On estimating the reliability after sequentially estimating the mean: The exponential case

Sequential estimation problems for the mean parameter of an exponential distribution has received much attention over the years. Purely sequential and accelerated sequential estimators and their asymptotic second-order characteristics have been laid out in the existing literature, both for minimum risk point as well as bounded length confidence interval estimation of the mean parameter. Having obtained a data set from such sequentially designed experiments, the paper investigates estimation problems for the associatedreliability function. Second-order approximations are provided for the bias and mean squared error of the proposed estimator of the reliability function, first under a general setup. An ad hoc bias-corrected version is also introduced. Then, the proposed estimator is investigated further under some specific sequential sampling strategies, already available in the literature. In the end, simulation results are presented for comparing the proposed estimators of the reliability function for moderate sample sizes and various sequential sampling strategies.     

Rough-and-ready assessment of the degree and importance of smoothing in functional estimation

In nonparametric estimation of functionals of a distribution, it may or may not be desirable, or indeed necessary, to introduce a degree of smoothing into this estimation. In this article, I describe a method for assessing, with just a little thought about the functional of interest, (i) whether smoothing is likely to prove worthwhile, and (ii) if so, roughly how much smoothing is appropriate (in order-of-magnitude terms). This rule-of-thumb is not guaranteed to be accurate nor does it give a complete answer to the smoothing problem. However, I have found it very useful over a number of years; many examples of its use, and limitations, are given.     

A Note on the Estimation of Non-Differentiable Functions of MuItinomial ProbabiIities

Abstract. Consider the problem of estimating f(θ ) where fis a given function and 8 is the unknown parameter of a multinomial distribution. In order to describe the asymptotic behaviour of the frequency substitution estimator, conventional methods typically require differentiability of f , and the error representations depend on the unknown parameter θ.
In this note, a pararneter-free bound for the mean square error is derived which requires continuity of f only.     

A Comparison of Methods for Poverty Estimation in Developing Countries

Small area estimation is a widely used indirect estimation technique for micro‐level geographic profiling. Three unit level small area estimation techniques—the ELL or World Bank method, empirical best prediction (EBP) and M‐quantile (MQ) — can estimate micro‐level Foster, Greer, & Thorbecke (FGT) indicators: poverty incidence, gap and severity using both unit level survey and census data. However, they use different assumptions. The effects of using model‐based unit level census data reconstructed from cross‐tabulations and having no cluster level contextual variables for models are discussed, as are effects of small area and cluster level heterogeneity. A simulation‐based comparison of ELL, EBP and MQ uses a model‐based reconstruction of 2000/2001 data from Bangladesh and compares bias and mean square error. A three‐level ELL method is applied for comparison with the standard two‐level ELL that lacks a small area level component. An important finding is that the larger number of small areas for which ELL has been able to produce sufficiently accurate estimates in comparison with EBP and MQ has been driven more by the type of census data available or utilised than by the model per se.     

Forecasting levels of log variables in vector autoregressions

Sometimes forecasts of the original variable are of interest, even though a variable appears in logarithms (logs) in a system of time series. In that case, converting the forecast for the log of the variable to a naïve forecast of the original variable by simply applying the exponential transformation is not theoretically optimal. A simple expression for the optimal forecast under normality assumptions is derived. However, despite its theoretical advantages, the optimal forecast is shown to be inferior to the naïve forecast if specification and estimation uncertainty are taken into account. Hence, in practice, using the exponential of the log forecast is preferable to using the optimal forecast.     

A number‐of‐modes reference rule for density estimation under multimodality

We consider kernel density estimation for univariate distributions. The question of interest is as follows: given that the data analyst has some background knowledge on the modality of the data (for instance, ‘data of this type are usually bimodal’), what is the adequate bandwidth to choose? We answer this question by extending Silverman's idea of ‘normal‐reference’ to that of ‘reference to a Gaussian mixture’. The concept is illustrated in the light of real data examples.     

A regularization approach to the many instruments problem

This paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite. In order to improve the small sample properties of standard instrumental variable (IV) estimators, we propose three modified IV estimators based on three different ways of inverting the covariance matrix of the instruments. These inverses involve a regularization or smoothing parameter. It should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation. We show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound. Higher-order analysis of the MSE reveals that the bias of the modified estimators does not depend on the number of instruments. Finally, we suggest a data-driven method for selecting the regularization parameter. Interestingly, our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument.     

Simultaneous confidence bands: Theory,implementation, and an application to SVARs

Simultaneous confidence bands are versatile tools for visualizing estimation uncertainty for parameter vectors, such as impulse response functions. In linear models, it is known that that the sup‐t confidence band is narrower than commonly used alternatives—for example, Bonferroni and projection bands. We show that the same ranking applies asymptotically even in general nonlinear models, such as vector autoregressions (VARs). Moreover, we provide further justification for the sup‐t band by showing that it is the optimal default choice when the researcher does not know the audience's preferences. Complementing existing plug‐in and bootstrap implementations, we propose a computationally convenient Bayesian sup‐t band with exact finite‐sample simultaneous credibility. In an application to structural VAR impulse response function estimation, the sup‐t band—which has been surprisingly overlooked in this setting—is at least 35% narrower than other off‐the‐shelf simultaneous bands.     

