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.     

Robust normal reference bandwidth for kernel density estimation

Bandwidth selection is the main problem of kernel density estimation, the most popular method of density estimation. The classical normal reference bandwidth usually oversmoothes the density estimate. The existing hi-tech bandwidths have computational problems (even may not exist) and are not robust against outliers in the sample. A highly robust normal reference bandwidth is proposed, which adapts to different types of densities.     

MSE-improvement of the least squares estimator by dropping variables

It is well known that dropping variables in regression analysis decreases the variance of the least squares (LS) estimator of the remaining parameters. However, after elimination estimates of these parameters are biased, if the full model is correct. In his recent paper, Boscher (1991) showed that the LS-estimator in the special case of a mean shift model (cf. Cook and Weisberg, 1982) which assumes no “outliers” can be considered in the framework of a linear regression model where some variables are deleted. He derived conditions under which this estimator outperforms the LS-estimator of the full model in terms of the mean squared error (MSE)-matrix criterion. We demonstrate that this approach can be extended to the general set-up of dropping variables. Necessary and sufficient conditions for the MSE-matrix superiority of the LS-estimator in the reduced model over that in the full model are derived. We also provide a uniformly most powerful F-statistic for testing the MSE-improvement.     

Improved forecasting of autoregressive series by weighted least squares approximate REML estimation

Restricted maximum likelihood (REML) estimation has recently been shown to provide less biased estimates in autoregressive series. A simple weighted least squares approximate REML procedure has been developed that is particularly useful for vector autoregressive processes. Here, we compare the forecasts of such processes using both the standard ordinary least squares (OLS) estimates and the new approximate REML estimates. Forecasts based on the approximate REML estimates are found to provide a significant improvement over those obtained using the standard OLS estimates.     

Nonparametric least squares estimation in derivative families

Cost function estimation often involves data on a function and a family of its derivatives. Such data can substantially improve convergence rates of nonparametric estimators. We propose series-type estimators which incorporate the various derivative data into a single nonparametric least-squares procedure. Convergence rates are obtained and it is shown that for low-dimensional cases, much of the beneficial impact is realized even if only data on ordinary first-order partials are available. In instances where root-n$n$ consistency is attained, smoothing parameters can often be chosen very easily, without resort to cross-validation. Simulations and an illustration of cost function estimation are included.     

Gamma-minimax estimation of a multivariate normal mean

Summary The mean vector of a multivariate normal distribution is to be estimated. A class Γ of priors is considered which consists of all priors whose vector of first moments and matrix of second moments satisfy some given restrictions. The Γ-minimax estimator under arbitrary squared error loss is characterized. The characterization follows from an application of a result of Browder and Karamardian published in Ichiishi (1983) which is a special version of a minimax inequality due to Ky Fan (1972). In particular, it is shown that within the set of all estimators a linear estimator is Γ-minimax. The authors would like to thank the Deutsche Forschungsgemeinschaft for financial support.     

Spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix

This paper considers spatial heteroskedasticity and autocorrelation consistent (spatial HAC) estimation of covariance matrices of parameter estimators. We generalize the spatial HAC estimator introduced by Kelejian and Prucha (2007) to apply to linear and nonlinear spatial models with moment conditions. We establish its consistency, rate of convergence and asymptotic truncated mean squared error (MSE). Based on the asymptotic truncated MSE criterion, we derive the optimal bandwidth parameter and suggest its data dependent estimation procedure using a parametric plug-in method. The finite sample performances of the spatial HAC estimator are evaluated via Monte Carlo simulation.     

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.     

Plug‐in bandwidth selector for recursive kernel regression estimators defined by stochastic approximation method

In this paper, we propose an automatic selection of the bandwidth of the recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the mean weighted integrated squared error, the recursive estimator will be better than the non‐recursive one for small sample setting in terms of estimation error and computational costs. We corroborated these theoretical results through simulation study and a real dataset.     

Estimating the Kullback–Liebler risk based on multifold cross‐validation

This paper concerns a class of model selection criteria based on cross‐validation techniques and estimative predictive densities. Both the simple or leave‐one‐out and the multifold or leave‐m‐out cross‐validation procedures are considered. These cross‐validation criteria define suitable estimators for the expected Kullback–Liebler risk, which measures the expected discrepancy between the fitted candidate model and the true one. In particular, we shall investigate the potential bias of these estimators, under alternative asymptotic regimes for m. The results are obtained within the general context of independent, but not necessarily identically distributed, observations and by assuming that the candidate model may not contain the true distribution. An application to the class of normal regression models is also presented, and simulation results are obtained in order to gain some further understanding on the behavior of the estimators.     

Generalized least squares inference in panel and multilevel models with serial correlation and fixed effects

In this paper, I consider generalized least squares (GLS) estimation in fixed effects panel and multilevel models with autocorrelation. The presence of fixed effects complicates implementation of GLS as estimating the fixed effects will typically render standard estimators of the covariance parameters necessary for obtaining feasible GLS estimates inconsistent. I focus on the case where the disturbances follow an AR(p) process and offer a simple to implement bias-correction for the AR coefficients. The usefulness of GLS and the derived bias-correction for the parameters of the autoregressive process is illustrated through a simulation study which uses data from the Current Population Survey.     

A uniform weak law of large numbers under π-mixing with application to nonlinear least squares estimation

Abstract  In B ierens (1981) we have derived a uniform weak law of large numbers for stochastically stable processes with respect to a finite-dependent base. In this paper we show that this uniform weak law carries over to stochastically stable processes with respect to a, more general, φ-mixing base. This generalization will be used for relaxing the conditions for weak consistency and asymptotic normality of nonlinear least squares estimators.     

