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High-Rate Vector Quantization for the Neyman-Pearson Detection of Correlated Processes
This paper investigates the effect of quantization on the performance of the
Neyman-Pearson test. It is assumed that a sensing unit observes samples of a
correlated stationary ergodic multivariate process. Each sample is passed
through an N-point quantizer and transmitted to a decision device which
performs a binary hypothesis test. For any false alarm level, it is shown that
the miss probability of the Neyman-Pearson test converges to zero exponentially
as the number of samples tends to infinity, assuming that the observed process
satisfies certain mixing conditions. The main contribution of this paper is to
provide a compact closed-form expression of the error exponent in the high-rate
regime i.e., when the number N of quantization levels tends to infinity,
generalizing previous results of Gupta and Hero to the case of non-independent
observations. If d represents the dimension of one sample, it is proved that
the error exponent converges at rate N^{2/d} to the one obtained in the absence
of quantization. As an application, relevant high-rate quantization strategies
which lead to a large error exponent are determined. Numerical results indicate
that the proposed quantization rule can yield better performance than existing
ones in terms of detection error.Comment: 47 pages, 7 figures, 1 table. To appear in the IEEE Transactions on
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25 Years of IIF Time Series Forecasting: A Selective Review
We review the past 25 years of time series research that has been published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982-1985; International Journal of Forecasting 1985-2005). During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have been published elsewhere during this period. Enormous progress has been made in many areas, but we find that there are a large number of topics in need of further development. We conclude with comments on possible future research directions in this field.Accuracy measures; ARCH model; ARIMA model; Combining; Count data; Densities; Exponential smoothing; Kalman Filter; Long memory; Multivariate; Neural nets; Nonlinearity; Prediction intervals; Regime switching models; Robustness; Seasonality; State space; Structural models; Transfer function; Univariate; VAR.
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