In this paper, we discuss the problem of testing the hypothesis that the underlying regression isa partial linear model. A test statistic, which is based on the quadratic form of a cusum process of residuals,is propos...In this paper, we discuss the problem of testing the hypothesis that the underlying regression isa partial linear model. A test statistic, which is based on the quadratic form of a cusum process of residuals,is proposed. The asymptotic distributions of the test statistic under null hypothesis and the local alternativehypothesis are given. The number simulation shows that the test is available.展开更多
In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Mar...In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.展开更多
基金This work was partly supported by the Knowledge Innovation Project of ChineseAcademy of Sciences (Grant No. KZCX2-SW-118) and the National Natural Science Foundation of China (Grant No. 19791093).
文摘In this paper, we discuss the problem of testing the hypothesis that the underlying regression isa partial linear model. A test statistic, which is based on the quadratic form of a cusum process of residuals,is proposed. The asymptotic distributions of the test statistic under null hypothesis and the local alternativehypothesis are given. The number simulation shows that the test is available.
基金Supported by National Natural Science Foundations of China(10271062,10571092)a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.HKU 7475/05H)
文摘In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.