MULTIPLE TESTING AND HETEROGENEOUS TREATMENT EFFECTS: RE‐EVALUATING THE EFFECT OF PROGRESA ON SCHOOL ENROLLMENT

The effect of a program or treatment may vary according to observed characteristics. In such a setting, it may not only be of interest to determine whether the program or treatment has an effect on some sub‐population defined by these observed characteristics, but also to determine for which sub‐populations, if any, there is an effect. This paper treats this problem as a multiple testing problem in which each null hypothesis in the family of null hypotheses specifies whether the program has an effect on the outcome of interest for a particular sub‐population. We develop our methodology in the context of PROGRESA, a large‐scale poverty‐reduction program in Mexico. In our application, the outcome of interest is the school enrollment rate and the sub‐populations are defined by gender and highest grade completed. Under weak assumptions, the testing procedure we construct controls the familywise error rate—the probability of even one false rejection—in finite samples. Similar to earlier studies, we find that the program has a significant effect on the school enrollment rate, but only for a much smaller number of sub‐populations when compared to results that do not adjust for multiple testing. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust Small Area Estimation under Spatial Non‐stationarity

The effective use of spatial information in a regression‐based approach to small area estimation is an important practical issue. One approach to account for geographic information is by extending the linear mixed model to allow for spatially correlated random area effects. An alternative is to include the spatial information by a non‐parametric mixed models. Another option is geographic weighted regression where the model coefficients vary spatially across the geography of interest. Although these approaches are useful for estimating small area means efficiently under strict parametric assumptions, they can be sensitive to outliers. In this paper, we propose robust extensions of the geographically weighted empirical best linear unbiased predictor. In particular, we introduce robust projective and predictive estimators under spatial non‐stationarity. Mean squared error estimation is performed by two analytic approaches that account for the spatial structure in the data. Model‐based simulations show that the methodology proposed often leads to more efficient estimators. Furthermore, the analytic mean squared error estimators introduced have appealing properties in terms of stability and bias. Finally, we demonstrate in the application that the new methodology is a good choice for producing estimates for average rent prices of apartments in urban planning areas in Berlin.     

Cassetti's New Method for the Identification of Patterns in Input–Output Matrices: An Alternative Formulation

The least upper bound on the overall proportional error that results from the simplification of an input—output matrix is a useful measure of the information loss. In particular, it is proven that some of the available results on this bound can be used to reduce the computations required for an optimal introduction of zeros. Furthermore, it is shown that the matrix that solves the simplification problem for any given level of error is generally not unique, so that it is possible to impose a priori constraints on the pattern of zeros in the matrix.     

Experienced and Novice Investors: Does Environmental Information Influence Investment Allocation Decisions?

Economic Value Added (EVA) is a performance measure that is being used by an increasing number of companies, but academic research on EVA is limited. In addition, all prior empirical academic studies on EVA have used the firm as the unit of analysis. In this study, we examine the effect of EVA on the performance of individual managers. Specifically, we examine whether managers on EVA-based bonus plans outperform managers on traditional accounting-based bonus plans. We are able to test this because we have access to an EVA-focused company that has managers on both EVA and traditional bonus plans. Our results suggest that managers on EVA bonus plans who understand the EVA concept perform better than managers on traditional bonus plans. However, we find some evidence that the increase in performance results from increased consistency or congruence in the manager's evaluation–reward process rather than from superiority of EVA as a performance measure. Also, we find that the effect of EVA bonuses and EVA understanding differs depending on the area of the firm in which the manager is employed. This suggests that EVA may not be a universally appropriate base for reward systems. *Mohan Lal passed away 24 July 2002. This paper is dedicated to him.     

Forensic Economics and the Wrongful Death of a Household Producer: Current Practices, Methodological Biases and Alternative Solutions of Losses

Abstract . A new frontier in forensic economics has emerged: expert testimony on the loss of earning capacity due to the wrongful death of a household producer not in the labor force. Forensic economics—the application of economic analysis by an expert witness—in this area is at an early stage of development. While several methods have been developed for estimating the value of household production, one method, in negligence cases, dominates in the courtroom: replacement cost. Reliance upon a single methodology seems unwise in light of the newness and complexity of research in the area of household production. There are promising alternative methods which could be used. Opportunity cost, family profile and value of service flows methodologies are good candidates. Potentially, the use of alternative methodologies could help provide a consistency check on the reasonableness of any one particular methodology. Presently, several constraints frustrate the task of refining the state of forensic economics in this area. However, progress can be made by, among other things, subjecting forensic economics in these cases to more thorough unbaised professional review such as is common in an older area, antitrust cases.     

