On the Adaptive Partition Approach to the Detection of Multiple Change-Points

With an adaptive partition procedure, we can partition a “time course” into consecutive non-overlapped intervals such that the population means/proportions of the observations in two adjacent intervals are significantly different at a given level . However, the widely used recursive combination or partition procedures do not guarantee a global optimization. We propose a modified dynamic programming algorithm to achieve a global optimization. Our method can provide consistent estimation results. In a comprehensive simulation study, our method shows an improved performance when it is compared to the recursive combination/partition procedures. In practice, can be determined based on a cross-validation procedure. As an application, we consider the well-known Pima Indian Diabetes data. We explore the relationship among the diabetes risk and several important variables including the plasma glucose concentration, body mass index and age

Consistent Pretesting for Jumps

If the intensity parameter in a jump diffusion model is identically zero, then parameters characterizing the jump size density cannot be identified. In general, this lack of identification precludes consistent estimation of identified parameters. Hence, it should be standard practice to consistently pretest for jumps, prior to estimating jump diffusions. Many currently available tests have power against the presence of jumps over a finite time span (typically a day or a week); and, as already noted by various authors, jumps may not be observed over finite time spans, even if the intensity parameter is strictly positive. Such tests cannot be consistent against non-zero intensity. Moreover, sequential application of finite time span tests usually leads to sequential testing bias, which in turn leads to jump discovery with probability one, in the limit, even if the true intensity is identically zero. This paper introduces tests for jump intensity, based on both in-fill and long-span asymptotics, which solve both the test consistency and the sequential testing bias problems discussed above, in turn facilitating consistent estimation of jump diffusion models

Consistent Pretesting for Jumps

If the intensity parameter in a jump diffusion model is identically zero, then parameters characterizing the jump size density cannot be identified. In general, this lack of identification precludes consistent estimation of identified parameters. Hence, it should be standard practice to consistently pretest for jumps, prior to estimating jump diffusions. Many currently available tests have power against the presence of jumps over a finite time span (typically a day or a week); and, as already noted by various authors, jumps may not be observed over finite time spans, even if the intensity parameter is strictly positive. Such tests cannot be consistent against non-zero intensity. Moreover, sequential application of finite time span tests usually leads to sequential testing bias, which in turn leads to jump discovery with probability one, in the limit, even if the true intensity is identically zero. This paper introduces tests for jump intensity, based on both in-fill and long-span asymptotics, which solve both the test consistency and the sequential testing bias problems discussed above, in turn facilitating consistent estimation of jump diffusion models

Environmental odor perception: testing regional differences on heterogeneity with application to odor perceptions in the area of Este (Italy)

One way to evaluate the hazard of environmental degradation of the quality of life in a place, because of bad odors, is to consider the heterogeneity of possible types and of possible sources of malodors. In the literature, the problem of comparing heterogeneities of types or of sources of odors in two geographical areas has not yet been dealt with the due attention. The main reason is that methodological proposals for tests for heterogeneity comparisons are very rare. We propose a permutation test based on the comparison of linear combinations of sampling indices of heterogeneity. The good power behavior, especially for small differences of the degrees of heterogeneity of the two compared areas, is proved through a Monte Carlo simulation study. The application of the test for heterogeneity comparisons on the data of the survey on odor perceptions in the region of Este (Italy) performed in 2010 shows the usefulness of the proposed methodology, which can be added, as a complementary analysis, to the classical established techniques for studying the environmental impact of odors like dispersion models, dynamic olfactometry, smell maps determination, and others