Concentration behavior of the penalized least squares estimator

Consider the standard nonparametric regression model and take as estimator the penalized least squares function. In this article, we study the trade‐off between closeness to the true function and complexity penalization of the estimator, where complexity is described by a seminorm on a class of functions. First, we present an exponential concentration inequality revealing the concentration behavior of the trade‐off of the penalized least squares estimator around a nonrandom quantity, where such quantity depends on the problem under consideration. Then, under some conditions and for the proper choice of the tuning parameter, we obtain bounds for this nonrandom quantity. We illustrate our results with some examples that include the smoothing splines estimator.     

Forecasting the UK economy with a medium-scale Bayesian VAR

We estimate a Bayesian VAR (BVAR) for the UK economy and assess its performance in forecasting GDP growth and CPI inflation in real time relative to forecasts from COMPASS, the Bank of England’s DSGE model, and other benchmarks. We find that the BVAR outperformed COMPASS when forecasting both GDP and its expenditure components. In contrast, their performances when forecasting CPI were similar. We also find that the BVAR density forecasts outperformed those of COMPASS, despite under-predicting inflation at most forecast horizons. Both models over-predicted GDP growth at all forecast horizons, but the issue was less pronounced in the BVAR. The BVAR’s point and density forecast performances are also comparable to those of a Bank of England in-house statistical suite for both GDP and CPI inflation, as well as to the official Inflation Report projections. Our results are broadly consistent with the findings of similar studies for other advanced economies.     

Determination of Discrete Spectrum in a Random Field

We consider a two dimensional frequency model in a random field, which can be used to model textures and also has wide applications in Statistical Signal Processing. First we consider the usual least squares estimators and obtain the consistency and the asymptotic distribution of the least squares estimators. Next we consider an estimator, which can be obtained by maximizing the periodogram function. It is observed that the least squares estimators and the estimators obtained by maximizing the periodogram function are asymptotically equivalent. Some numerical experiments are performed to see how the results work for finite samples. We apply our results on simulated textures to observe how the different estimators perform in estimating the true textures from a noisy data.     

Software for Learning and for Doing Statistics

The community of statisticians and statistics educators should take responsibility for the evaluation and improvement of software quality from the perspective of education. The paper will develop a perspective, an ideal system of requirements to critically evaluate existing software and to produce future software more adequate both for learning and doing statistics in introductory courses. Different kinds of tools and microworlds are needed. After discussing general requirements for such programs, a prototypical ideal software system will be presented in detail. It will be illustrated how such a system could be used to construct learning environments and to support elementary data analysis with exploratory working style.     

On the test of the correction mechanism for mis-pricing between assets using a statistical yield spread model

This paper investigates the existence of a correction mechanism for mis-pricing between Japanese stock and bond. By this correction mechanism we mean that when deviations occur from the equilibrium levels of the expected return differentials between stock and bond — the risk premium differentials, the market will tend to correct the mis-pricing and bring the expected return differentials back to the equilibrium levels. We assume that the yield spread between the predicted earnings price ratio of stock and the yield to maturity of bond reflects the risk premium between stock and bond, and estimate the equilibrium risk premium differentials and mis-prices between stock and bond by modelling their behaviors with a statistical yield spread model (SYS). Empirical results strongly indicate the existence of the mis-pricing correction mechanism, suggesting the inefficiency of securities markets.     

The over-optimism among experts in assessment and foresight

It is still disputed whether foresight exercises should be based on top-expert assessments or on a broader base of less specialised experts, and whether the self-rating of experts is an acceptable method. Using the German 1993 and the Austrian 1998 Technology Delphis, this study addresses both questions. Self-rating is, in fact, an appropriate method for selecting experts. But the assessment of self-rated top experts tend to suffer from an optimism bias due to the experts' involvement and their underestimation of realisation and diffusion problems. The degree of optimism is positively correlated with the degree of self-rated knowledge, and it is more pronounced for the least pioneering and for organizational innovations. Experts with top self-ratings working in business have a stronger optimism bias than those working in the academia or in the administration: Consistent with the insider hypothesis, they are most optimistic with regard to realisation, innovativeness, and potential leadership in economic exploitation. Given the optimism bias, foresight exercises should base their panels on a fair mixture of experts of different grades, with different types of knowledge and affiliation, and not only on top specialists of the respective field. Delphi-type exercises, therefore, offer an advantage relative to forum groups or small panels of specialists.     

Dynamic Panel Data Evidence on the Trade-Income Relation

This paper revisits the relationship between a country’s openness and its per capita income. Building on Frankel and Romer, it argues that a dynamic econometric specification similar to the ones used in empirical growth studies better fits the theoretical literature and also resolves some otherwise unresolved inconsistencies. The preferred econometric method is Blundell and Bond’s system-GMM estimator, which allows dealing with measurement error, weak instruments, and time-invariant country-specific effects. The findings confirm the existence of a strong effect of trade on income but fail to find evidence for trade as an independent factor of divergence. JEL no. F43, O40     

On Measuring the Value of a Nonmarket Good Using Market Data

We use line integral theory to lay out in a more general theoretical framework the conditions under which it is possible to measure with market data the welfare effects of a change in a nonmarket good. We present in detail a numerical method of measuring the value of nonmarket goods using market data, under either weak neutrality or weak complementarity. Our numerical method is more flexible than the existing analytical method because it can be used with any well-behaved Marshallian demand function, and can be used even when the willig condition does not hold.     

A Pricing and Hedging Comparison of Parametric and Nonparametric Approaches for American Index Options

This article investigates the extent to which options on theAustralian Stock Price Index can be explained by parametricand nonparametric option pricing techniques. In particular,comparisons are made of out-of-sample option pricing performanceand hedging performance. The dataset differs from many of thoseused previously in the empirical options pricing literaturein that it consists of American options. In addition, a broaderspectrum of techniques are considered: a spline-based nonparametrictechnique is considered in addition to the standard kernel techniques,while the performance of a Heston stochastic volatility modelis also considered. Although some evidence is found of superiorperformance by nonparametric techniques for in-sample pricing,the parametric methods exhibit a markedly better ability toexplain future prices and show superior hedging performance.