Adaptive procedures in convolution models with known or partially known noise distribution

In a convolution model, we observe random variables whose distribution is the convolution of some unknown density f and some known or partially known noise density g. In this paper, we focus on statistical procedures, which are adaptive with respect to the smoothness parameter tau of unknown density f, and also (in some cases) to some unknown parameter of the noise density g. In a first part, we assume that g is known and polynomially smooth. We provide goodness-of-fit procedures for the test H_0:f=f_0, where the alternative H_1 is expressed with respect to L_2-norm. Our adaptive (w.r.t tau) procedure behaves differently according to whether f_0 is polynomially or exponentially smooth. A payment for adaptation is noted in both cases and for computing this, we provide a non-uniform Berry-Esseen type theorem for degenerate U-statistics. In the first case we prove that the payment for adaptation is optimal (thus unavoidable). In a second part, we study a wider framework: a semiparametric model, where g is exponentially smooth and stable, and its self-similarity index s is unknown. In order to ensure identifiability, we restrict our attention to polynomially smooth, Sobolev-type densities f. In this context, we provide a consistent estimation procedure for s. This estimator is then plugged-into three different procedures: estimation of the unknown density f, of the functional \int f^2 and test of the hypothesis H_0. These procedures are adaptive with respect to both s and tau and attain the rates which are known optimal for known values of s and tau. As a by-product, when the noise is known and exponentially smooth our testing procedure is adaptive for testing Sobolev-type densities.Comment: 35 pages + annexe de 8 page

On (Not) Making Oneself Known

This chapter uses an exploration of the nature of selfhood in Hamlet to stage a discussion of the concept of literary knowledge. What does it mean to claim for our various practices of literary production that they can yield, collectively if not always individually, a “form of knowing”: that there exist distinctly literary ways of making sense of the world and thus of presenting it as an object of understanding? Making sense of this, this chapter argues, requires an account of the nature of narrative and the manner in which it bestows a distinct form of intelligibility upon the events it relates. Hamlet brings to view a striking feature of the nature of this intelligibility and its role in generating the forms of meaning that make Hamlet, and literary narrative more generally, elusive.</p

Limited Liability and the Known Unknown

Limited liability is a double-edged sword. On the one hand, limited lia-bility may help overcome investors’ risk aversion and facilitate capital formation and economic growth. On the other hand, limited liability is widely believed to contribute to excessive risk-taking and externaliza-tion of losses to the public. The externalization problem can be mitigated imperfectly through existing mechanisms such as regulation, mandatory insurance, and minimum capital requirements. These mechanisms would be more effective if information asymmetries between industry and poli-cymakers were reduced. Private businesses typically have better infor-mation about industry-specific risks than policymakers. A charge for limited liability entities—resembling a corporate income tax but calibrated to risk levels—could have two salutary effects. First, a well-calibrated limited liability tax could help compensate the public fisc for risks and reduce externalization. Second, a limited liability tax could force private industry actors to reveal information to policymakers and regulators, thereby dynamically improving the public response to externalization risk. Charging firms for limited liability at initially similar rates will lead relatively low-risk firms to forgo limited liability, while relatively high-risk firms will pay for limited liability. Policymakers will then be able to focus on the industries whose firms have self-identified as high risk, and thus develop more finely tailored regulatory responses. Because the ben-efits of making the proper election are fully internalized by individual firms, whereas the costs of future regulation or limited liability tax changes will be borne collectively by industries, firms will be unlikely to strategically mislead policymakers in electing limited or unlimited lia-bility. By helping to reveal private information and focus regulators’ at-tention, a limited liability tax could accelerate the pace at which poli-cymakers learn, and therefore, the pace at which regulations improve

The Known and the Unknown

Hello everyone and happy Wednesday! I\u27ve just emerged from another week in the world of CONTENTdm and I feel like I\u27m understanding more and more what it likes and what it doesn\u27t like. Thus far, I\u27ve added a digitized image of the reverse side of close to 30 Tipton photographs! [excerpt

