Modeling and simulation of the quality’s entropy

The aim of the present study is to define quality entropy as well as to illustrate some of its properties. The simulation of the mathematical model for quality entropy shall be performed by means of specialized software for mathematical problem simulation, such as Microsoft Excel that we have employed for this particular study. Our aim is to prove that quality entropy may be expanded to the notions of Markov source of quality and Bernoulli source of quality, by analogy with the Markov and Bernoulli sources employed in information theory. Likewise, the present study delineates some aspects regarding tolerance to quality entropy. The subject of entropy and its application of the management of quality has been approached by other authors as well (Dinu and Vod?, Revista Calitatea-acces la succes, anul 8(4): 60–61, 2007; Dinu, Revista Calitatea-acces la succes, anul 8(5): 62–63, 2007; Georgescu-Roegen, Legea Entropiei ?i Procesul Economic, 1979; Stamatiu, Proceedings of the 7th International Conference on Quality, Reability and Maintainabilty, 2000; Stamatiu, Proceeding of the 18th International Conference on Quality, Reliability and Maintainability, 2002). Through our transdisciplinary approach, we would like to contribute to the development of this subject.     

Employee Mental Illness: Managing the Hidden Epidemic

While the high prevalence of mental illness in workplaces is more readily documented in the literature than it was ten or so years ago, it continues to remain largely within the medical and health sciences fields. This may account for the lack of information about mental illness in workplaces (Dewa et al. Healthcare Papers 5:12–25, 2004) by operational managers and human resource departments even though such illnesses effect on average 17 % to 20 % of employees in any 12-month period (MHCC 2012; SAMHSA 2010; ABS 2007). As symptoms of mental illness have the capacity to impact negatively on employee work performance and/or attendance, the ramifications on employee performance management systems can be significant, particularly when employees choose to deliberately conceal their illness, such that any work concerns appear to derive from issues other than illness (Dewa et al. Healthcare Papers 5:12–25, 2004; De Lorenzo 2003). When employee non-disclosure of a mental illness impacts negatively in the workplace, it presents a very challenging issue in relation to performance management for both operational managers and human resource staff. Without documented medical evidence to show that impaired work performance and/or attendance is attributable to a mental illness, the issue of performance management arises. Currently, when there is no documented medical illness, performance management policies are often brought into place to improve employee performance and/or attendance by establishing achievable employee targets. Yet, given that in any twelve-month period at least a fifth of the workforce sustains a mental illness (MHCC 2012; SAMHSA 2010; ABS 2007), and that non-disclosure is significant (Barney et al. BMC Public Health 9:1–11, 2009; Munir et al. Social Science & Medicine 60:1397–1407, 2005) such targets may be unachievable for employees with a hidden mental illness. It is for these reasons that this paper reviews the incidence of mental illness in western economies, its costs, and the reasons why it is often concealed and proposes the adoption of what are termed ‘Buffer Stage’ policies as an added tool that organisations may wish to utilise in the management of hidden medical illnesses such as mental illness.     

Many ways of qualitative contrast in probabilistic theories of causality

Hitchcock (Synthese 97:335–364, 1993) argues that the ternary probabilistic theory of causality meets two problems due to the problem of disjunctive factors, while arguing that the unanimity probabilistic theory of causality, which is founded on the binary contrast, does not meet them. Hitchcock also argues that only the ternary theory conveys the information about complex relations of causal relevance. In this paper, I show that Eells’ solution (Probabilistic causality, Cambridge University Press, Cambridge, 1991), which is founded on the unanimity theory, meet the two problems. I also show that the unanimity theory too reveals complex relations of causal relevance. I conclude that the two probabilistic theories of causality carve up the same causal structure in two formally different and conceptually consistent ways. Hitchcock’s ternary theory inspires several major philosophers (Maslen, Causation and counterfactuals, pp. 341–357. MIT Press, Cambridge, 2004; Schaffer, Philos Rev 114, 297–328, 2005; Northcott, Phil Stud 139, 111–123, 2007; Hausman, The place of probability in science: In honor of Eelleys Eells (1953–2006), pp. 47–64, Springer, Dordrecht, 2010) who have recently developed the ternary theory or the quaternary theory. This paper leads them to reconsider the relation between the ternary theory and the binary theory.     

Unlacing hypercube percolation: a survey

The purpose of this note is twofold. First, we survey the study of the percolation phase transition on the Hamming hypercube $\{0,1\}^{m}$ obtained in the series of papers (Borgs et al. in Random Struct Algorithms 27:137–184, 2005; Borgs et al. in Ann Probab 33:1886–1944, 2005; Borgs et al. in Combinatorica 26:395–410, 2006; van der Hofstad and Nachmias in Hypercube percolation, Preprint 2012). Secondly, we explain how this study can be performed without the use of the so-called “lace expansion” technique. To that aim, we provide a novel simple proof that the triangle condition holds at the critical probability.     

