Least squares estimation for repeated surveys

Least squares estimation for repeated surveys is addressed. Several estimators of current level, change in level and average level over time are developed. Estimators include the recursive regression estimator, which is the best linear unbiased estimator based on all periods of the survey. The recursive regression estimator is designed to minimize the computational complexity associated with best linear unbiased estimation;We assume that the basic data consist of elementary estimators of the parameters of interest associated with different rotation groups and that their covariance structure is based on a components of variance model. Several theoretical results associated with the least squares estimation procedures are derived. In particular, we prove that (1) the recursive regression estimator of current level is optimal in the sense of minimum variance, and (2) the covariance matrix of the recursive least squares estimators converges to a positive definite matrix as the number of periods increases. The theoretical results are applicable to a wide range of estimation procedures and rotation designs;Several applications of the results to the estimation of selected labor force characteristics for the Current Population Survey are discussed. An estimated covariance structure for the data is used to compare alternative estimators and rotation designs. We address the issue of revision of previous estimates when additional observations become available at subsequent periods. We illustrate the fact that the revision of previous estimates provides optimal estimates of level and change which are internally consistent. We also describe a simple procedure for computing unrevised estimates of change whose variances are very close to those of the optimal estimator of change;The consequences of the time-in-sample effects on alternative estimators under assumptions of constant and time-varying time-in-sample effects are examined. Generally, the effect of including time-in-sample effects in the model is to increase the variance of the estimators. The increase in variance is a function of the type of restriction imposed and the length of period used to estimate the time-in-sample effects

Automatic variance control and variance estimation loops

A closed loop servo approach is applied to the problem of controlling and estimating variance in nonstationary signals. The new circuit closely resembles but is not the same as, automatic gain control (AGC) which is common in radio and other circuits. The closed loop nature of the solution to this problem makes this approach highly accurate and can be used recursively in real time

Testing the normality of the gravitational wave data with a low cost recursive estimate of the kurtosis

We propose a monitoring indicator of the normality of the output of a gravitational wave detector. This indicator is based on the estimation of the kurtosis (i.e., the 4th order statistical moment normalized by the variance squared) of the data selected in a time sliding window. We show how a low cost (because recursive) implementation of such estimation is possible and we illustrate the validity of the presented approach with a few examples using simulated random noises.Comment: 4 pages, 3 figures. In the Proceedings of the 3rd workshop on Physics in Signal and Image Processing (Grenoble), 200

Combining information in statistical modelling

How to combine information from different sources is becoming an important statistical area of research under the name of Meta Analysis. This paper shows that the estimation of a parameter or the forecast of a random variable can also be seen as a process of combining information. It is shown that this approach can provide sorne useful insights on the robustness properties of sorne statistical procedures, and it also allows the comparison of statistical models within a common framework. Sorne general combining rules are illustrated using examples from ANOVA analysis, diagnostics in regression, time series forecasting, missing value estimation and recursive estimation using the Kalman Filter

Recursive Compressed Sensing

We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in obtaining the next one, and b) recursive decoding, where the signal estimate from the previous window is utilized in order to achieve faster convergence in an iterative optimization scheme applied to decode the new one. To remove estimation bias, a two-step estimation procedure is proposed comprising support set detection and signal amplitude estimation. Estimation accuracy is enhanced by a non-linear voting method and averaging estimates over multiple windows. We analyze the computational complexity and estimation error, and show that the normalized error variance asymptotically goes to zero for sublinear sparsity. Our simulation results show speed up of an order of magnitude over traditional CS, while obtaining significantly lower reconstruction error under mild conditions on the signal magnitudes and the noise level.Comment: Submitted to IEEE Transactions on Information Theor

Improving forecast accuracy by combining recursive and rolling forecasts

This paper presents analytical, Monte Carlo, and empirical evidence on combining recursive and rolling forecasts when linear predictive models are subject to structural change. Using a characterization of the bias-variance tradeoff faced when choosing between either the recursive and rolling schemes or a scalar convex combination of the two, we derive optimal observation windows and combining weights designed to minimize mean square forecast error. Monte Carlo experiments and several empirical examples indicate that combination can often provide improvements in forecast accuracy relative to forecasts made using the recursive scheme or the rolling scheme with a fixed window width.Economic forecasting ; Econometric models