Least squares estimation in the monotone single index model

Semiparametric Least Squares Estimation of Monotone Single Index Models and Its Application to the Itelative Least Squares Estimation of Binary Choice Models

The Semiparametric Least Squares (SLS) estimation for single index models is studied. Applying the isometric regression by Ayer et al (1955), the method minimizes the mean squared errors with respect to both finite and infinite dimensional parameters. A proof of consistency and an upper bound of convergence rates is offered. As an application example of the SLS estimation, asymptotic normality ...

Penalized least squares for single index models

The single index model is a useful regression model. In this paper, we propose a nonconcave penalized least squaresmethod to estimate both the parameters and the link function of the single index model. Compared to other variable selection and estimation methods, the proposed method can estimate parameters and select variables simultaneously.When the dimension of parameters in the single indexm...

Least Squares estimation of two ordered monotone regression curves

In this paper, we consider the problem of finding the Least Squares estimators of two isotonic regression curves g◦ 1 and g◦ 2 under the additional constraint that they are ordered; e.g., g◦ 1 ≤ g◦ 2 . Given two sets of n data points y1, .., yn and z1, . . . , zn observed at (the same) design points, the estimates of the true curves are obtained by minimizing the weighted Least Squares criterio...

Least Squares Estimation

Recursive Least Squares Estimation

We start with estimation of a constant based on several noisy measurements. Suppose we have a resistor but do not know its resistance. So we measure it several times using a cheap (and noisy) multimeter. How do we come up with a good estimate of the resistance based on these noisy measurements? More formally, suppose x = (x1, x2, . . . , xn) T is a constant but unknown vector, and y = (y1, y2, ...