Identifiability of mean‐reverting measurement error with instrumental variable

In the context where one main regressor is measured with error and at least one instrumental variable is available for the correction of measurement error, this paper provides, to the best of our knowledge, a first point‐identification result on the variance of measurement error, the variance of latent variable, and their covariance. We show that the parameters are identified if the regression model is not de facto linear. We illustrate the method in an application to identify mean‐reverting measurement error, a typical issue in reported income where the measurement error of income is negatively correlated with the true income.     

Exploring Discrimination on the Basis of International Experience: The Colonial Mindset Bias in the Context Of Pakistan

Discrimination in the labor market has historically been associated with gender, race, ethnicity, and age. This article introduces another basis of discrimination—international experience—which may exist in developing countries because of a colonial mindset. The research is an exploratory study, based on an analysis of in‐depth semistructured interviews with 8 HR managers, 19 employees with international experience, and 24 employees without international experience (N = 51) working in the oil and gas and telecom sectors of Pakistan. Results indicate some initial evidence of a bias, and hence discrimination during recruitment for entry‐level positions. Findings also indicate that international experience may contribute to enhanced employment opportunities, career progress, and higher compensation at senior‐level leadership positions, leaving those without such experience at a disadvantage. While in some cases international experience may be a genuine occupational requirement (GOR), further research is needed to identify whether this is in fact a GOR for senior level positions in all types of organizations or indirect discrimination under the guise of GOR. Recommendations for HR managers and organizational leaders are also set out, which can be applied in practice to foster equality of opportunity in the workplace. © 2017 Wiley Periodicals, Inc.     

Another look at the naive estimator in a regression model

We consider the linear regression model where only a particular linear function of the dependent variables is observed, Stahlecker and Schmidt (1987) proposed a naive least squares (LS) estimator for regression coefficients in such a case. In this note we represent their estimator as a general ridge estimator. This observation leads to a view different from the previous work and provides an easy way of obtaining many important properties of the naive LS estimator. Our approach also gives some insight into the relationship between the naive LS estimator and the generalized least squares estimator.     

Imputation of Missing Item Responses: Some Simple Techniques

Among the wide variety of procedures to handle missing data, imputingthe missing values is a popular strategy to deal with missing itemresponses. In this paper some simple and easily implemented imputationtechniques like item and person mean substitution, and somehot-deck procedures, are investigated. A simulation study was performed based on responses to items forming a scale to measure a latent trait ofthe respondents. The effects of different imputation procedures onthe estimation of the latent ability of the respondents wereinvestigated, as well as the effect on the estimation of Cronbach'salpha (indicating the reliability of the test) and Loevinger'sH-coefficient (indicating scalability). The results indicate thatprocedures which use the relationships between items perform best,although they tend to overestimate the scale quality.     

On Estimators of the Nearest Neighbour Distance Distribution Function for Stationary Point Processes

There are three approaches for the estimation of the distribution function D(r) of distance to the nearest neighbour of a stationary point process: the border method, the Hanisch method and the Kaplan-Meier approach. The corresponding estimators and some modifications are compared with respect to bias and mean squared error (mse). Simulations for Poisson, cluster and hard-core processes show that the classical border estimator has good properties; still better is the Hanisch estimator. Typically, mse depends on r, having small values for small and large r and a maximum in between. The mse is not reduced if the exact intensity λ (if known) or intensity estimators from larger windows are built in the estimators of D(r); in contrast, the intensity estimator should have the same precision as that of λ D(r). In the case of replicated estimation from more than one window the best way of pooling the subwindow estimates is averaging by weights which are proportional to squared point numbers.     

基于DMC-Ⅱ数码航空摄影测量区域网布设研究

从航空摄影到基础地理信息数据产品的获取包括航空摄影、地面控制、空三加密、内业测图等几个阶段。相片控制测量是航空摄影测量的基础工作,通过空三加密获得内业测图所需的外方位元素数据。随着DMC等数字航摄仪应用到航测生产领域当中,DMC影像数据在全数字摄影测量中发挥了越来越重要的作用。本文利用DMC-II数码航空影像,通过实验对DMC-II数字航摄资料的在西南控制困难地区外业像控的布点方案、基线数量、点位位置采取不同方案进行内业加密问题进行研究、分析,总结区域网布点方案的规律性。     

Modelling Group Heterogeneity for Small Area Estimation Using M‐Quantiles

Small area estimation typically requires model‐based methods that depend on isolating the contribution to overall population heterogeneity associated with group (i.e. small area) membership. One way of doing this is via random effects models with latent group effects. Alternatively, one can use an M‐quantile ensemble model that assigns indices to sampled individuals characterising their contribution to overall sample heterogeneity. These indices are then aggregated to form group effects. The aim of this article is to contrast these two approaches to characterising group effects and to illustrate them in the context of small area estimation. In doing so, we consider a range of different data types, including continuous data, count data and binary response data.