Exponentiated half logistic distribution: Different estimation methods and joint confidence regions

In this article, we study the problem of estimating the unknown shape and scale parameters of the exponentiated half logistic distribution. For the maximum-likelihood estimation, we obtain a necessary and sufficient condition for the existence and uniqueness of maximum-likelihood estimates of the parameters. Inverse moment and modified inverse moment estimators are derived. Monte Carlo simulations are conducted to compare their performances. Two methods for constructing joint confidence regions for the two parameters are also proposed and their performances are discussed. A numerical example is presented to illustrate the methods.     

Transformed GARMA model: Properties and simulations

Real time series can present anomalies, like non-additivity, non-normality, and heteroscedasticity, which makes using GARMA models impossible. Our article introduces a new class of models called Transformed Generalized Autoregressive Moving Average (TGARMA) models that allow using transformations to guarantee the GARMA assumptions. We present an extensive simulation study of the influence of the transformation on GARMA estimation. We also propose using bootstrap methods to get more information about the distribution of the transformation parameter. We apply the methodology to data related to annual Swedish fertility rates.     

A study on imbalance support vector machine algorithms for sufficient dimension reduction

Li et al. (2011 Li, B., Artemiou, A., Li, L. (2011). Principal support vector machine for linear and nonlinear sufficient dimension reduction. Ann. Stat. 39:3182–3210.[Crossref], [Web of Science ®] , [Google Scholar]) presented the novel idea of using support vector machines (SVMs) to perform sufficient dimension reduction. In this work, we investigate the potential improvement in recovering the dimension reduction subspace when one changes the SVM algorithm to treat imbalance based on several proposals in the machine learning literature. We find out that in most situations, treating the imbalanced nature of the slices will help improve the estimation. Our results are verified through simulation and real data applications.     

Some families of group divisible designs

Generalizing methods of constructions of Hadamard group divisible designs due to Bush (1979), some new families of semi-regular or regular group divisible designs are produced. Furthermore, new nonisomorphic solutions for some known group divisible designs are given, together with useful group divisible designs not listed in Clatworthy (1973).     

On the norm of alias matrices in balanced fractional 2m factorial designs of resolution 2l + 1

The norm $\text{6A6 = {tr(A′A)}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ of the alias matrix A of a design can be used as a measure for selecting a design. In this paper, an explicit expression for 6A6 will be given for a balanced fractional 2^m factorial design of resolution 2l + 1 which obtained from a simple array with parameters (m; λ₀, λ₁,…, λ_m). This array is identical with a balanced array of strength m, m constraints and index set {λ₀, λ₁,…, λ_m}. In the class of the designs of resolution V (l = 2) obtained from S-arrays, ones which minimize 6A6 will be presented for any fixed N assemblies satisfying (i) m = 4, 11 ? N ? 16, (ii) m = 5, 16 ? N ? 32, and (iii) m = 6, 22 ? N ? 40.     

General definition and decomposition of projectors and some applications to statistical problems

A general definition of a set of projectors for decomposing a vector as the sum of vectors belonging to disjoint subspaces not necessarily spanning the whole space is given. Such projectors are defined only over the union of the disjoint subspaces. But their extension to the whole space is of some interest in statistical problems. Explicit expressions are obtained for projectors and their extensions in terms of matrices spanning the subspaces and g-inverses. Decomposition of a projector as the sum of projectors on subspaces is obtained and applied to problems arising in correlation analysis, analysis of variance and estimation of parameters in the Gauss-Markoff model.     

Estimating the structural dimension of regressions via parametric inverse regression

A new estimation method for the dimension of a regression at the outset of an analysis is proposed. A linear subspace spanned by projections of the regressor vector X , which contains part or all of the modelling information for the regression of a vector Y on X , and its dimension are estimated via the means of parametric inverse regression. Smooth parametric curves are fitted to the p inverse regressions via a multivariate linear model. No restrictions are placed on the distribution of the regressors. The estimate of the dimension of the regression is based on optimal estimation procedures. A simulation study shows the method to be more powerful than sliced inverse regression in some situations.     

Modeling low birth weights using threshold regression: results for U. S. birth data

Babies born live under 2,500 g or with a gestational age under 37 weeks are often inadequately developed and have elevated risks of infant mortality, congenital malformations, mental retardation, and other physical and neurological impairments. In this paper, we model birth weight as a first hitting time (FHT) of a birthing boundary in a Wiener process representing fetal development. We associate the parameters of the process and boundary with covariates describing maternal characteristics and the birthing environment using a relatively new regression methodology called threshold regression. Two FHT models for birth weight are developed. One is a mixture model and the other a competing risks model. These models are tested in a case demonstration using a 4%-systematic sample of the more than four million live births in the United States in 2002. An extensive data set for these births was provided by the National Center for Health Statistics. The focus of this paper is on the conceptual framework, models and methodology. A full empirical study is deferred to a later occasion.     

Variance least squares estimators for multivariate linear mixed model

Non-iterative, distribution-free, and unbiased estimators of variance components by least squares method are derived for multivariate linear mixed model. A general inter-cluster variance matrix, a same-member only general inter-response variance matrix, and an uncorrelated intra-cluster error structure for each response are assumed. Projection method is suggested when unbiased estimators of variance components are not nonnegative definite matrices. A simulation study is conducted to investigate the properties of the proposed estimators in terms of bias and mean square error with comparison to the Gaussian (restricted) maximum likelihood estimators. The proposed estimators are illustrated by an application of gene expression familial study.