Nonparametric regression - some approaches

In this paper we describe two approaches to nonparametric regression. First, we consider the nearest neighbour approach, as a procedure which serves mainly for obtaining an ad hoc smoothing and interpolating. Next, we describe the roughness penalty approach. This gives a certain compromise between the demand for goodness-of-fit of regression curve to the given data and the condition that the regression curve has not too many oscillations

Least orthogonal absolute deviations problem for generalized logistic function

We consider the existence of optimal parameters for generalized logistic model by least orthogonal absolute deviations, and prove the existence of such optimal solution, under the monotonicity condition on the data

A choice of norm in discrete approximation

We consider the problem of choice of norms in discrete approximation. First, we describe properties of the standard l_1, l_2 and l_ ∞ norms, and their essential characteristics for using as error criteria in discrete approximation. After that, we mention the possibility of applications of the so-called total least squares and total least l_p norm, for finding the best approximation. Finally, we take a look at some nonstandard, visual error criteria for qualitative smoothing

Nonparametric regression - some approaches

In this paper we describe two approaches to nonparametric regression. First, we consider the nearest neighbour approach, as a procedure which serves mainly for obtaining an ad hoc smoothing and interpolating. Next, we describe the roughness penalty approach. This gives a certain compromise between the demand for goodness-of-fit of regression curve to the given data and the condition that the regression curve has not too many oscillations

A choice of norm in discrete approximation

We consider the problem of choice of norms in discrete approximation. First, we describe properties of the standard l_1, l_2 and l_ ∞ norms, and their essential characteristics for using as error criteria in discrete approximation. After that, we mention the possibility of applications of the so-called total least squares and total least l_p norm, for finding the best approximation. Finally, we take a look at some nonstandard, visual error criteria for qualitative smoothing