The importance of incentives in influencing private retirement saving: known knowns and known unknowns

We summarise what economic theory predicts about how retirement savings decisions are affected by marginal withdrawal rates created by the tax, tax credit and benefit system, and by the information individuals are provided with. All these predictions vary across individuals with their circumstances. In documenting the incentives to save in a private pension provided by the tax, tax credit and benefit system we show that some individuals face a very strong incentive to place funds in a private pension at particular times during their working lives. Those who are basic rate taxpayers who expect to become higher rate taxpayers or move onto the taper of the Working Tax Credit have an incentive to delay making any private pension contributions until that time, while those expecting to move off that taper have an incentive to bring forward future pension contributions. When examining retirement saving it is important to consider both saving decisions and also the choice of retirement age. We cite previous evidence that both of these margins have been adjusted by individuals in the light of changed financial incentives. In particular there is evidence that spending by working age individuals was increased in the light of the introduction of the State Earnings-Related Pension Scheme. In addition evidence from West Germany and the United States shows that individuals' retirement ages can be affected substantially by changing financial incentives. There is less evidence of reduced spending by working age individuals in the light of the decision to index the Basic State Pension in line with prices rather than the greater of prices or earnings. New evidence from the English Longitudinal Study of Ageing shows that it is low and high wealth individuals who are most likely to be out of the labour market prior to the State Pension Age, though often for very different stated reasons. This suggests that if retirement incomes of those with low wealth are to be increased then increased labour market participation is perhaps a margin for them to adjust. Incentives to work and save are potentially affected by two recent UK reforms: the introduction of the two new tax credits (Working Tax Credit and Child Tax Credit) and the introduction of the Pension Credit. We present some preliminary evidence on whether the strong incentive to contribute to a private pension provided by the two new tax credits has boosted private pension participation, the results of which are somewhat inconclusive and are worthy of further research. Examining the distribution of current pensioner incomes with respect to the incentives induced by the Pension Credit reform we find that many single pensioners will see an unambiguous increase in the incentive to increase their private retirement income -- for example through increased saving or later retirement. There are still large numbers of single pensioners who see a reduction in the incentive to increase their retirement income, the majority of whom have private income which they might decide to reduce. Fewer individuals in pensioner couples are eligible for the Pension Credit. Despite this we find that a similar proportion faces a reduced incentive to acquire greater income as we did for single pensioners. If the expectations of individuals do not reflect the current rules of the system, then we cannot expect to observe responses fully in line with economic theory that is predicated on full information. Recent evidence from the English Longitudinal Study of Ageing suggests that on average individuals underestimate their longevity and overestimate the private pension income that they can expect to receive. On the other hand, expectations of being in paid employment at older ages are, on average, similar to the current proportions of older individuals who are in paid work and individuals' expectations of remaining in the labour market at older ages appear to square up with the marginal financial incentives to remain in work that are created by different types of pension scheme

If Archimedes would have known functions

These are notes and slides from a Pecha-Kucha talk given on March 6, 2013. The presentation tinkered with the question whether calculus on graphs could have emerged by the time of Archimedes, if the concept of a function would have been available 2300 years ago. The text first attempts to boil down discrete single and multivariable calculus to one page each, then presents the slides with additional remarks and finally includes 40 "calculus problems" in a discrete or so-called 'quantum calculus' setting. We also added some sample Mathematica code, gave a short overview over the emergence of the function concept in calculus and included comments on the development of calculus textbooks over time.Comment: 31 pages, 36 figure

A.D.XENOPOL, A LESS KNOWN ECONOMIST

Outstanding Romanian man of culture in the second half of the XIXa€™th century, known as remarkable historian, A.D.Xenopol was also a genuine economist, preoccupied not only by the theory but also by the practice of economics. I have achieved an investigA.D.Xenopol, economist, XIXth century, thematic works, of present interest