On Optimality of Bayesian Wavelet Estimators

Abstract.  We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of a mass function at zero and a Gaussian density. We show that in terms of the mean squared error, for the properly chosen hyperparameters of the prior, all the three resulting Bayesian wavelet estimators achieve optimal minimax rates within any prescribed Besov space     for p  ≥ 2. For 1 ≤  p  < 2, the Bayes Factor is still optimal for (2 s +2)/(2 s +1) ≤  p  < 2 and always outperforms the posterior mean and the posterior median that can achieve only the best possible rates for linear estimators in this case.     

Tax differentiation,lobbying, and welfare

To what extent a taxing authority should be granted the power to impose different tax schedules to different groups of taxpayers? Although the policy maker aims at maximizing social welfare, her tax policy may be distorted by the lobbying activity of taxpayers. In this political environment we characterize the conditions under which social welfare can be increased by restricting the set of tax instruments available to the policy maker; i.e., the scope of tax differentiation. We show that full differentiation is more costly, in terms of welfare distortions, when the lobbies are asymmetric in size, while minimal differentiation is more costly when the tax bases are asymmetric across different groups.     

Strategies for Europe proposals for science and technology policies industrial innovation in Europe

Europe's performance with respect to industrial innovation is compared to those of USA and Japan. The reasons for Europe's relatively poor performance are examined and related to institutional, cultural and social factors. An appropriate strategy for innovation in European industry is then defined.     

Partial and inverse autocorrelations in portmanteau-type tests for time series

We present a decomposition of the correlation coefficient between x_t and x_t?k into three terms that include the partial and inverse autocorrelations. The first term accounts for the portion of the autocorrelation that is explained by the inner variables {x_t?1 , x_t?2 , …, x _{t? k+1}}, the second one measures the portion explained by the outer variables {x _t+1, x _t+2, } ∪ {x _t?k?1, x _t?k?2,…} and the third term measures the correlation between x _t and x_t?k given all other variables. These terms, squared and summed, can form the basis of three portmanteau-type tests that are able to detect both deviation from white noise and lack of fit of an entertained model. Quantiles of their asymptotic sample distributions are complicated to derive at an adequate level of accuracy, so they are approximated using the Monte Carlo method. A simulation experiment is carried out to investigate significance levels and power of each test, and compare them to the portmanteau test.     

Statistical and computational tradeoff in genetic algorithm-based estimation

When a genetic algorithm (GA) is employed in a statistical problem, the result is affected by both variability due to sampling and the stochastic elements of algorithm. Both of these components should be controlled in order to obtain reliable results. In the present work we analyze parametric estimation problems tackled by GAs, and pursue two objectives: the first one is related to a formal variability analysis of final estimates, showing that it can be easily decomposed in the two sources of variability. In the second one we introduce a framework of GA estimation with fixed computational resources, which is a form of statistical and the computational tradeoff question, crucial in recent problems. In this situation the result should be optimal from both the statistical and computational point of view, considering the two sources of variability and the constraints on resources. Simulation studies will be presented for illustrating the proposed method and the statistical and computational tradeoff question.     

Portmanteau tests based on quadratic forms in the autocorrelations

Many white noise and goodness-of-fit tests are (asymptotically) written as quadratic forms in the ordinary autocorrelation estimates. The properties of such tests are studied by investigating the structure of the matrix of the quadratic form. We suggest to choose the matrix of the quadratic form in such a way that the power is maximized according to the information available about the alternative hypothesis. A simulation study sheds some light on the behavior of the test in finite samples. It is generally found more powerful than the most popular portmanteau tests, i.e., the Box and Pierce and the Ljung and Box tests.     

A Comparison of Address-Based Sampling (ABS) Versus Random-Digit Dialing (RDD) for General Population Surveys

Valid and reliable public health data are becoming more difficultto obtain through random-digit dial (RDD) telephone surveys.As a result, researchers are evaluating different survey designs(i.e., sampling frame and survey mode combinations) as complementsor alternatives to RDD. Traditionally, mail surveys of the generalpublic have been limited due to a lack of a complete samplingframe of households. Recent advances in electronic record keeping,however, have allowed researchers to develop a sample from aframe of addresses (e.g., the U.S. Postal Service Delivery SequenceFile, which appears to provide coverage which rivals or possiblyexceeds that obtained through RDD sampling methods). To testthe use of this frame for surveying adults aged 18 years andolder across a wide geographic area, a pilot study was conductedas part of the 2005 Behavioral Risk Factor Surveillance System(BRFSS). The pilot compared use of a traditional, RDD telephonesurvey methodology to an approach using a mail version of thequestionnaire completed by a random sample of households drawnfrom an address-based frame. The findings indicate that themail survey approach can achieve higher response rates in low-response-ratestates (<40%) than RDD (particularly when two mailings aresent). Additionally, the address frame with mail survey designprovides access to cell phone only households and offers costsavings over the telephone approach. The resulting sample, however,significantly overrepresents non-Hispanic whites and peoplewith higher levels of education.