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## Fiducial Theory for Free-Knot Splines

### Contemporary Developments in Statistical Theory (2014-01-01) 68: 155-189 , January 01, 2014

We construct the fiducial model for free-knot splines and derive sufficient conditions to show asymptotic consistency of a multivariate fiducial estimator. We show that splines of degree four and higher satisfy those conditions and conduct a simulation study to evaluate quality of the fiducial estimates compared to the competing Bayesian solution. The fiducial confidence intervals achieve the desired confidence level while tending to be shorter than the corresponding Bayesian credible interval using the reference prior. AMS 2000 subject classifications: Primary 62F99, 62G08; secondary 62P10.

## 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

## Nonparametric Bayes Estimation

### Bayesian Theory and Methods with Applications (2011-01-01) 1: 79-121 , January 01, 2011

For a long time there were a lot of unsuccessful efforts directed toward the solution of many nonparametric problems with the help of the Bayes approach. This can be explained mainly by difficulties a researcher encounter, when he attempts to find a suitable prior distribution, determined on a sample space. Such a distribution in nonparametric problems is chosen in the form of a set of probability distributions on the given sample space. The first work in this field where some progress has been achieved belongs to Ferguson. Ferguson formulated the requirements which must be imposed on a prior distribution

## A semiparametric regression cure model for doubly censored data

### Lifetime Data Analysis (2017-09-01): 1-17 , September 01, 2017

This paper discusses regression analysis of doubly censored failure time data when there may exist a cured subgroup. By doubly censored data, we mean that the failure time of interest denotes the elapsed time between two related events and the observations on both event times can suffer censoring (Sun in The statistical analysis of interval-censored failure time data. Springer, New York, 2006). One typical example of such data is given by an acquired immune deficiency syndrome cohort study. Although many methods have been developed for their analysis (De Gruttola and Lagakos in Biometrics 45:1–12, 1989; Sun et al. in Biometrics 55:909–914, 1999; 60:637–643, 2004; Pan in Biometrics 57:1245–1250, 2001), it does not seem to exist an established method for the situation with a cured subgroup. This paper discusses this later problem and presents a sieve approximation maximum likelihood approach. In addition, the asymptotic properties of the resulting estimators are established and an extensive simulation study indicates that the method seems to work well for practical situations. An application is also provided.

## 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