Directional output distance functions: endogenous directions based on exogenous normalization constraints

In response to a question raised by Knox Lovell, we develop a method for estimating directional output distance functions with endogenously determined direction vectors based on exogenous normalization constraints. This is reminiscent of the Russell measure proposed by Färe and Lovell (J Econ Theory 19:150–162, 1978). Moreover it is related to the slacks-based directional distance function introduced by Färe and Grosskopf (Eur J Oper Res 200:320–322, 2010a, Eur J Oper Res 206:702, 2010b). Here we show how to use the slacks-based function to estimate the optimal directions.     

Some results on constructing general minimum lower order confounding 2^{n-m} designs for n\le 2^{n-m-2}

Zhang et al. (Stat Sinica 18:1689–1705, 2008) introduced an aliased effect-number pattern for two-level regular designs and proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal designs. All the GMC \(2^{n-m}\) designs with \(N/4+1\le n\le N-1\) were constructed by Li et al. (Stat Sinica 21:1571–1589, 2011), Zhang and Cheng (J Stat Plan Inference 140:1719–1730, 2010) and Cheng and Zhang (J Stat Plan Inference 140:2384–2394, 2010), where \(N=2^{n-m}\) is run number and \(n\) is factor number. In this paper, we first study some further properties of GMC design, then we construct all the GMC \(2^{n-m}\) designs respectively with the three parameter cases of \(n\le N-1\) : (i) \(m\le 4\) , (ii) \(m\ge 5\) and \(n=(2^m-1)u+r\) for \(u>0\) and \(r=0,1,2\) , and (iii) \(m\ge 5\) and \(n=(2^m-1)u+r\) for \(u\ge 0\) and \(r=2^m-3,2^m-2\) .     

A note on R-optimal designs for multiresponse models

This paper considers the optimal design problem for multiresponse regression models. The $R$ -optimality introduced by Dette (J R Stat Soc B 59:97–110, 1997) for single response experiments is extended to the case of multiresponse parameter estimation. A general equivalence theorem for the $R$ -optimality is provided for multiresponse models. Illustrative examples of the $R$ -optimal designs for two multiresponse models are presented based on the general equivalence theorem.     

On Kullback–Leibler information of order statistics in terms of the relative risk

The representation of the entropy in terms of the hazard function and its extensions have been studied by many authors including Teitler et al. (IEEE Trans Reliab 35:391–395, 1986). In this paper, we consider a representation of the Kullback–Leibler information of the first \(r\) order statistics in terms of the relative risk (Park and Shin in Statistics, 2012), the ratio of hazard functions, and extend it to the progressively Type II censored data. Then we study the change in Kullback–Leibler information of the first \(r\) order statistics according to \(r\) and discuss its relation with Fisher information in order statistics.     

An optimal insurance design problem under Knightian uncertainty

This paper solves an optimal insurance design problem in which both the insurer and the insured are subject to Knightian uncertainty about the loss distribution. The Knightian uncertainty is modeled in a multi-prior g-expectation framework. We obtain an endogenous characterization of the optimal indemnity that extends classical theorems of Arrow (Essays in the Theory of Risk Bearing. Markham, Chicago 1971) and Raviv (Am Econ Rev 69(1):84–96, 1979) in the classical situation. In the presence of Knightian uncertainty, it is shown that the optimal insurance contract is not only contingent on the realized loss but also on another source of uncertainty coming from the ambiguity.     

On simplifying the calculations leading to designs with general minimum lower-order confounding

Motivated by the effect hierarchy principle, Zhang et al. (Stat Sinica 18:1689–1705, 2008) introduced an aliased effect number pattern (AENP) for regular fractional factorial designs and based on the new pattern proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal $2^{n-m}$ designs. Zhang et al. (Stat Sinica 18:1689–1705, 2008) proved that most existing criteria can be obtained by functions of the AENP. In this paper we propose a simple method for the calculation of AENP. The method is much easier than before since the calculation only makes use of the design matrix. All 128-run GMC designs with the number of factors ranging from 8 to 32 are provided for practical use.     

