Sub-sample Estimation Research Articles

Binding of nontarget microorganisms from food washes to anti-Salmonella and anti-E. coli O157 immunomagnetic beads: minimizing the errors of random sampling in extreme dilute systems

For most applications, 3-5 observations, or samplings (n), are utilized to estimate total aerobic plate count in an average population (μ) that is greater than about 50 cells, or colony forming units (CFU), per sampled volume. We have chosen to utilize a 6 × 6 drop plate method for bacterial colony selection because it offers the means to rapidly perform all requisite dilutions in a 96-well format and plate these dilutions on solid media using minimal materials. Besides traditional quantitative purposes, we also need to select colonies which are well-separated from each other for the purpose of bacterial identification. To achieve this goal using the drop plate format requires the utilization of very dilute solutions (μ < 10 CFUs per sampled drop). At such low CFU densities the sampling error becomes problematic. To address this issue we produced both observed and computer-generated colony count data and divided a large sample of individual counts randomly into N subsamples each with n = 2-24 observations (N × n = 360). From these data we calculated the average total mean-normalized (x⁻(tot), n = 360) deviation of the total standard deviation (s (tot)) from each jth subsample's estimate (s ( j )), which we call Δ. When either observed or computer-generated Δ values were analyzed as a function of x⁻(tot), a set of relationships (∞ ₋₂√ ⁻x(tot)) were generated which appeared to converge at an n of about 18 observations. This finding was verified analytically at even lower CFU concentrations (⁻x(tot) ≈ 1 − 10 CFUs per observation). Additional experiments using the drop plate format and n = 18 samplings were performed on food samples along with most probable number (MPN) analyses and it was found that the two enumeration methods did not differ significantly.

Estimating the underlying signal waveform, noise covariance and synchronization jitter from unsynchronized measurements

In this paper a new synchronization technique is presented for applications using repeated measurements or experiments with periodically excited signals. The objective with repeated or periodic measurements is often to retrieve an estimate of the (noise reduced) signal and its uncertainties. However, these measurements need to be synchronized to obtain accurate estimates. Existing synchronization techniques are limited to specific signal and noise conditions, such as white Gaussian noise or narrowband signals, to achieve good performance. The proposed method, not limited by these conditions, extracts statistical information regarding the underlying signal and the noise contained in the measurements, to obtain good synchronization (asymptotically optimal). The Cramér–Rao lower bound (CRLB) is derived for the synchronization problem, including bounds for the underlying signal waveform and the covariance of the measurement noise, both considered unknown. The method, which is shown to be the maximum-likelihood estimator (MLE) in both white and colored Gaussian noise, is compared with the CRLB along with standard sub-sample estimation and aligning techniques using Monte Carlo simulations. The results show significant mean square error (MSE) improvements compared to standard synchronization techniques. Synchronization results using the proposed technique are presented for repeated ultrasonic measurements, to validate the method in a real measurement situation, and to experimentally support theoretical results.

Continuous delay estimation with polynomial splines

Delay estimation is used in ultrasonic imaging to estimate blood flow, determine phase aberration corrections, and to calculate elastographic images. Several algorithms have been developed to determine these delays. The accuracy of these methods depends in differing ways on noise, bandwidth, and delay range. In most cases relevant to delay estimation in ultrasonics, a subsample estimate of the delay is required. We introduce two new delay algorithms that use cubic polynomial splines to continuously represent the delay. These algorithms are compared to conventional delay estimators, such as normalized cross correlation and autocorrelation, and to another spline-based method. We present simulations that compare the algorithms' performance for varying amounts of noise, delay, and bandwidth. The proposed algorithms have better performance, in terms of bias and jitter, in a realistic ultrasonic imaging environment. The computational requirements of the new algorithms also are considered.

Convex combinations of long memory estimates from different sampling rates

This paper investigates convex combinations of long memory estimates from both the original and sub-sampled data. Sub-sampling is carried out by decreasing the sampling rate, which leaves the long memory parameter unchanged. Any convex combination of these sub-sample estimates requires a preliminary correction for the bias observed at lower sampling rates, reported by Souza and Smith (2002). Through Monte Carlo simulations, we investigate the bias and the standard deviation of the combined estimates, as well as the root mean squared error (RMSE). Combining estimates can significantly lower the RMSE of a standard estimator (by about 30% on average for ARFIMA (0, d, 0) series), at the cost of inducing some bias.

Comparison of Mean Length at Age and Growth Parameters of Bluegills, Largemouth Bass, and Yellow Perch from Length‐Stratified Subsamples and Samples in Michigan Lakes

