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A multivariate Jacobi polynomials regression estimator associated with an ANOVA decomposition model
In this work, we construct a stable and fairly fast estimator for solving multidimensional non-parametric regression problems. The proposed estimator...
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An Interesting Class of Non-Kac Random Polynomials
As evident from classical results on random polynomials, it is difficult to derive the probability distribution of the number of real roots
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Use of primary decomposition of polynomial ideals arising from indicator functions to enumerate orthogonal fractions
A polynomial indicator function of designs is first introduced by Fontana et al. (J Stat Plan Inference 87:149–172, 2000) for two-level cases. They...
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On Accelerating Monte Carlo Integration Using Orthogonal Projections
Monte Carlo simulation is an indispensable tool in calculating high-dimensional integrals. Although Monte Carlo integration is notoriously known for...
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Cyclic Generators for Saturated Orthogonal Arrays
We consider saturated orthogonal arrays (OAs) that can be constructed by repeated cycling of a generator and addition of a final zero row. In...
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Properties of General Systems of Orthogonal Polynomials with a Symmetric Matrix Argument
There exists a large literature of the orthogonal polynomials (OPs) with a single variable associated with a univariate distribution. The theory of...
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Gaussian Systems, T-Hermite Polynomials, Moments, and Cumulants
Hermite polynomials have several applications in many fields of science. We start with the classical Hermite polynomials of one variable, which...
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Mixture Designs Constructed Using Taguchi’s Mixed Element Orthogonal Arrays
This paper proposes an algorithm for generating mixture designs based on Taguchi’s mixed element orthogonal arrays. The algorithm enables the...
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On new omnibus tests of uniformity on the hypersphere
Two new omnibus tests of uniformity for data on the hypersphere are proposed. The new test statistics exploit closed-form expressions for orthogonal...
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Semifoldover plans for three-level orthogonal arrays with quantitative factors
Although foldover designs can de-alias many effects, they involve at least twice the original number of runs. A semifoldover design, one kind of the...
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On a Simple Identity for the Conditional Expectation of Orthogonal Polynomials
Consider a two-dimensional random vector ( X , Y ) T . Let Q 0 , Q 1 ,… denote orthogonal polynomials with respect to the marginal distribution of X and let P
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On Nonparametric Density Estimation for Circular Data: An Overview
This paper provides a short review of modern smoothing methods for density and distribution functions dealing with circular data. We highlight the...
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Variance matrix estimation in multivariate classical measurement error models
Measurement errors are often encountered in several continuous variables in a data set, and various methods have been proposed to handle these...
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Matrix Transformations and Factorizations
In most applications of linear algebra, problems are solved by transformations of matrices. A given matrix (which represents some transformation of a...
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Design efficiency for minimum projection uniform designs with q levels
Minimum projection uniform designs and high efficient designs are two kinds of excellent designs in design of experiment. In this paper, design...
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Polynomial whitening for high-dimensional data
The inverse square root of a covariance matrix is often desirable for performing data whitening in the process of applying many common multivariate...
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Variants of non-symmetric correspondence analysis for nominal and ordinal variables
Non-symmetric correspondence analysis (NSCA) is a multivariate data analysis technique that has gained increasing attention in recent years. NSCA is...
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Linear Regression
Linear regression relates predictor variables and outcome variables, such as gene copy numbers and the level of a biomarker. The assumed linearity of...
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Numerical Integration
Integration is a very common requirement in quantitative finance. In some cases integrals can be evaluated analytically, or at least in terms of...
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Polynomial Series Expansions and Moment Approximations for Conditional Mean Risk Sharing of Insurance Losses
This paper exploits the representation of the conditional mean risk sharing allocations in terms of size-biased transforms to derive effective...
