Orthogonal series density estimation is a powerful nonparametric estimation methodology that allows one to analyze and present data at hand without any prior opinion about shape of an underlying density. The idea of construction of an adaptive orthogonal series density estimator is explained on the classical example of a direct sample from a univariate density. Data-driven estimators, which hav...

two latin squares of order $n$ are orthogonal if in their superposition, each of the$n^{2}$ ordered pairs of symbols occurs exactly once. colbourn, zhang and zhu, in a seriesof papers, determined the integers $r$ for which there exist a pair of latin squares oforder $n$ having exactly $r$ different ordered pairs in their superposition. dukes andhowell defined the same problem for latin squares ...

Biased regression is an alternative to ordinary least squares (OLS) regression, especially when explanatory variables are highly correlated. In this paper, we examine the geometrical structure of the shrinkage factors of biased estimators. We show that, in most cases, shrinkage factors cannot belong to [0, 1] in all directions. We also compare the shrinkage factors of ridge regression (RR), pri...

ly, regression is orthogonal projection in n-dimensional space. The data y are a vector of dimension n, which we consider an element of the vector space Rn. Let x1, . . ., xp denote the columns of X. Then

The paper proposes a novel construction algorithm for generalized Gaussian kernel regression models. Each kernel regressor in the generalized Gaussian kernel regression model has an individual diagonal covariance matrix, which is determined by maximizing the correlation between the training data and the regressor using a repeated guided random search based on boosting optimization. The standard...

Much of longitudinal data analysis begins with dimensionality reduction, i.e., the replacement of the T observations x1 , x2 , …, xT on an individual taken at times t1 , t2 , …, tT (not necessarily equally spaced) by a smaller number, P, of parameters which are then used to describe and compare growth processes. We focus on the class of polynomial growth curve models for one-sample data matrice...