A martingale-transform goodness-of-fit test for the form of the conditional variance

In the common nonparametric regression model the problem of testing for a specific parametric form of the variance function is considered. Recently Dette and Hetzler (2008) proposed a test statistic, which is based on an empirical process of pseudo residuals. The process converges weakly to a Gaussian process with a complicated covariance kernel depending on the data generating process. In the present paper we consider a standardized version of this process and propose a martingale transform to obtain asymptotically distribution free tests for the corresponding Kolmogorov-Smirnov and Cram\'{e}r-von-Mises functionals. The finite sample properties of the proposed tests are investigated by means of a simulation study.Comment: 24 pages

Some asymptotic properties of the spectrum of the Jacobi ensemble

For the random eigenvalues with density corresponding to the Jacobi ensemble $$c \cdot \prod_{i < j} | \lambda_i - \lambda_j |^\beta \prod^n_{i=1} (2 - \lambda_i)^a (2 + \lambda_i)^b I_{(-2,2)} (\lambda_i)$$ $(a, b > -1, \beta > 0)$ a strong uniform approximation by the roots of the Jacobi polynomials is derived if the parameters $a, b,$ $\beta$ depend on $n$ and $n \to \infty$. Roughly speaking, the eigenvalues can be uniformly approximated by roots of Jacobi polynomials with parameters $((2a+2)/\beta -1, (2b+2)/\beta-1)$, where the error is of order $\{\log n/(a+b) \}^{1/4}$. These results are used to investigate the asymptotic properties of the corresponding spectral distribution if $n \to \infty$ and the parameters $a, b$ and $\beta$ vary with $n$. We also discuss further applications in the context of multivariate random $F$-matrices.Comment: 20 pages, 2 figure

Moderate deviations for the eigenvalue counting function of Wigner matrices

We establish a moderate deviation principle (MDP) for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on fine asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson. The extension to large families of Wigner matrices is based on the Tao and Vu Four Moment Theorem and applies localization results by Erd\"os, Yau and Yin. Moreover we investigate families of covariance matrices as well.Comment: 20 page

Optimal experimental designs for inverse quadratic regression models

In this paper optimal experimental designs for inverse quadratic regression models are determined. We consider two different parameterizations of the model and investigate local optimal designs with respect to the $c$-, $D$- and $E$-criteria, which reflect various aspects of the precision of the maximum likelihood estimator for the parameters in inverse quadratic regression models. In particular it is demonstrated that for a sufficiently large design space geometric allocation rules are optimal with respect to many optimality criteria. Moreover, in numerous cases the designs with respect to the different criteria are supported at the same points. Finally, the efficiencies of different optimal designs with respect to various optimality criteria are studied, and the efficiency of some commonly used designs are investigated.Comment: 24 page

(WP 2009-01) Trust in Others: Does Religion Matter?

Though the recent literature offers intuitively appealing bases for, and evidence of a linkage among religious beliefs, religious participation and economic outcomes, evidence on a relationship between religion and trust is mixed. By allowing for an attendance effect, disaggregating Protestant denominations, and using a more extensive data set, probit models of the General Social Survey (GSS), 1975 through 2000, show that Black Protestants, Pentecostals, fundamentalist Protestants, and Catholics, trust others less than individuals who do not claim a preference for a particular denomination. For conservative denominations the effect of religion is though affiliation not attendance. In contrast, liberal Protestants trust others more and this effect is reinforced by attendance. The impact of religion on moderate Protestants is only through attendance, as frequency of attendance increases trust of others while the denomination effect is insignificant

(WP 2008-01) A Model of Religious Investment to Explain the Success of “Megachurches”

Despite their non-traditional approach, megachurches have grown significantly in the United States since 1980. This paper constructs a model of religious investment to examine how “seeker”-oriented megachurches succeed in attracting and retaining new members. The model illustrates that megachurches have been able to encourage additional religious investment through group-based activities. Hence, these activities may be viewed as a subsidy for religious investment. As a result, individuals associated with megachurches increase their religious investment relative to individuals associated with non-megachurches. Data from the FACT2000 survey provide evidence that megachurches employ groups to help subsidize individuals’ religious investment, and that the resulting religious capital rises among members of megachurches relative to members of non-megachurches

God and the Global Economy: Religion and Attitudes Towards Trade and Immigration in the United States

Using the results of a national identity survey, we test the impact of religious affiliation on trade and immigration-policy preferences of US residents while controlling for individual level of skill, political ideology and other important demographic characteristics. Our results show that religion is an important determinant of international-policy preferences as individuals who are pre-Vatican II Catholic or members of a fundamentalist Protestant denomination are more likely to prefer policies that restrict imports and immigration. Religiosity, in contrast, has a separate effect of moderating attitudes towards immigration. In addition, we find evidence of denominational effects among African Americans in that members of fundamentalist denominations tend to favour policies that restrict imports while others do not, implying that statistical results commonly attributed to racial effects may actually be a religion effect