Nonindependent Errors Research Articles

Data Analysis: A Model-Comparison Approach

1. Introduction to Data Analysis. 2. Simple Models: Definitions of Error and Parameter Estimates. 3. Simple Models: Models of Error and Sampling Distributions. 4. Simple Models: Statistical Inferences about Parameter Values. 5. Simple Regression: Estimating Models with a Single Continuous Predictor. 6. Multiple Regression: Models with Multiple Continuous Predictors. 7. Moderated and Nonlinear Regression Models. 8. One-Way ANOVA: Models with a Single Categorical Predictor. 9. Factorial ANOVA: Models with Multiple Categorical Predictors and Product Terms. 10. Models with Continuous and Categorical Predictors: ANCOVA. 11.Repeated-Measures ANOVA: Models with Nonindependent Errors. 12. Continuous Predictors with Nonindependent Observations. 13. Outliers and Ill-Mannered Error.

The Analysis of a Statistical Multiplexer with Nonindependent Arrivals and Errors

Most stochastic models for discrete time statistical multiplexers make the assumption that 1) arrivals are governed by a Bernoulli process and that 2) transmission errors or multiplexer failures are described by an independent error process. We study a multiplexer operating in a two state Markovian environment in which each state is characterized by its own Bernoulli arrival process and independent error process. We derive the probability generating function for the queue length distribution for such a system. We also consider two special cases of this model. One referred to as the saturated arrival model corresponds to a system in which during one of the two states, the saturated state, at least one arrival occurs during each discrete time unit. The other model, the breakdown model, corresponds to a system in which during one of the two states, the breakdown state, the multiplexer is inoperative. For both models, we generalize the analysis to cases in which the durations of the saturated state and breakdown state may take on values described by arbitrary distributions. Finally, we study the effects of different arrival processes and error processes on queue length behavior.

Effects of ARMA Errors on the Significance Tests for Regression Coefficients

Abstract It Is well known that nonindependent errors arising from autoregressive (AR) or moving average (MA) processes may reverse the conclusions of t or F tests for estimable functions of regression coefficients. We show that these conclusions can be reversed only if observed t or F values based on ordinary least squares (OLS) computations lie between certain lower and upper bounds. Our tabulations of these bounds are based on the Imhof [5] distribution of a ratio of quadratic forms in normal variables, and avoid some of the approximations used by Watson and Hannan [16].

Linear block codes for nonindependent errors

A computerised search procedure based on certain properties of the parity-check matrix of those block codes capable of correcting nonindependent errors is described which yields a considerable number of linear block codes that are capable of correcting random or burst errors.

Statistical Properties of Gilbert's Burst Noise Model

Simple statistical procedures for analyzing error data, e.g., in digital data transmission systems, are usually based on the assumption of independence. This paper studies the performance and potential utility of such simple statistical procedures in the case of nonindependent error occurrences. The burst noise model is selected for this purpose because of its neatness, its mathematical tractability, its built-in structure of dependence, and its importance in communication theory. We show that statistical procedures designed under the assumption of independence tend to be conservative for the burst noise model. For example, the usual binomial test will reject, on the average, more channels with small error rates than it would if the errors were independent. The case that the sample size n and the error rate ρ converge in such a way that nρ→ µ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> is also studied. It is shown that the error process can be approximated by a compound Poisson process in continuous time t. The statistical implications of this fact are also discussed.

Convergence of Distributions Generated by Stationary Stochastic Processes

Convergence of Distributions Generated by Stationary Stochastic Processes

Interpretation of the standard error of measurement when true scores and error scores on mental tests are not independent.

It is shown that for the case of non-independence of true scores and error scores interpretation of the standard error of measurement is modified in two ways. First, the standard deviation of the distribution of error scores is given by a modified equation. Second, the confidence interval for true score varies with the individual's observed score. It is shown that the equation, so=√[(N−O/a]+[so2(roō−roo)/roō]̄, where N is the number of items, O is the individual's observed score, a is the number of choices per item, so2 is observed variance, roo is test reliability as empirically determined, and roō is reliability for the case where only non-independent error is present, provides a more accurate interpretation of the test score of an individual.

Empirical estimates of intercorrelations among the components of scores on multiple-choice tests.

College students were instructed to indicate on various multiple-choice tests whether they “knew the answer” or “guessed” each item, and the results were treated as estimated true and error components of scores. The values of the intercorrelations of these components were similar to those given by a computer program described previously. The values found for all tests were consistent with the assumption that test scores consist of both independent and non-independent components of error and that the non-independent error component is relatively large.