On difference-based variance estimation in nonparametric regression when the covariate is high dimensional

Summary.  We consider the problem of estimating the noise variance in homoscedastic nonparametric regression models. For low dimensional covariates t  ∈  R ^d ,  d =1, 2, difference-based estimators have been investigated in a series of papers. For a given length of such an estimator, difference schemes which minimize the asymptotic mean-squared error can be computed for d =1 and d =2. However, from numerical studies it is known that for finite sample sizes the performance of these estimators may be deficient owing to a large finite sample bias. We provide theoretical support for these findings. In particular, we show that with increasing dimension d this becomes more drastic. If d 4, these estimators even fail to be consistent. A different class of estimators is discussed which allow better control of the bias and remain consistent when d 4. These estimators are compared numerically with kernel-type estimators (which are asymptotically efficient), and some guidance is given about when their use becomes necessary.     

Communicating Asset Risk: How Name Recognition and the Format of Historic Volatility Information Affect Risk Perception and Investment Decisions

An experiment examined how the type and presentation format of information about investment options affected investors' expectations about asset risk, returns, and volatility and how these expectations related to asset choice. Respondents were provided with the names of 16 domestic and foreign investment options, with 10-year historical return information for these options, or with both. Historical returns were presented either as a bar graph of returns per year or as a continuous density distribution. Provision of asset names allowed for the investigation of the mechanisms underlying the home bias in investment choice and other asset familiarity effects. Respondents provided their expectations of future returns, volatility, and expected risk, and indicated the options they would choose to invest in. Expected returns closely resembled historical expected values. Risk and volatility perceptions both varied significantly as a function of the type and format of information, but in different ways. Expected returns and perceived risk, not predicted volatility, predicted portfolio decisions.     

Studienmotivation, Erwerbspartizipation und der Einstieg in den Arbeitsmarkt

Increased student enrollment in public universities has led to a debate on curricula reform with a view to limiting the length of study, particularly by introducing tuition fees for long-time students. It is implicitly assumed in this debate that all students are full-time students. We investigate why and to what extent students participate in the labor market. Furthermore, we study the effects of part-time work on the time it takes to graduate, to find employment and on the level of earnings. We analyze two data sets, first, a survey among students enrolled at the University of Bern conducted during summer 2001 (N = 3360) and secondly, a survey of all university graduates in Switzerland conducted in 2001 (N = 7005). The results show that labor market participation increases the time it takes students to reach graduation. However, labor market experience reduces the time it takes graduates to find employment and increases their earnings by 4 percent if their experience was related to the subject being studied. Labor market participation bearing no relation to university studies has no negative effects on graduate entrance into the labor market. Thus, the study suggests that student participation in the labor market has more beneficial effects than disadvantages. In light of these results curricula reforms should take into account the possibility of gaining labor market experience.     

Nonparametric validation of similar distributions and assessment of goodness of fit

In this paper the problem of assessing the similarity of two cumulative distribution functions F and G is considered. An asymptotic test based on an α-trimmed version of Mallows distance Γ_α( F , G ) between F and G is suggested, thus demonstrating the similarity of F and G within a preassigned Γ_α( F , G ) neighbourhood at a controlled type I error rate. The test proposed is applied to the validation of goodness of fit and for the nonparametric assessment of bioequivalence. It is shown that Γ_α( F , G ) can be interpreted as average and population equivalence. Our approach is illustrated by various examples.     

Stock and Commodity Exchanges [Die Börse (1894)]

Theory and Society -     

Minimax Rates for Estimating the Variance and its Derivatives in Non–Parametric Regression

In this paper the van Trees inequality is applied to obtain lower bounds for the quadratic risk of estimators for the variance function and its derivatives in non–parametric regression models. This approach yields a much simpler proof compared to previously applied methods for minimax rates. Furthermore, the informative properties of the van Trees inequality reveal why the optimal rates for estimating the variance are not affected by the smoothness of the signal g . A Fourier series estimator is constructed which achieves the optimal rates. Finally, a second–order correction is derived which suggests that the initial estimator of g must be undersmoothed for the estimation of the variance.     

On 'class exploitation' in Canada†

Two things make Carl Cuneo's recent (1978) paper on 'rates of exploitation' in Canada remarkable. The first is the magnitudes involved. Cuneo's preferred measure of surplus value (RSV₇), for instance, shows a more than seven-fold increase from 1917 to 1971, indicating a quite spectacular shift in favour of capital in relative income shares in Canadian manufacturing industry. The second thing that makes Cuneo's paper remarkable is the extent to which his findings are inconsistent with findings on income shares reported by 'bourgeois' economists. In a survey of the literature Pen (1971: 164 ff.), for example, reports that in the advanced capitalist economies, the share of income accruing to labour in the economy as a whole has increased substantially and that even if one confines one's attention to the private sector the share of manual workers has not decreased but remained more or less constant in spite of the relative decline in their numbers.¹ Now, it is true that the studies reviewed by Pen approach the problem of income shares with the categories of 'bourgeois' economics while Cuneo approaches the problem with what he regards as Marxist categories, and it is conceivable that this might have accounted for the radical difference in the findings. But still, differences of such magnitude in the trends reported in the shares of capital and labour both give pause and urge a close scrutiny.