Computations involved in Bayesian approach to practical model selection problems are usually very difficult. Computational simplifications are sometimes possible, but are not generally applicable. There is a large lit...Computations involved in Bayesian approach to practical model selection problems are usually very difficult. Computational simplifications are sometimes possible, but are not generally applicable. There is a large literature available on a methodology based on information theory called Minimum Description Length (MDL). It is described here how many of these techniques are either directly Bayesian in nature, or are very good objective approximations to Bayesian solutions. First, connections between the Bayesian approach and MDL are theoretically explored;thereafter a few illustrations are provided to describe how MDL can give useful computational simplifications.展开更多
The iterative equation is an equality with an unknown function and its iterates,most of which found from references are a linear combination of those iterates.In this paper,we work on an iterative equation with multip...The iterative equation is an equality with an unknown function and its iterates,most of which found from references are a linear combination of those iterates.In this paper,we work on an iterative equation with multiplication of iterates of the unknown function.First,we use an exponential conjugation to reduce the equation on R+to the form of the linear combination on R,but those known results on the linear combination were obtained on a compact interval or a neighborhood near a fixed point.We use the Banach contraction principle to give the existence,uniqueness and continuous dependence of continuous solutions on R+that are Lipschitzian on their ranges,and construct its continuous solutions on R_(+)sewing piece by piece.We technically extend our results on R_(+)to R_(-)and show that none of the pairs of solutions obtained on R+and R_(-)can be combined at the origin to get a continuous solution of the equation on the whole R,but can extend those given on R+to obtain continuous solutions on the whole R.展开更多
We study the asymptotic distribution of the L1 regression estimator under general condi-tions with matrix norming and possibly non i.i.d.errors.We then introduce an appropriate bootstrap procedure to estimate the dist...We study the asymptotic distribution of the L1 regression estimator under general condi-tions with matrix norming and possibly non i.i.d.errors.We then introduce an appropriate bootstrap procedure to estimate the distribution of this estimator and study its asymptotic properties.It is shown that this bootstrap is consistent under suitable conditions and in other situations the bootstrap limit is a random distribution.展开更多
文摘Computations involved in Bayesian approach to practical model selection problems are usually very difficult. Computational simplifications are sometimes possible, but are not generally applicable. There is a large literature available on a methodology based on information theory called Minimum Description Length (MDL). It is described here how many of these techniques are either directly Bayesian in nature, or are very good objective approximations to Bayesian solutions. First, connections between the Bayesian approach and MDL are theoretically explored;thereafter a few illustrations are provided to describe how MDL can give useful computational simplifications.
基金supported by National Institute of Technology Karnataka Surathkal through Senior Research Fellowship and Indian Statistical Institute Bangalore in the form of a Visiting Scientist position through the Jagadish Chandra Bose Fellowship of Professor Badekkila Venkataramana Rajarama Bhatsupported by Science and Engineering Research Board,Department of Science and Technology,Government of India(Grant No.ECR/2017/000765)supported by National Natural Science Foundation of China(Grant Nos.11831012,12171336 and 11821001).
文摘The iterative equation is an equality with an unknown function and its iterates,most of which found from references are a linear combination of those iterates.In this paper,we work on an iterative equation with multiplication of iterates of the unknown function.First,we use an exponential conjugation to reduce the equation on R+to the form of the linear combination on R,but those known results on the linear combination were obtained on a compact interval or a neighborhood near a fixed point.We use the Banach contraction principle to give the existence,uniqueness and continuous dependence of continuous solutions on R+that are Lipschitzian on their ranges,and construct its continuous solutions on R_(+)sewing piece by piece.We technically extend our results on R_(+)to R_(-)and show that none of the pairs of solutions obtained on R+and R_(-)can be combined at the origin to get a continuous solution of the equation on the whole R,but can extend those given on R+to obtain continuous solutions on the whole R.
基金supported by J.C. Bose National Fellowship, Government of India
文摘We study the asymptotic distribution of the L1 regression estimator under general condi-tions with matrix norming and possibly non i.i.d.errors.We then introduce an appropriate bootstrap procedure to estimate the distribution of this estimator and study its asymptotic properties.It is shown that this bootstrap is consistent under suitable conditions and in other situations the bootstrap limit is a random distribution.
