Abstract The Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete time, second-order stationary stochastic process. As the sample size varies, the coefficients determine what is called a Levinson–Durbin sequence. A generalized Levinson– Durbin sequence is also defined, and we note that binomial c...

For { t y } a discrete time, second-order stationary process, the Levinson-Durbin recursion is used to determine the coefficients , jk α j=1, … , k, of the best linear predictor of 1 + k y , , ˆ 1 1 1 y y y kk k k k α α − − − = + L best in the sense of minimizing the mean square error. The coefficients jk α determine a Levinson-Durbin sequence. A generalized Levinson-Durbin sequence, a special ...

Modern, high dimensional data has renewed investigation on instrumental variables (IV) analysis, primary focusing on estimation of the included endogenous variable under sparsity and little attention towards specification tests. This paper studies in high dimensions the Durbin-Wu-Hausman (DWH) test, a popular specification test for endogeneity in IV regression. We show, surprisingly, that the D...

An important concern in an observational study is whether or not there is unmeasured confounding, that is, unmeasured ways in which the treatment and control groups differ before treatment, which affect the outcome. We develop a test of whether there is unmeasured confounding when an instrumental variable (IV) is available. An IV is a variable that is independent of the unmeasured confounding a...

This article proposes nonparametric inference procedures for analyzing microarray gene expression data that are reliable, robust, and simple to implement. They are conceptually transparent and require no special-purpose software. The analysis begins by normalizing gene expression data in a unique way. The resulting adjusted observations consist of gene-treatment interaction terms (representing ...

OBJECTIVE To investigate the outcome in children perinatally infected with HIV-1 whose mothers received zidovudine (ZDV) monotherapy in pregnancy. DESIGN Observational retrospective study of a prospectively recruited cohort. SETTING Italian Register for HIV Infection in Children. PATIENTS A group of 216 children perinatally infected with HIV-1, born in 1992-1997 and derived prospectively ...

Dependent Variable: Y Method: Least Squares Date: 05/23/00 Time: 05:55 Sample: 1 33 Included observations: 33 Variable Coefficient Std. Error t-Statistic Prob. C 102192.4 12799.83 7.983891 0.0000 N -9074.674 2052.674 -4.420904 0.0001 P 0.354668 0.072681 4.879810 0.0000 I 1.287923 0.543294 2.370584 0.0246 R-squared 0.618154 Mean dependent var 125634.6 Adjusted R-squared 0.578653 S.D. dependent v...