Polar sets of fractional Brownian sheets

The properties of the polar sets are discussed for a real-valued (N, d)-fractional Brownian sheet with Hurst index. Sufficient conditions and necessary conditions for a compact set to be polar for the fractional Brownian sheet are proved. The infimum of Hausdorff dimensions of its polar sets are also obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity. Research supported by the National Natural Foundation of China (10471148), the Sci-tech Innovation Item for Excellent Young and Middle-Aged University Teachers of Educational Department of Hubei (200316).     

Cardinality-based equality of opportunities

We study possible rankings of opportunity profiles. An opportunity profile is a list of opportunity sets, one for each agent in the society. We compare profiles on the basis of the notion of “equality of opportunities”. Our main results show the necessary and sufficient conditions for this comparison to be made using exclusively the information provided by two cardinal measures: the number of common alternatives in all sets of a given profile and the difference between the number of alternatives in the individual sets. We also show that, under additional axioms, we can combine these criteria only in a weighted procedure or in some lexicographic refinements of a weighted procedure.      

On-duty and Off-duty: Employee Right to Privacy and Employer’s Right to Control in the Private Sector

The changing legal landscape of the right of the employer to control and monitor employee behavior is examined. Two distinct areas are defined: behavioral monitoring and behavioral restrictions. Relevant statutory laws and the developing common law are discussed. We also examine potential employee reactions to such policies by evaluating the reactions of graduate students to six employer policies including weight restrictions, grooming requirements, use of GPS locators, drug testing, ban on off-duty smoking, and email and internet monitoring. Students responded to these policies by determining the reasonable interest of the employer in the behaviors being monitored or controlled and the manner in which policies were implemented. Their comments suggest that employees may accept some level of monitoring or behavioral restrictions if the employer can make a convincing social account of the need for a policy. Additionally, the policy must be clearly communicated and properly implemented. However, restrictions on off-duty behavior were typically poorly received with the exception of illegal drug use.     

Contingent payments in selection contests

The early literature on research contests stressed the advantages of a fixed prize in inspiring R&D effort. More recently the focus has moved towards endogenizing the rewards to research activity in these tournament settings, since this can induce extra effort or enhance the surplus of the buyer. We focus on a research contest as a means of selecting a partner for an R&D enterprise, in an informational setting in which the established providers of R&D services know more about each others’ relative capabilities than does the buyer/sponsor. An alternative use of our model is in choosing between prospective patentees where the Patent Trading Office has less information on the patents than the competitors. This asymmetry creates a source of inefficiency if a rank order contest is used as a selection device; we show how the contest can be modified to improve selection efficiency, while maintaining its simplicity (as only ordinal information is required). The modification that we suggest involves endogenizing the prizes that are awarded contingent upon whether a contestant wins or loses the contest. Furthermore, the payment system and the selection mechanism are detail-free. This paper is part of the project “The Knowledge-Based Society” sponsored by the Research Council of Norway (project 172603/V10).     

Generalized linear mixed models with informative dropouts and missing covariates

Generalized linear mixed models (GLMM) are useful in many longitudinal data analyses. In the presence of informative dropouts and missing covariates, however, standard complete-data methods may not be applicable. In this article, we consider a likelihood method and an approximate method for GLMM with informative dropouts and missing covariates. The methods are implemented by Monte–Carlo EM algorithms combined with Gibbs sampler. The approximate method may lead to inconsistent estimators but is computationally more efficient than the likelihood method. The two methods are evaluated via a simulation study for longitudinal binary data, and appear to perform reasonably well. A dataset on mental distress is analyzed in details.     

The Limit Distribution of the Bootstrap for the Unit Root Test Statistic when the Residuals are Dependent

In this article, the unit root test for the AR(1) model with dependent residuals is considered. We adopt a bootstrap procedure to bootstrap the residuals with bootstrap sample size m less than the size n of the original sample. Under the assumptions that m → ∞ and m/n → 0, the convergence in probability of the bootstrap distribution function is established. Research supported by National Natural Science Foundation of China (No. 10471126)     

Variation diminishing property of densities of uniform generalized order statistics

Let f _*,r , r ≥ 1, denote the density function of rth uniform generalized order statistics as defined by Kamps (1995) or Cramer and Kamps (2003). We prove the following variation diminishing property: the number of zeros in (0,1) of any linear combination does not exceed the number of sign changes in the sequence (a ₁, . . . ,a _r ). This result is applied to study monotonicity and convexity properties of f _*,r .     

Characterization of Normal Distribution Related to Two Samples Based on Regression

Characterization of normal distribution related to two samples based on second conditional moments has been obtained. This characterization has been transformed to a characterization based on the UMVU estimators of the density function. These results are generalized to k samples from normal distributions. Finally applications of these characterization results to goodness-of-fit test are discussed.     

On Minimally-supported <Emphasis Type="Italic">D</Emphasis>-optimal Designs for Polynomial Regression with Log-concave Weight Function

This paper studies minimally-supported D-optimal designs for polynomial regression model with logarithmically concave (log-concave) weight functions. Many commonly used weight functions in the design literature are log-concave. For example, and exp(−x ²) in Theorem 2.3.2 of Fedorov (Theory of optimal experiments, 1972) are all log-concave. We show that the determinant of information matrix of minimally-supported design is a log-concave function of ordered support points and the D-optimal design is unique. Therefore, the numerically D-optimal designs can be constructed efficiently by cyclic exchange algorithm.     

Are the BRIC countries overtaking intermediate countries in the race for international R&D? The case of Spain

The emergence of Brazil, Russia, India and China (BRIC) as international locations for foreign direct investment in R&D is a sign that multinationals are relocating their technological activities to new territories. This trend may weaken the supremacy of the developed countries until now considered leaders in innovation, and may mean the loss of the competitive advantages enjoyed by the countries considered intermediate innovators. This paper examines the situation of Spain as a typical intermediate economy and compares it to its main competitors among the BRICs. Based on eight case studies of subsidiaries with R&D centres in Spain, we conclude that the policies adopted by certain emerging economies to develop their national innovation systems are proving effective and that these countries now pose a threat to intermediate economies. However, the BRICs still lag behind in terms of the security of their institutional framework; this situation leaves intermediate countries in an advantageous position.