M-estimators for single-index model using B-spline

The single-index model is an important tool in multivariate nonparametric regression. This paper deals with M-estimators for the single-index model. Unlike the existing M-estimator for the single-index model, the unknown link function is approximated by B-spline and M-estimators for the parameter and the nonparametric component are obtained in one step. The proposed M-estimator of unknown function is shown to attain the convergence rate as that of the optimal global rate of convergence of estimators for nonparametric regression according to Stone (Ann Stat 8:1348–1360, 1980; Ann Stat 10:1040–1053, 1982), and the M-estimator of parameter is $\sqrt{n}$ -consistent and asymptotically normal. A small sample simulation study showed that the M-estimators proposed in this paper are robust. An application to real data illustrates the estimator’s usefulness.     

Estimation and inference in parametric deterministic frontier models

In this paper we consider parametric deterministic frontier models. For example, the production frontier may be linear in the inputs, and the error is purely one-sided, with a known distribution such as exponential or half-normal. The literature contains many negative results for this model. Schmidt (Rev Econ Stat 58:238–239, 1976) showed that the Aigner and Chu (Am Econ Rev 58:826–839, 1968) linear programming estimator was the exponential MLE, but that this was a non-regular problem in which the statistical properties of the MLE were uncertain. Richmond (Int Econ Rev 15:515–521, 1974) and Greene (J Econom 13:27–56, 1980) showed how the model could be estimated by two different versions of corrected OLS, but this did not lead to methods of inference for the inefficiencies. Greene (J Econom 13:27–56, 1980) considered conditions on the distribution of inefficiency that make this a regular estimation problem, but many distributions that would be assumed do not satisfy these conditions. In this paper we show that exact (finite sample) inference is possible when the frontier and the distribution of the one-sided error are known up to the values of some parameters. We give a number of analytical results for the case of intercept only with exponential errors. In other cases that include regressors or error distributions other than exponential, exact inference is still possible but simulation is needed to calculate the critical values. We also discuss the case that the distribution of the error is unknown. In this case asymptotically valid inference is possible using subsampling methods.     

An unbiased model comparison test using cross-validation

Social scientists often consider multiple empirical models of the same process. When these models are parametric and non-nested, the null hypothesis that two models fit the data equally well is commonly tested using methods introduced by Vuong (Econometrica 57(2):307–333, 1989) and Clarke (Am J Political Sci 45(3):724–744, 2001; J Confl Resolut 47(1):72–93, 2003; Political Anal 15(3):347–363, 2007). The objective of each is to compare the Kullback–Leibler Divergence (KLD) of the two models from the true model that generated the data. Here we show that both of these tests are based upon a biased estimator of the KLD, the individual log-likelihood contributions, and that the Clarke test is not proven to be consistent for the difference in KLDs. As a solution, we derive a test based upon cross-validated log-likelihood contributions, which represent an unbiased KLD estimate. We demonstrate the CVDM test’s superior performance via simulation, then apply it to two empirical examples from political science. We find that the test’s selection can diverge from those of the Vuong and Clarke tests and that this can ultimately lead to differences in substantive conclusions.     

Valuation of fixed and variable rate mortgages: binomial tree versus analytical approximations

The recombining binomial tree approach, which has been initiated by Cox et?al. (J Financ Econ 7: 229?C263, 1979) and extended to arbitrary diffusion models by Nelson and Ramaswamy (Rev Financ Stud 3(3): 393?C430, 1990) and Hull and White (J Financ Quant Anal 25: 87?C100, 1990a), is applied to the simultaneous evaluation of price and Greeks for the amortized fixed and variable rate mortgage prepayment option. We consider the simplified binomial tree approximation to arbitrary diffusion processes by Costabile and Massabo (J Deriv 17(3): 65?C85, 2010) and analyze its numerical applicability to the mortgage valuation problem for some Vasicek and CIR-like interest rate models. For fixed rates and binomial trees with about thousand steps, we obtain very good results. For the Vasicek model, we also compare the closed-form analytical approximation of the callable fixed rate mortgage price by Xie (IAENG Int J Appl Math 39(1): 9, 2009) with its binomial tree counterpart. With respect to the binomial tree values one observes a systematic underestimation (overestimation) of the callable mortgage price (prepayment option price) analytical approximation. This numerical discrepancy increases at longer maturities and becomes impractical for a valuable estimation of the prepayment option price.     

An examination of ex-ante factors and their influence on equity carve-out long-term performance

This study examines the influence of several ex-ante factors on three-year market-adjusted returns of two-stage carve-out combinations from 1988 to 2006. We observe that several factors maintain their significance over a three-year period after equity carve-out ex-dates. Also, we report that, contrary to Vijh (J Bus 75(1):153–190, 1999), negative three-year carve-out returns are statistically significant. In addition, we note that negative combination carve-out/spin-off three-year returns are higher than those of carve-outs acquired by third parties or reacquired by their parents. Moreover, we observe that our independent variables explain 14.56% of the multiple regression three-year returns for carve-outs. Also, our negative correlation of three-year returns with initial period returns supports the “leaning against the wind” hypothesis of Loughran and Ritter (Rev Financ Stud 15(2):413–443, 2002). In addition, our results for the post-bubble period (2001–2006) provide an extension of the changing issuer objective function noted by Loughran and Ritter (Financ Manage 35(3):23–51, 2004) for IPOs and Hogan and Olson (J Financ Res 27(4):521–537, 2004) for equity carve-outs.     

