3,228 research outputs found

    Asymptotic normality of the Parzen-Rosenblatt density estimator for strongly mixing random fields

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    We prove the asymptotic normality of the kernel density estimator (introduced by Rosenblatt (1956) and Parzen (1962)) in the context of stationary strongly mixing random fields. Our approach is based on the Lindeberg's method rather than on Bernstein's small-block-large-block technique and coupling arguments widely used in previous works on nonparametric estimation for spatial processes. Our method allows us to consider only minimal conditions on the bandwidth parameter and provides a simple criterion on the (non-uniform) strong mixing coefficients which do not depend on the bandwith.Comment: 16 page

    "The daily grunt": middle class bias and vested interests in the 'Getting in Early' and 'Why Can't They Read?' reports.

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    It is a long-standing and commonly held belief in the UK and elsewhere that the use of elite forms of language reflects superior intellect and education. Expert opinion from sociolinguistics, however, contends that such a view is the result of middle-class bias and cannot be scientifically justified. In the 1960s and 1970s,such luminaries as Labov (1969) and Trudgill (1975) were at pains to point out to educationalists, with some success, that this 'deficit 'view of working-class children's communicative competence is not a helpful one. However, a close reading of recent think-tank reports and policy papers on language and literacy teaching in schools reveals that the linguistic deficit hypothesis has resurfaced and is likely to influence present-day educational policy and practice. In this paper I examine in detail the findings, claims and recommendations of the reports and I argue that they are biased, poorly researched and reflect the vested interests of certain specialist groups, such as speech and language therapists and companies who sell literacy materials to schools. I further argue that we need to, once again, inject the debate with the social dimensions of educational failure, and we need to move away from the pathologisation of working-class children's language patterns

    Ranking Investment Projects

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    This paper describes conditions under which one investment project dominates a second project in terms of net present value, irrespective of the choice of the discount rate. The resulting partial ordering of projects has certain similarities to stochastic dominance. However, the structure of the net present value function leads to characterizations that are quite specific to this context. Our theorems use Bernstein's (1915) innovative results on the representation and approximation of polynomials, as well as other general results from the theory of equations, to characterize the partial ordering. We also show how the ranking is altered when the range of discount rates is limited or the rate varies period by period.

    The social construction of time in contemporary education: implications for technology, equality and Bernstein's 'conditions for democracy'

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    This article discusses how the introduction of technology has led to a fundamental shift in the relationship between education and time. As a means of analysing the extent of such changes on pupils from different backgrounds, I use Bernstein's 'conditions for democracy' (Bernstein, 2000) as a framework for evaluating the impact new understandings of time in education are having on disadvantaged social groups in England. I conclude that Bernstein's framework presents a useful way of illuminating the complex interplay of personal agency and the external environment. Consequently, here we see that new definitions of time in education, specifically with regard to synchronous versus asynchronous learning, have resulted in new inequalities for those in deprived areas

    Writing design

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    The complexity of design is defined in terms of four classes of object - product, programme, process and philosophy - the four 'P's of design. A range of possibilities for writing about these objects is outlined with reference to their methodological implications. Six formats for research presentation are described, each of which relates directly to a common type of designerly enquiry and embraces a productive account of the four 'P's. In conclusion, some observations are made on the value of such research and the opportunities it presents for developing the design discipline

    Complete Monotonicity of the Representative Consumer's Discount Factor

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    A univariate real-valued function is said to be completely monotone if it takes positive values and alternate the signs of its higher order derivatives, starting from everywhere negative first derivatives. We prove that the representative consumer's discount factor of a continuous-time economy under uncertainty is a power function of some completely monotone function of time satisfying certain boundary conditions if and only if it may be derived from a group of consumers having constant and equal relative risk aversion, and constant and yet possibly unequal discount rates.Complete monotonicity, discount factor, discount rate, representative consumer, expected utility, time additivity, relative risk aversion, Bernstein's theorem

    Complete Monotonicity of the Representative Consumer's Discount Factor

    Get PDF
    A univariate real-valued function is said to be completely monotone if it takes positive values and alternate the signs of its higher order derivatives, starting from everywhere negative first derivatives. We prove that the representative consumer's discount factor of a continuous-time economy under uncertainty is a power function of some completely monotone function of time satisfying certain boundary conditions if and only if it may be derived from a group of consumers having constant and equal relative risk aversion, and constant and yet possibly unequal discount rates.Complete monotonicity, discount factor, discount rate, representative consumer, expected utility, time additivity, relative risk aversion, Bernstein's theorem.
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