Model checking for regressions: an approach bridging between local smoothing and global smoothing methods

朱力行

<p>&nbsp;<span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">For regression models, most of the existing model checking tests can be categorized into the broad class of local smoothing tests and of global smoothing tests.</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">Compared with global smoothing tests, local smoothing tests can only detect local</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">alternatives distinct from the null hypothesis at a much slower rate when the dimension of predictor vector is high, but can be more sensitive to oscillating alternatives.</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">In this paper, we suggest a projection-based test in multivariate scenarios to bridge</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">between the local and global smoothing-based methodologies such that the test can</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">benefit from the advantages of the two types of tests. The test construction rests on</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">a kernel-based method and the resulting test becomes a distance-based test with a</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">closed form. Wild bootstrap is applied to determine the critical values. Simulation</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">results show that the proposed test has better performance than some typical competitors in this area when dimension goes higher. A real data example is analyzed to</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">show its usefulness.</span></p>

2019-12-20(Friday)10:30-11:30

D236

English

统计系

统计系

独立讲座

冯峥晖

<p><span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">朱力行，香港浸会大学数学系教授，统计研究咨询中心主任</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">AAAS、ASA、IMS成员，ISI当选成员</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">国家自然科学奖获得者</span><br style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;" /> <span style="color: rgb(51, 51, 51); font-family: &quot;PingFang SC&quot;, &quot;Lantinghei SC&quot;, &quot;Helvetica Neue&quot;, Arial, &quot;Microsoft YaHei&quot;, &quot;WenQuanYi Micro Hei&quot;, &quot;Heiti SC&quot;, &quot;Segoe UI&quot;, sans-serif; font-size: 14px;">洪堡研究奖获得者</span></p>