The Cross-Product Estimator in Matched Case-Control Studies
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This paper is devoted to a study of the unmatched cross-product estimator of relative risk in a I : M matched case-control study. It is shown that this estimator is consistent for the ‘case-adjusted relative risk’ in rare disease settings. The cross-product estimator has a much wider range of applicability than the classical matched methods, which require a conditionally independent binomial model with a common odds ratio. In general, the methods estimate different parameters. However, in the special situation where the risk factor classification of cases and matched controls are unconditionally independent, the two definitions of relative risk do agree. When this does occur, the proposed method is asymptotically superior to the classical methods. This paper also considers the optimal number of matched controls per case and sample size selection.
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We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for consistency and asymptotic normality of the estimators, which hold when both the cross-sectional dimension $n$ and the sample size $T$ tend to infinity. Special emphasis is placed on identification. First, we show that the common and…