shape of the population of the sampling averages and the population from which the individuals are drawn, and about the difficulties which arise when the populations are non-Gaussian.     

Estimation of the mean in ranked set sampling with non responses

The estimation of the population mean when ranked set sampling [rss] is used for selecting the sample and non responses [nr] are present, is studied. The nr stratum is sub sampled using simple random sampling with replacement. Two strategies are analyzed. One of them is based on the selection of a sub sample from the nr in each cycle. The other uses sub samples selected among the nr in each rank.  The accuracy of the proposed estimators is characterized by the corresponding expected variances. Simulations and real life data are used for analyzing the behavior of them. Acknowledgements: This paper was developed partially during the visit of the author to Université des Antilles et Gouyane. The author gratefully acknowledges the helpful suggestions of the referees and thanks the support of DAAD for visiting Humboldt University where a version of the paper version was made.     

Edgeworth expansions for realized volatility and related estimators

This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we derive Edgeworth expansions for such estimators. The expansions are developed in the framework of small-noise asymptotics. The results have application to Cornish–Fisher inversion and help setting intervals more accurately than those relying on normal distribution.     

A nonsymmetric sequential test

A one-sided testing problem based on an i.i.d. sample of observations is considered. The usual one-sided sequential probability ratio test would be based on a random walk derived from these observations. Here we propose a sequential test where the random walk is replaced by Lindleys random walk which starts anew at zero as soon as it becomes negative. We derive the asymptotics of the expected sample size and the error probabilities of this sequential test. We discuss the advantages of this test for certain nonsymmetric situations.Acknowledgement. The authors thank the referee for helpful comments and suggestions. Their research was supported by the German Research Foundation (DFG) and the Russian Foundation for Basic Research (RFBR).     

An approximation to the finite sample distribution of Zellner's seemingly unrelated regression estimator

A multiple equation model of the seemingly unrelated regressions type is considered. We derive an Edgeworth expansion up to 0(T^-1), where T is the sample size, of the finite sampls distribution function of the seemingly unrelated regression estimator of the parameters in thie model. We examine the two-equation case where our results can be related to exact theory in the special case of orthogonal exogenous variables and we take as a particular numerical example Zellner's original application to micro-investment functions.     

Estimation of correlation for a finite universe

Summary The formula for thePearsonion correlation coefficient, based on a simple random sample, is a consistent estimator of the parent correlation between two given measurable characteristics of the elements of a finite universe. However, when the universe is stratified, and the elements in each stratum are drawn without replacement and with equal probabilities at each draw, the formula for a consistent estimator is much more complex. Generally speaking, the formula for a consistent estimator of the parent correlation varies with the sampling design. The results of this paper are relevant to the analysis of sociological data obtained through sample surveys. In the literature of the theory of statistical sampling the problem of estimating the correlation between pairs of variate values of the identifiable elements constituting a universe has so far not been considered. Needless to say the solution of this problem has an important bearing on sociological studies based on sample surveys.     

Record values from generalized Pareto distribution and associated inference

In this paper, we derive exact explicit expressions for the single, double, triple and quadruple moments of the upper record values from a generalized Pareto distribution. We then use these expressions to compute the mean, variance, and the coefficients of skewness and kurtosis of certain linear functions of record values. Finally, we develop approximate confidence intervals for the location and scale parameters of the generalized Pareto distribution using the Edgeworth approximation and compare them with the intervals constructed through Monte Carlo simulations. Received: June 1999     

中国城镇化进程对房地产价格影响的实证分析

使用城镇化率、流动人口占比、城镇居民人均总收入和房屋竣工面积4个变量指标来反映我国城镇化进程,运用随机效应面板数据模型,对比分析2005—2013年全国、较发达省份和发展中省份的城镇化进程对房地产价格的影响。实证研究表明：城镇化率提高、流动人口占比增加,对房价的影响实际非常有限;城镇居民人均总收入水平的增加才是引起房价上涨的最重要因素;房屋竣工面积的扩大则引起房价的下跌。区域对比研究还发现,由于城镇化进程不同,相比较发达省份,发展中省份的外来务工人员产生了更有效的住房需求。     

The shared reward dilemma on structured populations

In this paper we study the recently introduced “shared reward dilemma” (Cuesta et al. in J Theor Biol 251:253–263, 2008) in the presence of a structure governing the interactions among the population. The shared reward dilemma arises when the prisoner’s dilemma is supplemented with a second stage in which a fixed reward is equally distributed among all cooperators. We first extend our previous results on the equilibrium structure of this game to the case of a one-shot game taking place on a regular network. Subsequently, we consider an evolutionary version of the game on both lattices and random networks. We show that the evolutionary game on graphs exhibits important differences with the case of well-mixed populations. In particular, there exists an important parameter range in which the cooperation is boosted and a single cooperator can invade a population of defectors. We study the dependence of the cooperation levels on the neighborhood size, finding that on random networks the level of cooperation reached decreases as the neighborhood size increases. Moreover, square lattices favor cooperation more than random networks, and on them cooperation may be almost full for certain parameter regions even for large neighborhood sizes. Further, we show that the effect of the population structure is never detrimental for cooperation. We interpret our results in terms of weak versus strong temptation and discuss the nontrivial issues involved in trying to promote cooperation exogenously by means of such a reward mechanism.     

Higher order properties of the wild bootstrap under misspecification

We examine the higher order properties of the wild bootstrap (Wu, 1986) in a linear regression model with stochastic regressors. We find that the ability of the wild bootstrap to provide a higher order refinement is contingent upon whether the errors are mean independent of the regressors or merely uncorrelated with them. In the latter case, the wild bootstrap may fail to match some of the terms in an Edgeworth expansion of the full sample test statistic. Nonetheless, we show that the wild bootstrap still has a lower maximal asymptotic risk as an estimator of the true distribution than a normal approximation, in shrinking neighborhoods of properly specified models. To assess the practical implications of this result we conduct a Monte Carlo study contrasting the performance of the wild bootstrap with a normal approximation and the traditional nonparametric bootstrap.     