A necessary and sufficient condition for justifying non-parametric likelihood with censored data

The non-parametric likelihood L(F) for censored data, including univariate or multivariate right-censored, doubly-censored, interval-censored, or masked competing risks data, is proposed by Peto (Appl Stat 22:86–91, 1973). It does not involve censoring distributions. In the literature, several noninformative conditions are proposed to justify L(F) so that the GMLE can be consistent (see, for examples, Self and Grossman in Biometrics 42:521–530 1986, or Oller et al. in Can J Stat 32:315–326, 2004). We present the necessary and sufficient (N&S) condition so that \(L(F)\) is equivalent to the full likelihood under the non-parametric set-up. The statement is false under the parametric set-up. Our condition is slightly different from the noninformative conditions in the literature. We present two applications to our cancer research data that satisfy the N&S condition but has dependent censoring.     

Imputation methods of missing data for estimating the population mean using simple random sampling with known correlation coefficient

This paper considers three ratio estimators of the population mean using known correlation coefficient between the study and auxiliary variables in simple random sample when some sample observations are missing. The suggested estimators are compared with the estimators of Singh and Horn (Metrika 51:267–276, 2000), Singh and Deo (Stat Pap 44:555–579, 2003) and Kadilar and Cingi (Commun Stat Theory Methods 37:2226–2236, 2008). They are compared with other imputation estimators based on the mean or a ratio. It is found that the suggested estimators are approximately unbiased for the population mean. Also, it turns out that the suggested estimators perform well when compared with the other estimators considered in this study.     

Design-based distribution function estimation for stigmatized populations

In this paper, we discuss in a general framework the design-based estimation of population parameters when sensitive data are collected by randomized response techniques. We show in close detail the procedure for estimating the distribution function of a sensitive quantitative variable and how to estimate simultaneously the population prevalence of individuals bearing a stigmatizing attribute and the distribution function for the members belonging to the hidden group. The randomized response devices by Greenberg et al. (J Am Stat Assoc 66:243–250, 1971), Franklin (Commun Stat Theory Methods 18:489–505, 1989), and Singh et al. (Aust NZ J Stat 40:291–297 1998) are here considered as data-gathering tools.     

Double symmetry model and its decompositions in square contingency tables having ordered categories

In this paper, we have employed the non-standard log-linear models to fit the double symmetry models and some of its decompositions to square contingency tables having ordered categories. SAS PROC GENMOD was employed to fit these models although we could similarly have used GENLOG in SPSS or GLM in STATA. A SAS macro generates the factor or scalar variables required to fit these models. Two sets of \(4 \times 4\) unaided distance vision data that have been previously analyzed in (Tahata and Tomizawa, Journal of the Japan Statistical Society 36:91–106, 2006) were employed for verification of results. We also extend the approach to the Danish \(5 \times 5\) Mobility data as well as to the \(3 \times 3\) Danish longitudinal study data of subjective health, firstly reported in (Andersen, The Statistical Analysis of Categorical Data, Springer:Berlin, 1994) and analyzed in (Tahata and Tomizawa, Statistical Methods and Applications 19:307–318, 2010). Results obtained agree with those published in previous literature on the subject. The approaches suggest here eliminate any programming that might be required in order to apply these class of models to square contingency tables.     

Asymptotic infimum coverage probability for interval estimation of proportions

In this paper, we discuss asymptotic infimum coverage probability (ICP) of eight widely used confidence intervals for proportions, including the Agresti–Coull (A–C) interval (Am Stat 52:119–126, 1998) and the Clopper–Pearson (C–P) interval (Biometrika 26:404–413, 1934). For the A–C interval, a sharp upper bound for its asymptotic ICP is derived. It is less than nominal for the commonly applied nominal values of 0.99, 0.95 and 0.9 and is equal to zero when the nominal level is below 0.4802. The \(1-\alpha \) C–P interval is known to be conservative. However, we show through a brief numerical study that the C–P interval with a given average coverage probability \(1-\gamma \) typically has a similar or larger ICP and a smaller average expected length than the corresponding A–C interval, and its ICP approaches to \(1-\gamma \) when the sample size goes large. All mathematical proofs and R-codes for computation in the paper are given in Supplementary Materials.