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## The Method of Random Groups

### Introduction to Variance Estimation (2007-01-01): 21-106 , January 01, 2007

###
*Abstract*

The random group method of variance estimation amounts to selecting two or more samples from the population, usually using the same sampling design for each sample; constructing a separate estimate of the population parameter of interest from each sample and an estimate from the combination of all samples; and computing the sample variance among the several estimates. Historically, this was one of the first techniques developed to simplify variance estimation for complex sample surveys. It was introduced in jute acreage surveys in Bengal by Mahalanobis (1939, 1946), who called the various samples *interpenetrating samples*. Deming (1956), the United Nations Subcommission on Statistical Sampling (1949), and others proposed the alternative term *replicated samples*. Hansen, Hurwitz, and Madow (1953) referred to the *ultimate cluster* technique in multistage surveys and to the *random group* method in general survey applications. Beginning in the 1990s, various writers have referred to the *resampling* technique. All of these terms have been used in the literature by various authors, and all refer to the same basic method. We will employ the term *random group* when referring to this general method of variance estimation.

## Dickey-Fuller Tests

### International Encyclopedia of Statistical Science (2011-01-01): 385-388 , January 01, 2011

## Multivariate Time Series

### Introduction to Time Series and Forecasting (2016-01-01): 227-257 , January 01, 2016

Many time series arising in practice are best considered as components of some vector- valued (multivariate) time series {*X*_{t}} having not only serial dependence within each component series {*X*_{ti}} but also interdependence between the different component series {*X*_{ti}} and {*X*_{tj}}, *i* ≠ *j*. Much of the theory of univariate time series extends in a natural way to the multivariate case; however, new problems arise.

## Components of Statistics

### International Encyclopedia of Statistical Science (2011-01-01): 274-275 , January 01, 2011

## Web-based Multi-center Data Management System for Clinical Neuroscience Research

### Journal of Medical Systems (2010-02-01) 34: 25-33 , February 01, 2010

Modern clinical research often involves multi-center studies, large and heterogeneous data flux, and intensive demands of collaboration, security and quality assurance. In the absence of commercial or academic management systems, we designed an open-source system to meet these requirements. Based on the Apache-PHP-MySQL platform on a Linux server, the system allows multiple users to access the database from any location on the internet using a web browser, and requires no specialized computer skills. Multi-level security system is implemented to safeguard the protected health information and allow partial or full access to the data by individual or class privilege. The system stores and manipulates various types of data including images, scanned documents, laboratory data and clinical ratings. Built-in functionality allows for various search, quality control, analytic data operations, visit scheduling and visit reminders. This approach offers a solution to a growing need for management of large multi-center clinical studies.

## The Spectral Analysis of Stationary Interval Functions

### Selected Works of David Brillinger (2012-01-01): 25-55 , January 01, 2012

We consider stationary. additive. interval functions X(Δ). These are vector valued stochastic processes having real intervals Δ = (α, β] as domain, having finite dimensional distributions invariant under time translation and satisfying

## Point Processes

### Analysis of Neural Data (2014-01-01): 563-603 , January 01, 2014

At the beginning of this book, in Example 1.1 (p. 3), we described the activity of a neuron recorded from the supplementary eye field. Interpreting Fig. 1.1 we said that, toward the end of each trial, the neuron fired more rapidly under one experimental condition than under the other.

## Estimation of semiparametric regression model with longitudinal data

### Lifetime Data Analysis (2010-04-01) 16: 271-298 , April 01, 2010

In a longitudinal study, an individual is followed up over a period of time. Repeated measurements on the response and some time-dependent covariates are taken at a series of sampling times. The sampling times are often irregular and depend on covariates. In this paper, we propose a sampling adjusted procedure for the estimation of the proportional mean model without having to specify a sampling model. Unlike existing procedures, the proposed method is robust to model misspecification of the sampling times. Large sample properties are investigated for the estimators of both regression coefficients and the baseline function. We show that the proposed estimation procedure is more efficient than the existing procedures. Large sample confidence intervals for the baseline function are also constructed by perturbing the estimation equations. A simulation study is conducted to examine the finite sample properties of the proposed estimators and to compare with some of the existing procedures. The method is illustrated with a data set from a recurrent bladder cancer study.

## Implied distributions in multiple change point problems

### Statistics and Computing (2012-07-01) 22: 981-993 , July 01, 2012

A method for efficiently calculating exact marginal, conditional and joint distributions for change points defined by general finite state Hidden Markov Models is proposed. The distributions are not subject to any approximation or sampling error once parameters of the model have been estimated. It is shown that, in contrast to sampling methods, very little computation is needed. The method provides probabilities associated with change points within an interval, as well as at specific points.

## Linear Regression

### Analysis of Neural Data (2014-01-01): 309-359 , January 01, 2014

Regression is the central method in the analysis of neural data. This is partly because, in all its guises, it is the most widely applied technique.