Simplified simplicial depth for regression and autoregressive growth processes
نویسندگان
چکیده
منابع مشابه
Simplified Simplicial Depth for Regression and Autoregressive Growth Processes
We simplify simplicial depth for regression and autoregressive growth processes in two directions. At first we show that often simplicial depth reduces to counting the subsets with alternating signs of the residuals. The second simplification is given by not regarding all subsets of residuals. By consideration of only special subsets of residuals, the asymptotic distributions of the simplified ...
متن کاملDistribution-free tests for polynomial regression based on simplicial depth
A general approach for developing distribution free tests for general linear models based on simplicial depth is presented. In most relevant cases, the test statistic is a degenerated U-statistic so that the spectral decomposition of the conditional expectation of the kernel function is needed to derive the asymptotic distribution. A general formula for this conditional expectation is derived. ...
متن کاملTests for multiple regression based on simplicial depth
A general approach for developing distribution free tests for general linear models based on simplicial depth is applied to multiple regression. The tests are based on the asymptotic distribution of the simplicial regression depth, which depends only on the distribution law of the vector product of regressor variables. Based on this formula, the spectral decomposition and thus the asymptotic di...
متن کاملOn algorithms for simplicial depth
Simplicial depth is a way to measure how deep a point is among a set of points. EEcient algorithms to compute it are important to the usefulness of its applications, such as in multivariate analysis in statistics. A straightforward method takes O(n d+1) time when the points are in d-dimensional space. We discuss an algorithm that takes O(n 2) time when the points are in three-dimensional space,...
متن کاملApproximating the Simplicial Depth
Let P be a set of n points in d-dimensions. The simplicial depth, σP (q) of a point q is the number of d-simplices with vertices in P that contain q in their convex hulls. The simplicial depth is a notion of data depth with many applications in robust statistics and computational geometry. Computing the simplicial depth of a point is known to be a challenging problem. The trivial solution requi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Planning and Inference
سال: 2016
ISSN: 0378-3758
DOI: 10.1016/j.jspi.2016.01.005