Weak convergence of sums of moving averages in the α-stable domain of attraction

Skorohod has shown that the convergence of sums of i.i.d. random variables to an a-stable Levy motion, with 0 < a < 2, holds in the weak-J1 sense. J1 is the commonly used Skorohod topology. We show that for sums of moving averages with at least two nonzero coefficients, weak-J1 conver- gence cannot hold because adjacent jumps of the process can coalesce in the limit; however, if the moving average coefficients are positive, then the adjacent jumps are essentially monotone and one can have weak-M1 con- vergence. M1 is weaker than J1, but it is strong enough for the sup and inf functionals to be continuous

Generalized powers of strongly dependent random variables

Generalized powers of strongly dependent random variablesDobrushin, Major and Taqqu have studied the weak convergence of normalized sums of Hm(Yk) where Hm is the Hermite polynomial of order m and where {Yk} is a strongly dependent stationary Gaussian sequence. The limiting process Zm(t) is non-Gaussian when m > l. We study here the weak convergence to Zm(t) of normalized sums of stationary sequences {Uk}. These Uk can be off-diagonal multilinear forms or they can be of the form Uk = pm(\) where the polynomial pm is a generalized power and where \ is a strongly dependent non-Gaussian finite variance moving average.Research supported by the National Science Foundation grant ECS-84-08524 at Cornell Universit

Probability bounds for M-Skorohod oscillations

Originally published as a Technical Report 1 Oct 86-30 Sep 1987, for North Carolina Univ At Chapel Hill Center For Stochastic Processes. Source: Defense Technical Information Center: http://www.dtic.mil/docs/citations/ADA187981Billingsley developed a widely used method for proving weak convergence with respect to the sup-norm and J -Skorohod topologies, once convergence of the finite-dimensional distributions has been established. Billingsley's method works not only for J oscillations, but also for M oscillations. This is done by identifying a common property of the J and M functions, called sub-triadditivity, and then showing that Billingsley's approach in the case of the J function can be adequately modified to apply to any sub-triadditive function.https://www.sciencedirect.com/science/article/pii/0304414989900665?via=ihubPublished versio

A cross-national analysis of the relations between school choice and effectiveness differences between private-dependent and public schools

We apply propensity score matching to the estimation of differential school effectiveness between the publicly funded private sector and the public one, in a sample of 26 countries. This technique allows us to distinguish between school choice and school effectiveness processes and thus, to account for selectivity issues involved in the comparison of the two. Concerning school choice, we found two patterns: a choice of the upwardly mobile parents for private schools and a preference for segregation by (lower-) middle class parents. As regards school effectiveness, our results indicate that, after controlling for selectivity, a substantial advantage in reading achievement remains among students in publicly funded private schools in ten out of the 26 countries.school choice; school effectiveness; private-dependent and public schools; international comparison; PISA data

School sector variation on non-cognitive dimensions: are denominational schools different?

Denominational schooling makes up an important part of European educational systems. Given its specificity, denominational schooling can be expected to place a greater weight on values teaching and moral education. As such, it may be more effective in bringing about certain attitudes and opinions. It also may be more successful in creating a warm and caring atmosphere, thus helping students to better emotionally connect to the school community. This paper set out to empirically test some of these hypotheses by making use of three waves of data collected in the framework of the Program for International Student Assessment study. We compare public and publicly supported private (as a proxy to denominational) schools on two dimensions, namely the emotional integration with the rest of the school community, and the concern and feelings of responsibility towards the environment. But for Austria, Belgium and Spain, no evidence could be found that the type of the school has any impact on the reported psychological adaptation to the school. In these three countries, publicly supported private schools tend to be more successful in integrating their students. Also students in public and private dependent schools were equally environment oriented, taking into account several student and school characteristics. The lack of schooling sector differences in attaining non-cognitive aims may have at least three causes. First, ecological issues could be salient enough not to necessitate any special religious or moral reinforcement in order to gain traction. Second, public schools may use religious education or ethics just as fruitfully and consequently, they are just as successful in values and norms transmission. Third, it is possible that schools play a minor role in introducing students to environmental dilemmas and concerns, this role being taken over by the family or the media.public schools; private schools; non-cognitive; value teaching; psychological integration; PISA data

Choice and Effectiveness of Private and Public Schools in six countries. A reanalysis of three PISA data sets

In international comparative studies on academic achievement, the distinction between private government-dependent schools and private-independent schools has been proven particularly important for understanding the differences in the effectiveness of the private and public school sectors. Despite the fact that higher achievement scores in the private sector are mainly due to their intake selectivity, private-dependent schools tend to outperform public school in most countries if these differences are taken into account. Using a more rigorous statistical technique to control for selectivity in the analysis of three PISA data sets, it is demonstrated that the substantive advantage in the efficacy of private-dependent schools compared to public schools remains for Germany and the Netherlands.private schools; public schools; PISA data; cross-national comparison; educational achievement

School sector variation on non-cognitive dimensions: are denominational schools different?

Denominational schooling makes up an important part of European educational systems. Given its specificity, denominational schooling can be expected to place a greater weight on values teaching and moral education. As such, it may be more effective in bringing about certain attitudes and opinions. It also may be more successful in creating a warm and caring atmosphere, thus helping students to better emotionally connect to the school community. This paper set out to empirically test some of these hypotheses by making use of three waves of data collected in the framework of the Program for International Student Assessment study. We compare public and publicly supported private (as a proxy to denominational) schools on two dimensions, namely the emotional integration with the rest of the school community, and the concern and feelings of responsibility towards the environment. But for Austria, Belgium and Spain, no evidence could be found that the type of the school has any impact on the reported psychological adaptation to the school. In these three countries, publicly supported private schools tend to be more successful in integrating their students. Also students in public and private dependent schools were equally environment oriented, taking into account several student and school characteristics. The lack of schooling sector differences in attaining non-cognitive aims may have at least three causes. First, ecological issues could be salient enough not to necessitate any special religious or moral reinforcement in order to gain traction. Second, public schools may use religious education or ethics just as fruitfully and consequently, they are just as successful in values and norms transmission. Third, it is possible that schools play a minor role in introducing students to environmental dilemmas and concerns, this role being taken over by the family or the media

A Cross-national analysis of the relations between school choice and effectiveness differences between private-independent and public schools

We apply propensity score matching to the estimation of the disparity in school effectiveness between the privately owned, privately funded school sector and the public one in a sample of 25 countries in Europe, America and Asia. This technique allows us to distinguish between school choice and school effectiveness processes and thus, to account for selectivity induced variation in school effectiveness. We find two broad patterns of private independent school choice: the choice as a social class reproduction choice; and the choice of an outsider’s for a good-equipped school. As regards school effectiveness, our results show that, after controlling for selectivity and school choice processes, the initial higher reading scores of students in private-independent schools become comparable to those public schools students in a majority of countries. However, in a few countries average reading scores remain higher in the private independent sector even after introducing controls for school choice induced selectivity. The opposite pattern, namely of higher average reading scores in the public sector has also been found in four countries