Gamma-admissibility of estimators in the one-parameter exponential family

Summary Admissibility of estimators under vague prior information on the distribution of the unknown parameter is studied which leads to the notion of gamma-admissibility. A sufficient condition for an estimator of the formδ(x)=(ax+b)/(cx+d) to be gamma-admissible in the one-parameter exponential family under squared error loss is established. As an application of this result two equalizer rules are shown to be unique gamma-minimax estimators by proving their gamma-admissibility.     

Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model <Emphasis Type="Bold">AX=B</Emphasis>

A multivariate measurement error model AXB is considered. The errors in [A,B] are rowwise independent, but within each row the errors may be correlated. Some of the columns are observed without errors, and in addition the error covariance matrices may differ from row to row. The total covariance structure of the errors is supposed to be known up to a scalar factor. The fully weighted total least squares estimator of X is studied, which in the case of normal errors coincides with the maximum likelihood estimator. We give mild conditions for weak and strong consistency of the estimator, when the number of rows in A increases. The results generalize the conditions of Gallo given for a univariate homoscedastic model (where B is a vector), and extend the conditions of Gleser given for the multivariate homoscedastic model. We derive the objective function for the estimator and propose an iteratively reweighted numerical procedure.Acknowledgements.A. Kukush is supported by a postdoctoral research fellowship of the Belgian office for Scientific, Technical and Cultural Affairs, promoting Scientific and Technical Collaboration with Central and Eastern Europe. S. Van Huffel is a full professor with the Katholieke Universiteit Leuven. This paper presents research results of the Belgian Programme on Interuniversity Poles of Attraction (IUAP Phase V-22), initiated by the Belgian State, Prime Ministers Office-Federal Office for Scientific, Technical and Cultural Affairs, of the Concerted Research Action (GOA) projects of the Flemish Government MEFISTO-666 (Mathematical Engineering for Information and Communication Systems Technology), of the IDO/99/03 project (K.U. Leuven) Predictive computer models for medical classification problems using patient data and expert knowledge, of the FWO projects G.0200.00, G.0078.01 and G.0270.02. The scientific responsibility is assumed by its authors. The authors would like to thank Maria Luisa Rastello and Amedeo Premoli for bringing the EW-TLS problem to their attention. The authors are grateful to two anonymous referees for the valuable comments.     

Knowledge transformation in project networks: A speech act level cross‐boundary analysis

Researchers stress the importance of understanding knowledge transformation in projects. To explore how knowledge is transformed across organizational and specialization boundaries in project networks, we observed 22 knowledge transformation cases in two project networks. We found that new knowledge was created across specialization boundaries and that knowledge was altered across organizational boundaries. When both organizational and specialization boundaries were crossed, new knowledge was created. From these findings, we developed a set of propositions and formulated these into a model of knowledge transformation in project networks. This research contributes to a better understanding of knowledge transformation processes and outcomes in project networks.     

Generalized P‐values and Bayesian evidence in the one‐sided testing problems under exponential distributions

The problem of comparing the frequentist evidence and the Bayesian evidence in the one‐sided testing problems has been widely treated and many researches revealed that these two methods can reach an agreement approximately. However, most of the previous work dealt mainly with situations without nuisance parameters. Since the presence of nuisance parameters is very common in practice, whether these two kinds of evidence still reach an agreement is a problem worthy of study. In this article, we establish in a systematic way under the exponential distributions the agreement of the Bayesian evidence and the generalized frequentist evidence (the generalized P‐value) for a variety of one‐sided testing problems where the nuisance parameters are involved.     

Age diversity and firm performance in an emerging economy: Implications for cross‐cultural human resource management

This study tests the effect of age diversity on firm performance among international firms. Based on the resource‐based view of the firm, it argues that age diversity among employees will influence firm performance. Moreover, it argues that two contextual variables—a firm's level of market diversification and its country of origin—influence the relationship between age diversity and firm performance. By testing relevant hypotheses in a major emerging economy, that is, the People's Republic of China, this study finds a significant and positive effect of age diversity and a significant interactive effect between age diversity and firm strategy on profitability. We also find a significant relationship between age diversity and firm profitability for firms from Western societies, but not for firms from East Asian societies. The paper concludes by discussing the implications of this study's findings. © 2011 Wiley Periodicals, Inc.     

Inferential Implications of Over‐Parametrization: A Case Study in Incomplete Categorical Data

In the context of either Bayesian or classical sensitivity analyses of over‐parametrized models for incomplete categorical data, it is well known that prior‐dependence on posterior inferences of nonidentifiable parameters or that too parsimonious over‐parametrized models may lead to erroneous conclusions. Nevertheless, some authors either pay no attention to which parameters are nonidentifiable or do not appropriately account for possible prior‐dependence. We review the literature on this topic and consider simple examples to emphasize that in both inferential frameworks, the subjective components can influence results in nontrivial ways, irrespectively of the sample size. Specifically, we show that prior distributions commonly regarded as slightly informative or noninformative may actually be too informative for nonidentifiable parameters, and that the choice of over‐parametrized models may drastically impact the results, suggesting that a careful examination of their effects should be considered before drawing conclusions.     

On the Use of Auxiliary and Paradata for Dealing With Non‐sampling Errors in Household Surveys

In this paper, we consider the use of auxiliary and paradata for dealing with non‐response and measurement errors in household surveys. Three over‐arching purposes are distinguished: response enhancement, statistical adjustment, and bias exploration. Attention is given to the varying focus at the different phases of statistical production from collection, processing to analysis, and how to select and utilize the useful auxiliary and paradata. Administrative register data provide the richest source of relevant auxiliary information, in addition to data collected in previous surveys and censuses. Due to their importance in effective dealings with non‐sampling errors, one should make every effort to increase their availability in the statistical system and, at the same time, to develop efficient statistical methods that capitalize on the combined data sources.