Type system provides a precise description of a programming language. This is a prerequisite for the implementation and use of language. It also conducts mechanical and transparent type-checking on programs to preven...Type system provides a precise description of a programming language. This is a prerequisite for the implementation and use of language. It also conducts mechanical and transparent type-checking on programs to prevent the occurrence of execution error during the running of programs. So, it can be said that, on the one hand, type system works as a formal tool to do mathematical analysis of language; on the other hand, it is a formal method for rigorously and precisely designing and implementing language. In this paper, some basic concepts of type system are discussed first. And then, the implementation of a graph- rewriting- based functional language - SClean's type system is given in details. It is hoped that the proposed method of using and implementing type system is of practical usefulness.展开更多
This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squa...This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n-1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.展开更多
A type checking method for the functional language LFC is presented. A distinct feature of LFC is that it uses Context-Free (CF) languages as data types to represent compound data structures. This makes LFC a dynamica...A type checking method for the functional language LFC is presented. A distinct feature of LFC is that it uses Context-Free (CF) languages as data types to represent compound data structures. This makes LFC a dynamically typed language. To improve efficiency, a practical type checking method is presented, which consists of both static and dynamic type checking. Although the inclusion relation of CF languages is not decidable, a special subset of the relation is decidable, i.e., the sentential form relation, which can be statically checked. Moreover, most of the expressions in actual LFC programs appear to satisfy this relation according to the statistic data of experiments. So, despite that the static type checking is not complete, it undertakes most of the type checking task. Consequently the run-time efficiency is effectively improved. Another feature of the type checking is that it converts the expressions with implicit structures to structured representation. Structure reconstruction technique is presented.展开更多
We suggest the score type tests for goodness-of-fit of conditional heteroscedasticity models in both univariate and multivariate time series.The tests can detect the alternatives converging to the null at a parametric...We suggest the score type tests for goodness-of-fit of conditional heteroscedasticity models in both univariate and multivariate time series.The tests can detect the alternatives converging to the null at a parametric rate.Weight functions are involved in the construction of the tests,which provides us with the flexibility to choose scores,especially under directional alternatives,for enhancing power performance.Furthermore,when the alternatives are not directional,we construct asymptotically distribution-free maximin tests for a large class of alternatives.A possibility to construct score-based omnibus tests is discussed when the alternative is saturated.The power performance is also investigated.A simulation study is carried out and a real data is analyzed.展开更多
基金the National Natural Science Foundation of China (No.69931040), and is also supported by Defense Science and Technology Fundi
文摘Type system provides a precise description of a programming language. This is a prerequisite for the implementation and use of language. It also conducts mechanical and transparent type-checking on programs to prevent the occurrence of execution error during the running of programs. So, it can be said that, on the one hand, type system works as a formal tool to do mathematical analysis of language; on the other hand, it is a formal method for rigorously and precisely designing and implementing language. In this paper, some basic concepts of type system are discussed first. And then, the implementation of a graph- rewriting- based functional language - SClean's type system is given in details. It is hoped that the proposed method of using and implementing type system is of practical usefulness.
基金grant from the Research Grants Council of Hong Kong
文摘This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n-1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.
文摘A type checking method for the functional language LFC is presented. A distinct feature of LFC is that it uses Context-Free (CF) languages as data types to represent compound data structures. This makes LFC a dynamically typed language. To improve efficiency, a practical type checking method is presented, which consists of both static and dynamic type checking. Although the inclusion relation of CF languages is not decidable, a special subset of the relation is decidable, i.e., the sentential form relation, which can be statically checked. Moreover, most of the expressions in actual LFC programs appear to satisfy this relation according to the statistic data of experiments. So, despite that the static type checking is not complete, it undertakes most of the type checking task. Consequently the run-time efficiency is effectively improved. Another feature of the type checking is that it converts the expressions with implicit structures to structured representation. Structure reconstruction technique is presented.
基金supported by the Research Grants Council of Hong Kong (Grant No.HKBU2030/07P)Wu Jianhong was also supported by National Natural Science Foundation of China (Grant No.11001238)+2 种基金Humanities and Social Sciences in Chinese University (Grant No.07JJD790154)Zhejiang Provincial Natural Science Foundation of China (Grant No.Y6090172)Science Fund for Young Scholars of Zhejiang Gongshang University,China (Grant No.Q09-12)
文摘We suggest the score type tests for goodness-of-fit of conditional heteroscedasticity models in both univariate and multivariate time series.The tests can detect the alternatives converging to the null at a parametric rate.Weight functions are involved in the construction of the tests,which provides us with the flexibility to choose scores,especially under directional alternatives,for enhancing power performance.Furthermore,when the alternatives are not directional,we construct asymptotically distribution-free maximin tests for a large class of alternatives.A possibility to construct score-based omnibus tests is discussed when the alternative is saturated.The power performance is also investigated.A simulation study is carried out and a real data is analyzed.
