Model misspecification effects for biased samples

The model misspecification effects on the maximum likelihood estimator are studied when a biased sample is treated as a random one as well as when a random sample is treated as a biased one. The relation between the existence of a consistent estimator under model misspecification and the completeness of the distribution is also considered. The cases of the weight invariant distribution and the scale parameter distribution are examined and finally an example is presented to illustrate the results.     

One-sided hyperbolic simultaneous confidence bands for multiple and polynomial regression models

A simultaneous confidence band is a useful statistical tool in a simultaneous inference procedure. In recent years several papers were published that consider various applications of simultaneous confidence bands, see for example Al-Saidy et al. (Biometrika 59:1056–1062, 2003), Liu et al. (J Am Stat Assoc 99:395–403, 2004), Piegorsch et al. (J R Stat Soc 54:245–258, 2005) and Liu et al. (Aust N Z J Stat 55(4):421–434, 2014). In this article, we provide methods for constructing one-sided hyperbolic imultaneous confidence bands for both the multiple regression model over a rectangular region and the polynomial regression model over an interval. These methods use numerical quadrature. Examples are included to illustrate the methods. These approaches can be applied to more general regression models such as fixed-effect or random-effect generalized linear regression models to construct large sample approximate one-sided hyperbolic simultaneous confidence bands.     

Some general points on the $$I^2$$-measure of heterogeneity in meta-analysis

Meta-analysis has developed to be a most important tool in evaluation research. Heterogeneity is an issue that is present in almost any meta-analysis. However, the magnitude of heterogeneity differs across meta-analyses. In this respect, Higgins’ \(I^2\) has emerged to be one of the most used and, potentially, one of the most useful measures as it provides quantification of the amount of heterogeneity involved in a given meta-analysis. Higgins’ \(I^2\) is conventionally interpreted, in the sense of a variance component analysis, as the proportion of total variance due to heterogeneity. However, this interpretation is not entirely justified as the second part involved in defining the total variation, usually denoted as \(s^2\), is not an average of the study-specific variances, but in fact some other function of the study-specific variances. We show that \(s^2\) is asymptotically identical to the harmonic mean of the study-specific variances and, for any number of studies, is at least as large as the harmonic mean with the inequality being sharp if all study-specific variances agree. This justifies, from our point of view, the interpretation of explained variance, at least for meta-analyses with larger number of component studies or small variation in study-specific variances. These points are illustrated by a number of empirical meta-analyses as well as simulation work.     

R-optimal designs for multi-factor models with heteroscedastic errors

In this paper, we consider the R-optimal design problem for multi-factor regression models with heteroscedastic errors. It is shown that a R-optimal design for the heteroscedastic Kronecker product model is given by the product of the R-optimal designs for the marginal one-factor models. However, R-optimal designs for the additive models can be constructed from R-optimal designs for the one-factor models only if sufficient conditions are satisfied. Several examples are presented to illustrate and check optimal designs based on R-optimality criterion.     

In search of efficient network structures: the needle in the haystack

Searching for efficient networks can prove a very difficult analytical and even computational task. In this paper, we explore the possibility of using the genetic algorithms (GA) technique to identify efficient network structures in the case of non-trivial payoff functions. The robustness of this method in predicting optimal networks is tested on the two simple stylized models introduced by Jackson and Wolinsky (1996), for which the efficient networks are known over the whole state space of the parameters’ values. This approach allows us to obtain new exploratory results in the case of the linear-spatialized connections model proposed by Johnson and Gilles (Rev Econ Des 5:273–299, 2000), for which the efficient allocation of bilateral connections is driven by contradictory forces that push either for a centralized structure around a coordinating agent, or for only locally and evenly distributed connections. Murat Yıldızoğlu gratefully acknowledges the support of the CCRDT program of Aquitaine Region.     

Influence analysis for Poisson inverse Gaussian regression models based on the EM algorithm

For Poisson inverse Gaussian regression models, it is very complicated to obtain the influence measures based on the traditional method, because the associated likelihood function involves intractable expressions, such as the modified Bessel function. In this paper, the EM algorithm is employed as a basis to derive diagnostic measures for the models by treating them as a mixed Poisson regression with the weights from the inverse Gaussian distributions. Several diagnostic measures are obtained in both case-deletion model and local influence analysis, based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. Two numerical examples are given to illustrate the results.     

Efficiency and productivity change in Ukrainian health care

The study analyses technical efficiency and efficiency change of 193 community hospitals and polyclinics across Ukraine, for the years 1997–2001. These facilities are a subset of the medical institutions in rural Ukraine; they are identical w.r.t. their function in the health system and share the same departmental structure. The data comprise the number of beds in the hospitals, the number of staff employed in the hospitals as well as the polyclinics connected to the hospitals, the number of inpatient and outpatient admissions as well as the number of surgical procedures, lab tests, X-rays performed and the number of deaths and deaths after surgery. Because of the known sensitivity of traditional nonparametric frontier estimators to outlier observations, we employ an order-m estimator, a robust technique, to assess the efficiency of these health care providers as well as changes of their productivity time. The efficiency scores are calculated with an output-oriented model; they are close to unity for hospitals whereas polyclinics seem somewhat less efficient. The Malmquist-indices averaged over all observations are close to unity indicating that productivity does not change over during our observation period. But, depending on the period and the region, substantial deviations from unity can be observed.

The long-run performance of diversifying firms

The corporate diversification literature presents a puzzle. Short-horizon event studies report positive abnormal returns around the announcement of a diversifying event, while studies that examine diversified firms find evidence that diversified firms are worth less than specialized firms (a diversification discount). If diversification is value destroying, perhaps the destruction occurs over longer periods than have been previously tested. This paper tests the hypothesis that diversifying firms have negative long-run abnormal performance following diversification by examining a sample of specialized firms that have a diversifying event from 1978 through 1998. The firms are tracked for up to five years past their diversification year. There is evidence that value is destroyed for small firms that diversify but enhanced for larger firms that diversify.