Journal ArticleDOI
Point Estimates of Ordinates of Concave Functions
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TLDR
In this paper, a method for obtaining maximum likelihood estimates of points on a surface of unspecified algebraic form when ordinates of the points are required to satisfy a set of linear inequalities is developed.Abstract:
A method is developed for obtaining maximum likelihood estimates of points on a surface of unspecified algebraic form when ordinates of the points are required to satisfy a set of linear inequalities. A production function with one variable input is considered in some detail. In this case the restrictions follow from the assumption of non-increasing returns. An illustrative computation is worked out using a procedure based on equivalence between the estimation problem and a certain saddle point problem. Alternative procedures for production functions with two variable inputs are sketched.read more
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High-Dimensional Statistics: A Non-Asymptotic Viewpoint
TL;DR: This book provides a self-contained introduction to the area of high-dimensional statistics, aimed at the first-year graduate level, and includes chapters that are focused on core methodology and theory - including tail bounds, concentration inequalities, uniform laws and empirical process, and random matrices.
Journal ArticleDOI
An Algorithm for Restricted Least Squares Regression
TL;DR: In this article, a simple iterative algorithm is presented and shown to converge to the desired solution for minimizing a least square expression subject to side constraints, which is a commonly occurring problem in statistics.
Journal ArticleDOI
Some Estimators for a Linear Model With Random Coefficients
Clifford Hildreth,James P. Houck +1 more
TL;DR: In this article, the linear model given by is considered and a number of consistent estimators of the coefficients, βk, and the variances of the errors are developed and a few properties of the estimators are noted.
References
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Journal ArticleDOI
A Stochastic Approximation Method
Herbert Robbins,Sutton Monro +1 more
TL;DR: In this article, a method for making successive experiments at levels x1, x2, ··· in such a way that xn will tend to θ in probability is presented.
Book ChapterDOI
On the Experimental Attainment of Optimum Conditions
George E. P. Box,K. B. Wilson +1 more
TL;DR: The work described in this article is the result of a study extending over the past few years by a chemist and a statistician, which has come about mainly in answer to problems of determining optimum conditions in chemical investigations, but they believe that the methods will be of value in other fields where experimentation is sequential and the error fairly small.
Journal ArticleDOI
Experimental Determination of the Maximum of a Function
Journal ArticleDOI
Recent advances in finding best operating conditions
TL;DR: This paper is a revision of a paper presented at the 1952 annual meeting of the American Statistical Association and aims to clarify the aims and methodology of this work and provide a basis for future research.