| dc.contributor.author | Fan, Rocky Yuk-Keung. | en_US |
| dc.date.accessioned | 2014-10-21T12:36:03Z | |
| dc.date.available | 1994 | |
| dc.date.issued | 1994 | en_US |
| dc.identifier.other | AAINN98842 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10222/55438 | |
| dc.description | In this thesis we present a finite sample approximation for the marginal densities of a multivariate M-estimator. The result is particularly useful in robust statistics where an estimator usually is defined implicitly and does not have a closed form, and for small sample problems where the asymptotic results may not be reliable. | en_US |
| dc.description | Precisely, let Y$\sb1,\... ,Y\sb{n}$ be independent m-dimensional random observations such that each observation has a density function which is parameterized by a p-dimensional parameter $\eta$. Let $\\eta$ be an M-estimator of $\eta$, the solution of the system | en_US |
| dc.description | $${1\over n}\Sigma\sbsp{l=1}{n} \Psi\sb{jl}(Y\sb{l},\\eta) = 0,\ j = 1,\...,p.$$Our primary objective is to derive an approximation for the marginal densities of a component in $\\eta$ under $\eta = \eta\sb0.$ The result is then extended to a real-valued function $\rho(\\eta),\ \rho : Re\sp\rho \to \Re$, and finally to a real-valued vector $\rho(\\eta) = \{\rho\sb1(\\eta),\...,\rho\kappa(\\eta)\},\ \rho : Re\sp\rho \to Re\sp{k},\ k \le p$. | en_US |
| dc.description | We begin with an overview of the general problem and some background information. Then we derive the main results and discuss the relationship among our approach and some existing techniques for the problem. In addition, we implement the approximations for several location-scale and multiple regression examples. Finally, we discuss the limitation and some potential applications of our results. | en_US |
| dc.description | Thesis (Ph.D.)--Dalhousie University (Canada), 1994. | en_US |
| dc.language | eng | en_US |
| dc.publisher | Dalhousie University | en_US |
| dc.publisher | | en_US |
| dc.subject | Statistics. | en_US |
| dc.title | Approximations for marginal densities of M-estimators. | en_US |
| dc.type | text | en_US |
| dc.contributor.degree | Ph.D. | en_US |
