Estimating smooth monotone functions

Many situations call for a smooth strictly monotone function f of arbitrary flexibility. The family of functions defined by the differential equation D  ² f  = w Df , where w is an unconstrained coefficient function comprises the strictly monotone twice differentiable functions. The solution to this equation is f = C ₀ + C ₁  D ⁻¹{exp( D ⁻¹ w )}, where C ₀ and C ₁ are arbitrary constants and D ⁻¹ is the partial integration operator. A basis for expanding w is suggested that permits explicit integration in the expression of f . In fitting data, it is also useful to regularize f by penalizing the integral of w ² since this is a measure of the relative curvature in f . Applications are discussed to monotone nonparametric regression, to the transformation of the dependent variable in non-linear regression and to density estimation.     

Financial hardship assistance behind the scenes: Insights from financial counsellors

Financial hardship, in a credit society such as Australia, can affect almost anyone. To protect consumers from the negative impacts of financial hardship—which can include the stresses of enforcement action and disconnection from essential services—legal protections have been incorporated into the regulatory frameworks for the consumer credit, energy, water and telecommunications sectors. In this article, we outline the findings of our study, which used a survey of financial counsellors around Australia and focus group interviews with Victorian financial counsellors to examine how these legal protections are being implemented by service providers in these four sectors. Our findings highlight a tendency on the part of service providers to take a generic, one‐size‐fits‐all approach to compliance with these legal protections that prevents them from effectively assisting consumers struggling with debt. We discuss the particular shortcomings of this approach in the context of consumers living on low incomes—especially Centrelink incomes—and outline the policy implications of our findings for assisting these vulnerable groups.     

Curve registration by local regression

Functional data analysis involves the extension of familiar statistical procedures such as principal‐components analysis, linear modelling and canonical correlation analysis to data where the raw observation is a function x, (t). An essential preliminary to a functional data analysis is often the registration or alignment of salient curve features by suitable monotone transformations h_i(t). In effect, this conceptualizes variation among functions as being composed of two aspects: phase and amplitude. Registration aims to remove phase variation as a preliminary to statistical analyses of amplitude variation. A local nonlinear regression technique is described for identifying the smooth monotone transformations h_i, and is illustrated by analyses of simulated and actual data.     

Penalized regression with model‐based penalties

Nonparametric regression techniques such as spline smoothing and local fitting depend implicitly on a parametric model. For instance, the cubic smoothing spline estimate of a regression function ∫ μ based on observations ti, Yi is the minimizer of Σ{Yi ‐ μ(ti)}² + λ∫(μ′′)². Since ∫(μ″)² is zero when μ is a line, the cubic smoothing spline estimate favors the parametric model μ(t) = α_o + α₁t. Here the authors consider replacing ∫(μ″)² with the more general expression ∫(Lμ)² where L is a linear differential operator with possibly nonconstant coefficients. The resulting estimate of μ performs well, particularly if Lμ is small. They present an O(n) algorithm for the computation of μ. This algorithm is applicable to a wide class of L's. They also suggest a method for the estimation of L. They study their estimates via simulation and apply them to several data sets.     

Workplace Bullying,Mobbing and General Harassment: A Review

Research into workplace bullying has continued to grow and mature since emerging from Scandinavian investigations into school bullying in the late 1970s. Research communities now exist well beyond Scandinavia, including Europe, the UK, Australia, Asia and the USA. While the terms ‘harassment’ and ‘mobbing’ are often used to describe bullying behaviour, ‘workplace bullying’ tends to be the most consistently used term throughout the research community. In the past two decades especially, researchers have made considerable advances in developing conceptual clarity, frameworks and theoretical explanations that help explain and address this very complex, but often oversimplified and misunderstood, phenomenon. Indeed, as a phenomenon, workplace bullying is now better understood with reasonably consistent research findings in relation to its prevalence; its negative effects on targets, bystanders and organizational effectiveness; and some of its likely antecedents. However, as highlighted in this review, many challenges remain, particularly in relation to its theoretical foundations and efficacy of prevention and management strategies. Drawing on Affective Events Theory, this review advances understanding through the development of a new conceptual model and analysis of its interrelated components, which explain the dynamic and complex nature of workplace bullying and emphasize current and future debates. Gaps in the literature and future research directions are discussed, including the vexing problem of developing an agreed definition of workplace bullying among the research community, the emergence of cyberbullying, the importance of bystanders in addressing the phenomenon and the use of both formal and informal approaches to prevention and intervention.     

