Alan H. Dorfman

Bias robust estimation in finite populations using nonparametric calibration

A Standard problem in sample survey inference is that of predicting the finite population total H of a function h(y) of a random variable Y. The model-based approach to this problem first defines a working model ξ for Y and then predicts H by estimating its expectation under ξ, conditional on the sample values of Y. This approach leads to biased predictions if ξ is incorrect. We explore an automatic solution to this misspecification bias that uses nonparametric regression to define a robust (but inefficient) predictor of H, and then calibrates this predictor for its bias under ξ. An application to prediction of the finite population distribution function of a population of Australian beef farms is presented.

The Sato–Vartia index and the monotonicity axiom

Abstract The Sato–Vartia index is believed to be on a par with the Fisher ideal index in terms of its ability to satisfy index number axioms or tests. Yet we show that this index fails to satisfy the monotonicity axiom, and we provide formulas for the point at which a Sato–Vartia price index becomes non-monotonic in prices. In fact, requiring monotonicity for initial as well as final prices rules out not only the Sato–Vartia index but all log-change price indexes whose weights depend upon initial or final expenditure shares. Since cost of living index theory leads naturally to the Sato–Vartia index, as well as to other log-change indexes, there is an irreconcilable tension between the standard axiomatics for indexes, and cost of living index theory.

A Note on Variance Estimation for the Regression Estimator in Double Sampling

Abstract Double sampling of a finite population occurs when a sample from the population is itself sampled, with the intent of measuring varites in the subsample not already available in the sample. An important example is the regression estimator for means or totals, which uses values of an auxiliary variable from the full sample to estimate the mean of a variable of interest that is available only on the subsample. This article concerns estimation of the variance of the regression estimator. The estimators of variance recommended by Cochran rely solely on the subsample data, at least to first order. This article note proposes variance estimators that make better use of the entire sample.

Visualizing cereal world

We discuss the basic theory of price indices. These form the basis for the Consumer Price Index in the United States. We note situations which can lead to non-robustness and volatility in several different price indices. An experiment to replace survey-based data with point of sales scanner data is being carried out. We visually explore the scanner data and conclude that certain aspects of scanner data can lead to non-robustness of commonly used price indices.