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.     

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.     

Economic design of one-sided screening procedures based on a correlated variable with all parameters unknown

Summary Economic design of one-sided screening procedures for improving outgoing product quality based on a screening variable is considered for the case with all parameters unknown. It is assumed that the performance and screening variables are jointly normally distributed and that costs are incurred by screening inspection, acceptance of an imperfect item, and disposition of a rejected one. A method for finding optimal cutoff value based on the predictive distribution is presented.     

Cardinality-based equality of opportunities

We study possible rankings of opportunity profiles. An opportunity profile is a list of opportunity sets, one for each agent in the society. We compare profiles on the basis of the notion of “equality of opportunities”. Our main results show the necessary and sufficient conditions for this comparison to be made using exclusively the information provided by two cardinal measures: the number of common alternatives in all sets of a given profile and the difference between the number of alternatives in the individual sets. We also show that, under additional axioms, we can combine these criteria only in a weighted procedure or in some lexicographic refinements of a weighted procedure.      

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.     

Measurement error and panel data1

The underidentification of linear models with measurement error does not necessarily extend to panel data models, as has been shown by GAiliches and Hausman (1986). We discuss and extend some of their results for a simple case and address particular issues concerning identification and asymptotic variances.     

Use of Statistics in the Monetary Policy of the Czech National Bank: The Case of a Country in Transition

In the presented text the authors judge the importance of statistics in the monetary policy of the Czech National Bank (CNB) over the course of the economic transformation process, with particular consideration of changing statistical needs and the possibilities and limits of statistical data exploitation in the monetary analyses. The importance of statistics lies on the level of collection and processing of statistical information and on the level of use of statistical methods to analyse data. Since the start of the 1990s the requirements for statistics were significantly influenced by monetary policy. In the period 1990–1997, monetary targeting was the primary influential factor. Since 1998, the monetary policy is influenced by inflation targeting. Statistical priorities switched from monetary data to economy and financial market data. Much progress has been made in the use of statistical methods for analysing data. Statistics available at present cover the CNB's standard monetary-policy requirements and are on par with those in developed countries. Its further development will reflect the standard changes taking place in the more advanced countries.     

Memory recall errors in retrospective surveys: A reverse record check study

This paper reports on a study to compare self-reports during an interview with staff who attended a University health centre in Turkey, with the records of visits to the same health centre over the previous 12 months. Design of the study reflects the effects of importance of the event, duration since the event, frequency of the occurrence of the event, measurement scale of the event, and bounded and unbounded recalling. In order to assess the extent of recall error, responses to retrospective questions on health centre visits are compared with administrative records. Statistical models are proposed for short and long term human memory recall error effects on responses.     

氡气场观测数据的统计分析

通过在原状土层中选定测孔进行观测数据的统计分析表明,孔中温度的作用、大气压力的作用、孔中温度与大气压力的交互作用、孔中温度与湿度的交互作用、大气压力与湿度的交互作用及孔中温度、大气压力、湿度三者之间的交互作用对氡气场没有显著影响;湿度对氡气场有显著影响。