A law of the iterated logarithm for Grenander's estimator

In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If $f(t_0) > 0$, $f'(t_0) < 0$, and $f'$ is continuous in a neighborhood of $t_0$, then \begin{eqnarray*} \limsup_{n\rightarrow \infty} \left ( \frac{n}{2\log \log n} \right )^{1/3} ( \widehat{f}_n (t_0 ) - f(t_0) ) = \left| f(t_0) f'(t_0)/2 \right|^{1/3} 2M \end{eqnarray*} almost surely where $M \equiv \sup_{g \in {\cal G}} T_g = (3/4)^{1/3}$ and T_g \equiv \mbox{argmax}_u \{ g(u) - u^2 \} ; here ${\cal G}$ is the two-sided Strassen limit set on $R$. The proof relies on laws of the iterated logarithm for local empirical processes, Groeneboom's switching relation, and properties of Strassen's limit set analogous to distributional properties of Brownian motion.Comment: 11 pages, 3 figure

Prime ministers & Civil Service reform 1960-74

PhDThis thesis anatomises the high watermark of belief in administrative and institutional remedies to the deeply-felt relative economic and absolute military decline of Britain in the years after the Second. World War. It analyses the second half of the Macmillan years, the administration of Sir Alec Douglas-Home, the first two premierships of Harold Wilson (but not the period from 1974-76 which saw little reformist activity) and the three-and-a-half years that Edward Heath occupied No. 10 Downing Street. The approach has been to look at the prime ministers' plans, examine how these were embraced by the Civil Service and analyse the results. The period 1960-74 saw a great many major reforms to the machinery of government, all of which are analysed. Significant new findings include the struggle over the demarcation `concordat' between the Treasury and the Department of Economic Affairs in 1964; the way that the Prime Minister's Principal Private Secretary acted against the senior civil servant handling the reception of the Fulton Report; the fact that Harold Wilson developed a keen interest in the `hiving off' of parts of the public sector in 1969; how, after the Heath Government was elected in 1970, the Civil Service took the massive political planning undertaken prior to government and effectively cherry-picked what it wanted, turning the dynamism for reform to its own advantage; the remarkable lack of interest in Programme Analysis and Review; and the way that the Central Policy Review Staff was sidelined in Heath's last weeks

Teachers' attempts to integrate research-based principles into the teaching of numeracy with post-16 learners

This paper describes some outcomes of a nine-month design-based research study into the professional development of 24 numeracy teachers with post-16 learners. The teachers were encouraged to integrate eight research-based teaching principles into their classroom practices as they implemented a set of discussion-based mathematics learning resources. A mixed methods approach was used to evaluate the outcomes, including interviews and classroom observation. The paper examines: teachers’ perceptions of the project; the reasons why they found some pedagogical principles more difficult to incorporate than others and the factors that enabled and impeded their use of the learning resources. In particular it is noted that the principles that teachers considered to be most important were not the ones that they were observed using most effectively. The paper concludes by considering the implications of the research for initial and continuing teacher education

Professional Values and Practice

The professional code of the General Teaching Council lists eight new standards, each of them analysed here in detail using questions and activities to describe what trainee teachers need to know, understand and demonstrate as they work towards Qualified Teacher Status. Each of the eight standards cover the following issues: expectations, diversity and achievement personal and professional values values in the classroom values, rights and responsibilities in the wider community the community of the school professional relationships personal and professional development professional responsibility. This practical and jargon-free guide features an extensive range of examples and suggestions for further reading, designed to help those in their early professional development

Professional Values and Practice

The professional code of the General Teaching Council lists eight new standards, each of them analysed here in detail using questions and activities to describe what trainee teachers need to know, understand and demonstrate as they work towards Qualified Teacher Status. Each of the eight standards cover the following issues: expectations, diversity and achievement personal and professional values values in the classroom values, rights and responsibilities in the wider community the community of the school professional relationships personal and professional development professional responsibility. This practical and jargon-free guide features an extensive range of examples and suggestions for further reading, designed to help those in their early professional development

A Review and update of the Health of the Nation Outcome Scales (HoNOS)

Summary Aims and method: The Health of the Nation Outcome Scales (HoNOS) and older adults version (HoNOS 65+) have been used widely for 20 years but their glossaries have not been revised to reflect clinicians’ experiences or changes in service delivery. The Royal College of Psychiatrists convened an international advisory board, with UK, Australian and New Zealand expertise, to identify desirable amendments. The aim was to improve rater experience by removing ambiguity and inconsistency in the glossary rather than more radical revision. Results Changes proposed to the HoNOS are reported. HoNOS65+ changes will be reported separately. Based on the views and experience of the countries involved a series of amendments were identified. Clinical implications While effective clinician training remains critically important, these revisions aim to improve intra- and inter-rater reliability and improve validity. Next steps will depend on feedback from HoNOS users. Reliability and validity testing will depend on funding. Declaration of interest None

Broadband Records of Earthquakes in Deep Gold Mines and a Comparison with Results from SAFOD, California

For one week during September 2007, we deployed a temporary network of field recorders and accelerometers at four sites within two deep, seismically active mines. The ground-motion data, recorded at 200 samples/sec, are well suited to determining source and ground-motion parameters for the mining-induced earthquakes within and adjacent to our network. Four earthquakes with magnitudes close to 2 were recorded with high signal/noise at all four sites. Analysis of seismic moments and peak velocities, in conjunction with the results of laboratory stick-slip friction experiments, were used to estimate source processes that are key to understanding source physics and to assessing underground seismic hazard. The maximum displacements on the rupture surfaces can be estimated from the parameter Rv, where v is the peak ground velocity at a given recording site, and R is the hypocentral distance. For each earthquake, the maximum slip and seismic moment can be combined with results from laboratory friction experiments to estimate the maximum slip rate within the rupture zone. Analysis of the four M 2 earthquakes recorded during our deployment and one of special interest recorded by the in-mine seismic network in 2004 revealed maximum slips ranging from 4 to 27 mm and maximum slip rates from 1.1 to 6:3 m=sec. Applying the same analyses to an M 2.1 earthquake within a cluster of repeating earthquakes near the San Andreas Fault Observatory at Depth site, California, yielded similar results for maximum slip and slip rate, 14 mm and 4:0 m=sec

Review and update of the Health of the Nation Outcome Scales for Elderly People (HoNOS65+)

Aims and method The Health of the Nation Outcome Scales for Elderly People (HoNOS65+) has been used widely for 20 years, but has not been updated to reflect contemporary clinical practice. The Royal College of Psychiatrists convened an advisory board, with expertise from the UK, Australia and New Zealand, to propose amendments. The aim was to improve rater experience when using the HoNOS65+ glossary by removing ambiguity and inconsistency, rather than a more radical revision. Results Views and experience from the countries involved were used to produce a series of amendments intended to improve intra- and interrater reliability and improve validity. This update will be called HoNOS Older Adults to reflect the changing nature of the population and services provided to meet their needs. These improvements are reported verbatim, together with the original HoNOS65+ to aid comparison. Clinical implications Formal examination of the psychometric properties of the revised measure is needed. However, clinician training will remain crucial