Statistical Data Fusion

The following sections are included:

• Dedication
• Preface
• Contents

A great deal of the statistical literature deals with a single sample coming from a distribution, univariate or multivariate, and the problem is to identify the distribution or parts thereof by an array of estimation and testing procedures. As such, this practice neglects to bring in information from other sources which could improve the desired inference. Similarly, given time series records, the analysis quite often is based on a single time series, not considering many other related time series to bear upon the problem of interest such as prediction.

This chapter deals with inference for density ratio models, first for onedimensional, and then for p-dimensional tilt functions.

The following sections are included:

• Introduction
• The Bivariate Case
  • Case-Control Application
• The General Multivariate Case
  • Kernel Density Estimation Using Fused Data
  • Bandwidth selection for ĝl
• Semiparametric Regression
  • Case-Control Application
  • Marginalized Empirical Likelihood

This chapter addresses the large sample properties of the estimators of the α’s and β’s and of the estimator of the reference distribution function Ĝ (x) in the density ratio model (1.21) under a slight change of notation.

The following sections are included:

• Introduction
• Normal or Not?
• TS Prediction by Out of Sample Fusion
  • Mortality Prediction
  • Southern Oscillation Index Prediction
  • Unemployment Insurance Weekly Claims
  • Forecasting Mortality Rates
  • Application to VaR Estimation
• Interval Estimation of Small Tail Probabilities
  • Confidence Intervals for Tail Probabilities
  • Repeated Out of Sample Fusion (ROSF)
  • Illustration of ROSF

The following sections are included:

• Introduction
• Simple Weighted Systems of Distributions
  • Likelihood
  • Prior
• Posterior Simulation
• Bayesian Inference
  • Estimation
  • Example: Radar Meteorology
  • Test of Hypotheses
  • Example: Radar Meteorology (Continuation)
• Discussion

This chapter concerns small area estimation under informative sampling and nonresponse. As we shall see, there is an interesting connection between the small area problem, as formulated in the present chapter, and the ideas presented hitherto regarding fusing or merging of information, except that here fusion is addressed as “borrowing strength” from areas where information is available. We shall also see examples of weighted distributions and the appeal to computer generated random data presented in previous chapters.

The following section is included:

• Index