加纳凯蓬供水扩建工程里程碑支付的探讨

里程碑支付是国际工程总承包中一种常见的支付方式,具有操作程序简单、管理工作量小等优点受到业主方的青睐,同样,总包商如果能利用好这种支付手段,在减少支付工作量的同时又能取得最大的经济效益,本文以加纳凯蓬供水扩建工程为例,重点从支付项目设置、分解以及各项比例的确定等方面做了分析和研究。     

Least squares fitting of an affine function and strength of association for interval-valued data

The ultimate goal of this paper is to determine a measure of the degree of dependence between two interval-valued random sets, when the dependence is intended in the sense of an affine function relating these random elements. For this purpose, a general study on the least squares fitting of an affine function for interval-valued data is first carried out, where the least squares method we will present considers that squared residuals are based on a generalized metric on the space of nonempty compact intervals, and output and input random mechanisms are modelled by means of convex compact random sets. For the general case of nondegenerate convex compact random sets, solutions are presented in an algorithmic way, and the few cases leading to nonunique solutions are characterized. On the basis of this regression study we later introduce and analyze a well-defined determination coefficient of two interval-valued random sets, which will allow us to quantify the strength of association between them, and an algorithm for the computation of the coefficient has been also designed. Finally, a real-life example illustrates the study developed in the paper.  The research in this paper has been partially supported by DGESIC Grants DGE-99-PB98-1534 and DGE-98-PB97-1282 of the Spanish MEC. Their financial support is gratefully acknowledged. Acknowledgements. The authors are deeply grateful to Professor Wolfgang N?ther from the University of Freiberg and their colleagues Professors Norberto Corral, Miguel López-Dı′az and Ignacio MartVnez for their valuable comments and suggestions in connection with this paper. The real-life data which illustrate the study in this paper have been supplied by Aurora Fonseca, Head of the Servicio de Nefrologı′a, and Miguel de Zárraga, General Medical Manager, from the Hospital Valle del Nalón de Langreo in Asturias; we want to thank them sincerely for their collaboration and support.     

Panel design effects on response rates and response quality

To understand changes in individuals' opinions and attitudes, it would be best to collect data through panels. Such panels, however, often cause irritation among respondents, resulting in low response rates and low response quality. We address whether this problem can be alleviated by designing a panel survey in an alternative way. For this purpose, we perform two field studies where we measure the effects of several panel design characteristics on response rates and response quality. These characteristics include the number of waves and the time between subsequent waves, which may be either fixed or random. Our findings suggest that response rates and response quality can be improved significantly by surveying at random time intervals. It is then crucial that panel members are not informed about the dates they will be surveyed, because in this case, respondents are less likely to develop expectations as to when they will be surveyed again. The methodology we put forward can be used to improve the efficiency of a panel study by carefully calibrating the studies' panel design parameters.     

Bayesian estimation of inefficiency heterogeneity in stochastic frontier models

Estimation of the one sided error component in stochastic frontier models may erroneously attribute firm characteristics to inefficiency if heterogeneity is unaccounted for. However, unobserved inefficiency heterogeneity has been little explored. In this work, we propose to capture it through a random parameter which may affect the location, scale, or both parameters of a truncated normal inefficiency distribution using a Bayesian approach. Our findings using two real data sets, suggest that the inclusion of a random parameter in the inefficiency distribution is able to capture latent heterogeneity and can be used to validate the suitability of observed covariates to distinguish heterogeneity from inefficiency. Relevant effects are also found on separating and shrinking individual posterior efficiency distributions when heterogeneity affects the location and scale parameters of the one-sided error distribution, and consequently affecting the estimated mean efficiency scores and rankings. In particular, including heterogeneity simultaneously in both parameters of the inefficiency distribution in models that satisfy the scaling property leads to a decrease in the uncertainty around the mean scores and less overlapping of the posterior efficiency distributions, which provides both more reliable efficiency scores and rankings.     

Nonresponse in panel data: The impact on estimates of a life cycle consumption function

If missing observations in a panel data set are not missing at random, many widely applied estimators may be inconsistent. In this paper we examine empirically several ways to reveal the nature and severity of the selectivity problem due to nonresponse, as well as a number of methods to estimate the resulting models. Using a life cycle consumption function and data from the Expenditure Index Panel from the Netherlands, we discuss simple procedures that can be used to assess whether observations are missing at random, and we consider more complicated estimation procedures that can be used to obtain consistent or efficient estimates in case of selectivity of attrition bias. Finally, some attention is paid to the differences in identification, consistency, and efficiency between inferences from a single wave of the panel, a balanced sub-panel, and an unbalanced panel.     

Stochastic methods in population forecasting

"This paper presents a stochastic version of the demographic cohort-component method of forecasting future population. In this model the sizes of future age-sex groups are non-linear functions of random future vital rates. An approximation to their joint distribution can be obtained using linear approximations or simulation. A stochastic formulation points to the need for new empirical work on both the autocorrelations and the cross-correlations of the vital rates. Problems of forecasting declining mortality and fluctuating fertility are contrasted. A volatility measure for fertility is presented. The model can be used to calculate approximate prediction intervals for births using data from deterministic cohort-component forecasts. The paper compares the use of expert opinion in mortality forecasting with simple extrapolation techniques to see how useful each approach has been in the past. Data from the United States suggest that expert opinion may have caused systematic bias in the forecasts."