Health Status of Temporary Migrants in Urban Areas in Vietnam1

The rapid economic growth after economic reform, known in Viet Nam as “Doi Moi”, and the growing scope of urban migration raise specific questions for social policy, including migration and health policies. This paper compares issues of health status and its determinants as they affect temporary urban migrants versus permanent urban migrants and non‐migrants. The analyses utilize multivariate logistic regression and data from the 1997 Vietnam Migration and Health Survey. The results show that temporary migrants staying in guest houses are most vulnerable to health problems. Though most of them are initially healthier, their reported health deteriorates faster than other groups of urban residents. The findings also present important implications for the current migration and health policies in Vietnam: 1) A special attention should be given to temporary migrants in guest houses; 2) Different priorities in health policy should be applied to different groups of migrants and non‐migrants; 3) The current population management policy by registration system needs to be reviewed; 4) Providing clean water is one of the most important ways to improve health of temporary migrants; 5) Targeting educational investments and reducing unemployment would likely to improve overall health; 6) A higher priority on health policies targeting women would likely pay dividends, and; 7) Improving management and collaboration between government offices and interested partners is important to improving health status and reducing inequity.     

Examining the Firm's Value Creation Process: A Managerial Perspective of the Firm's Value Offering Strategy and Performance

The primary pursuit of any business is to understand what customers value and to create that value for them. While customers are the final arbiter of value, it is the firm's role to explore, interpret and deliver value based on what they believe customers are seeking. Based on this premise we adopt the firm's perspective on value creation to extend both Bowman and Ambrosini's theoretical framework and the work of DeSarbo, Jedidi and Sinha and focus on two issues. The first is the strategic emphasis firms place on the design and delivery of their value offering. The second is the extent the firm's value offering explains performance differentials at the customer‐centric performance level. We present a conceptual model of how firms gain positional advantage via their value offering and the realized outcomes they achieve. We present two approaches to modelling the firm's value offering (type II and type IV models) and articulate the theoretical underpinnings and results for these models. Our results validate the conceptualization of the firm's value offering and suggest that creating superior value offerings enables firms to achieve superiority in customer‐centric performance.     

The Distribution of Sums of Certain I.I.D. Pareto Variates

ABSTRACT

Though the Pareto distribution is important to actuaries and economists, an exact expression for the distribution of the sum of n i.i.d. Pareto variates has been difficult to obtain in general. This article considers Pareto random variables with common probability density function (pdf) f(x) = (α/β) (1 + x/β)^α+1 for x > 0, where α = 1,2,… and β > 0 is a scale parameter. To date, explicit expressions are known only for a few special cases: (i) α = 1 and n = 1,2,3; (ii) 0 < α < 1 and n = 1,2,…; and (iii) 1 < α < 2 and n = 1,2,…. New expressions are provided for the more general case where β > 0, and α and n are positive integers. Laplace transforms and generalized exponential integrals are used to derive these expressions, which involve integrals of real valued functions on the positive real line. An important attribute of these expressions is that the integrands involved are non oscillating.     

Nonparametric density estimation for censored survival data: Regression-spline approach

A method for nonparametric estimation of density based on a randomly censored sample is presented. The density is expressed as a linear combination of cubic M -splines, and the coefficients are determined by pseudo-maximum-likelihood estimation (likelihood is maximized conditionally on data-dependent knots). By using regression splines (small number of knots) it is possible to reduce the estimation problem to a space of low dimension while preserving flexibility, thus striking a compromise between parametric approaches and ordinary nonparametric approaches based on spline smoothing. The number of knots is determined by the minimum AIC. Examples of simulated and real data are presented. Asymptotic theory and the bootstrap indicate that the precision and the accuracy of the estimates are satisfactory.     

Curve registration

Functional data analysis involves the extension of familiar statistical procedures such as principal components analysis, linear modelling, and canonical correlation analysis to data where the raw observation x_i is a function. An essential preliminary to a functional data analysis is often the registration or alignment of salient curve features by suitable monotone transformations h_i of the argument t , so that the actual analyses are carried out on the values x_i { h_i ( t )}. This is referred to as dynamic time warping in the engineering literature. In effect, this conceptualizes variation among functions as being composed of two aspects: horizontal and vertical, or domain and range. A nonparametric function estimation technique is described for identifying the smooth monotone transformations h_i , and is illustrated by data analyses. A second-order linear stochastic differential equation is proposed to model these components of variation.