Fiducial distribution in a power series family

Abstract

In this article the interest is on finding the fiducial distribution of the parameter, when the probability distribution belongs to the power series family, as in Johnson et al. (1992 Johnson, N. L., S. Kotz, and A. W. Kemp. 1992. Univariate discrete distributions. New York, NY: John Wiley and Sons. [Google Scholar]). Recently in Nájera and O’Reilly (2017 Nájera, E., and F. O’Reilly. 2017. On fiducial generators. Communications Statistics - Theory Methods 46 (5):2232–2248. doi:10.1080/03610926.2015.1040505.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) an argument is given to obtain a unique fiducial in the Bernoulli case. An attempt is made here to define some sort of invariance in a power series distribution so that, as was done in the Bernoulli case, one may find a unique invariant fiducial for the parameter. The Bernoulli case is reviewed in detail and the Poisson and negative binomial cases are addressed.     

Using High-Frequency Data in Dynamic Portfolio Choice

This article evaluates the economic benefit of methods that have been suggested to optimally sample (in an MSE sense) high-frequency return data for the purpose of realized variance/covariance estimation in the presence of market microstructure noise (Bandi and Russell, 2005a Bandi , F. M. , Russell , J. R. ( 2005a ). Realized covariation, realized beta, and microstructure noise . Working paper . [Google Scholar], 2008 Bandi , F. M. , Russell , J. R. ( 2008 ). Microstructure noise, realized variance, and optimal sampling . Review of Economic Studies , forthcoming . [Google Scholar]). We compare certainty equivalents derived from volatility-timing trading strategies relying on optimally-sampled realized variances and covariances, on realized variances and covariances obtained by sampling every 5 minutes, and on realized variances and covariances obtained by sampling every 15 minutes. In our sample, we show that a risk-averse investor who is given the option of choosing variance/covariance forecasts derived from MSE-based optimal sampling methods versus forecasts obtained from 5- and 15-minute intervals (as generally proposed in the literature) would be willing to pay up to about 80 basis points per year to achieve the level of utility that is guaranteed by optimal sampling. We find that the gains yielded by optimal sampling are economically large, statistically significant, and robust to realistic transaction costs.     

A set of independent sequential residuals for the multivariate regression model

In this paper a set of residuals for the multivariate linear regression model is introduced. These residuals are shown to be independent with known distributions which do not depend on the parameters of the model. Transformations of the mentioned residuals may be used to construct exact α goodness-of-fit tests for the multivariate regression model.     

A “maximum node clustering” problem

In this note we introduce a graph problem, called Maximum Node Clustering (MNC). We prove that the problem (which is easily shown to be strongly NP-complete) can be approximated in polynomial time within a ratio arbitrarily close to 2. For the special case where the graph is a tree, the problem is NP-complete in the ordinary sense; for this case we present a pseudopolynomial algorithm based on dynamic programming, and a related Fully Polynomial Time Approximation Scheme (FPTAS). Also, the tree case is shown to be exactly solvable in time, where n is the number of nodes.     

Training x Trainee Interactions in a family planning intervention

This study investigated the effects of introducing a family planning counseling model at clinics of Peru's Ministry of Health. Providers trained in the model presented greater quality of care and longer counseling sessions than did controls. The main effects, however, were misleading. Nearly all of the quality improvements were contributed by 37% of the trained providers; they had already been better performers at the pretest and complied with the new counseling model's requirement of job aid use at the posttest. The recognition that a majority of trained providers did not profit from training posed a challenge that led to improvements in the model. Training x Trainee Interactions should be explored in evaluations.     

Efficient algorithms for the max k -vertex cover problem

Given a graph  \(G(V,E)\) of order  \(n\) and a constant \(k \leqslant n\) , the max  \(k\) -vertex cover problem consists of determining  \(k\) vertices that cover the maximum number of edges in  \(G\) . In its (standard) parameterized version, max  \(k\) -vertex cover can be stated as follows: “given  \(G,\) \(k\) and parameter  \(\ell ,\) does  \(G\) contain  \(k\) vertices that cover at least  \(\ell \) edges?”. We first devise moderately exponential exact algorithms for max  \(k\) -vertex cover, with time-complexity exponential in  \(n\) but with polynomial space-complexity by developing a branch and reduce method based upon the measure-and-conquer technique. We then prove that, there exists an exact algorithm for max  \(k\) -vertex cover with complexity bounded above by the maximum among  \(c^k\) and  \(\gamma ^{\tau },\) for some \(\gamma < 2,\) where  \(\tau \) is the cardinality of a minimum vertex cover of  \(G\) (note that \({\textsc {max}}\,\) k \({\textsc {\!-vertex cover}}{} \notin \mathbf{FPT}\) with respect to parameter  \(k\) unless \(\mathbf{FPT} = \mathbf{W[1]}\) ), using polynomial space. We finally study approximation of max  \(k\) -vertex cover by moderately exponential algorithms. The general goal of the issue of moderately exponential approximation is to catch-up on polynomial inapproximability, by providing algorithms achieving, with worst-case running times importantly smaller than those needed for exact computation, approximation ratios unachievable in polynomial time.     

A multidimensional employment quality index for Brazil, 2002–11

In countries where informal, insecure jobs are widespread, traditional labour market indicators – such as the unemployment rate, labour force participation rate and wages – are not necessarily the most meaningful. The authors use a multidimensional employment quality index to analyse the Brazilian labour market over the period 2002–11, across three dimensions: earnings, formality (measured by the existence of an employment contract and social security contributions) and job tenure. The results show a significant increase in employment quality overall, especially in the years 2009–11, but with considerable differences between wage employees and self‐employed workers, and between industries.     

A pseudo-values regression model for non-fatal event free survival in the presence of semi-competing risks

Statistical Methods & Applications - During follow-up patients may experience non-fatal events related to disease progression and death. This is a “semi-competing risks” setting, as...