Orthogonal Projection in Teaching Regression and Financial Mathematics
نویسنده
چکیده
Two improvements in teaching linear regression are suggested. The first is to include the population regression model at the beginning of the topic. The second is to use a geometric approach: to interpret the regression estimate as an orthogonal projection and the estimation error as the distance (which is minimized by the projection). Linear regression in finance is described as an example of practical applications of the population regression model.
منابع مشابه
Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames
Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...
متن کاملModelling Decision Problems Via Birkhoff Polyhedra
A compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. Directed Hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. Sets of extrema of Birkhoff polyhedra are mapped to tours ...
متن کاملA Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization
Nonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem. At each step of ALS algorithms two convex least square problems should be solved, which causes high com...
متن کاملContractive gauge functions in strongly orthogonal metric spaces
Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...
متن کاملNonparametric Regression in Environmental Statistics
This article provides an introduction to the major types of nonparametric regression techniques, including kernel, spline and orthogonal projection methods. Practical aspects of the methods and their applicability in environmental statistics are emphasized through examples and discussion. Topics covered include bandwidth selection, non-parametric regression in multiple dimensions, and methods f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010