The problem of proving generalization bounds for the performance of learning algorithms can be formulated as a problem of bounding the bias and variance of estimators of the expected error. We show how various stability assumptions can be employed for this purpose. We provide a necessary and sufficient stability condition for bounding the bias and variance for the Empirical Risk Minimization al...

Total variance is a statistical tool developed for improved estimates of frequency stability at averaging times up to half the test duration. As a descriptive statistic, Total variance performs an exact decomposition of the sample variance of the frequency residuals into components associated with descending frequency octaves. As an estimator of Allan variance, Total variance has modest bias an...

Eversince its discovery by Gerletti and Bini (1938), electro-convulsive therapy (E. C. T.) has continued to occupy a central place in the therapeutic armamentarium of psychiatrists. Despite abhorrence from some quarters, it is still being practiced as one of the cheapest and safest, and yet one of the most effective therapeutic techniques in the whole of medical science (Kalinowsky, 1975; Royal...

This paper examines conditions for the uniqueness of an equilibrium price distribution in stochastic macroeconomic models with rational expectations. A model is developed in which many price distributions, each with a finite variance, satisfy the equilibrium requirements of rationality. Hence, the condition that the variance of the equilibrium price distribution be finite, or equivalently, that...

The least mean fourth (LMF) algorithm has several stability problems. Its stability depends on the variance and distribution type of the adaptive filter input, the noise variance, and the initialization of filter weights. A global solution to these stability problems was presented recently for a normalized LMF (NLMF) algorithm. The analysis is done in context of adaptive noise cancellation with...

Example Description 1 Tracer lot stability data { classical linear mixed eeects model 2 Pill dissolution data { classical linear mixed eeects model 3 Rat pup weight data { classical linear mixed eeects model 4 CD4 trajectories { linear mixed model with nonconstant intra-subject variance 5 Soybean growth study { nonlinear mixed model with nonconstant within-plot variance 6 Population PK study of...