AbstractEstimates of mean length at age and von Bertalanffy growth parameters estimated from mean length at age can be biased if based only on age information collected from length‐stratified subsamples. However, historic data are often limited to length‐stratified subsample summaries. To evaluate the potential for using historic length‐stratified subsamples to compare the average growth of fishes among Michigan lakes, we quantified the subsample bias in estimates of the mean lengths at ages 1–10 and von Bertalanffy growth parameters for bluegills Lepomis macrochirus, largemouth bass Micropterus salmoides, and yellow perch Perca flavescens. In regression analysis of estimates based on subsamples and full samples, only two of nine possible tests indicated significant bias in subsamples relative to samples. The mean lengths at ages 1–10 based on subsamples were not biased. Von Bertalanffy growth parameters indicated no bias for bluegill asymptotic length L∞, largemouth bass early growth rate ω, and yellow perch ω. In contrast, bluegill ω estimates were lower when estimated from subsamples than when estimated from samples, and the bias increased with the magnitude of the sample parameter estimate. While regression tests showed that subsample estimates were generally linearly related to sample estimates, the magnitude of the variability in relative bias around von Bertalanffy estimates across lakes was large for all species tested. Our findings suggest that mean lengths at ages 1–10 for bluegills, largemouth bass, and yellow perch estimated from length‐stratified subsamples were not generally biased, but large variation in von Bertalanffy growth parameter estimates limits their usefulness for among‐lake comparisons. Therefore, historic growth data sets that lack complete sampling information (e.g., full‐sample length frequencies and individual fish from subsamples rather than summaries) can still provide meaningful comparisons of growth among lakes or over time if comparisons are limited to mean lengths at ages 1–10.

Comparison of shift estimation strategies in spectral elastography

This paper compares the performance of various spectral shift estimators for use in spectral elastography, namely, the normalized cross-correlation (NCC), sum squared difference (SSD) and sum absolute difference (SAD). Simulation and experimental results demonstrate that the spectral SSD-based elastographic method exhibits no marked difference in performance compared to the more computationally costly NCC-based approach, which has conventionally been the preferred estimator in spectral elastography. The spectral SAD-based strain estimator, despite being computationally less burdening, failed to exhibit performance comparable to that of the NCC- and SSD-based techniques. Furthermore, though spectral subsample estimation techniques using a cosine-fit interpolation method outperformed that of the parabolic-fit method in terms of both reduced bias errors and standard deviations, the latter was analyzed in this study due to computational simplicity. The role of spectral density was evaluated without and with parabolic-based subsample interpolation. Based on minimizing computational complexity, it is concluded that a (low density) spectral SSD strain estimator coupled with parabolic-based subsample estimation is the preferred choice for spectral elastography.

Assessing Isotropy for Spatial Point Processes

A common assumption while analyzing spatial point processes is direction invariance, i.e., isotropy. In this article, we propose a formal nonparametric approach to test for isotropy based on the asymptotic joint normality of the sample second-order intensity function. We derive an L(2) consistent subsampling estimator for the asymptotic covariance matrix of the sample second-order intensity function and use this to construct a test statistic with a chi(2) limiting distribution. We demonstrate the efficacy of the approach through simulation studies and an application to a desert plant data set, where our approach confirms suspected directional effects in the spatial distribution of the desert plant species.

Heterogeneous expectations in the foreign exchange market

In this study a regime-switching approach is applied to estimate the chartist and fundamentalist (c&f) exchange rate model originally proposed by Frankel and Froot (1986). The c&f model is tested against alternative regime-switching specifications applying likelihood ratio tests. Nested atheoretical models like the popular segmented trends model suggested by Engel and Hamilton (1990) are rejected in favour of the multi-agent model. Our findings turned out to be relatively robust when assessing the models’ sub-sample estimates and out-of-sample performance.

Subsampling the distribution of diverging statistics with applications to finance

In this paper we propose a subsampling estimator for the distribution of statistics diverging at either known or unknown rates when the underlying time series is strictly stationary and strong mixing. Based on our results we provide a detailed discussion of how to estimate extreme order statistics with dependent data and present two applications to assessing financial market risk. Our method performs well in estimating Value at Risk and provides a superior alternative to Hill's estimator in operationalizing Safety First portfolio selection.

The discrete-time quadrature subsample estimation of delay

A high-resolution discrete-time delay estimator for determining the delay between two periodic signals is described. The technique is based upon the principles of analog quadrature detection and is relatively simple to implement digitally. Simulations in the presence of system noise show that the delay estimator does not exhibit any significant bias and outperforms other estimators in medium to high SNR situations.

On the Estimation of the Consumption-Wealth Ratio: Cointegrating Parameter Instability and its Implications for Stock Return Forecasting

This paper investigates if the parameters of the cointegration among consumption, asset wealth, and labor income are stable over the post-war sample period. Although Lettau and Ludvigson (2001a) find that the estimated consumption-wealth ratio (CAY) is a strong predictor of aggregate stock returns, the instability of the cointegrating parameters suggests that the empirical applications of CAY are problematic. Our empirical results from subsample estimations, stability tests, error correction coefficients estimations, and rolling regressions all indicate substantial changes in the cointegrating parameter estimates over the sample period, which translates into the deteriorating forecasting power of CAY for aggregate stock returns.

Development of a technique to determine adequate sample size using subsampling and return interval estimation

To better manage aquatic and riparian ecosystems, knowledge of streamflow return intervals is essential. This leads hydrologists and planners to often question how many years of record are necessary to adequately estimate streamflow characteristics. We propose a nonparametric technique that uses subsampling and return interval estimation to help determine adequate sample size, in order to help answer this question. This technique was applied to 51 years of streamflow record from an untreated catchment known as East St. Louis Creek in the Fraser Experimental Forest. Subsamples of consecutive streamflow record ranging in size from 5 to 25 years were used to empirically estimate the 1.5-, 5-, and 15-year return intervals. These subsample estimates were compared to the ‘true’ return intervals, which were calculated using the entire period of record. Results showed that an ability to estimate these return intervals within 50% of the true return interval levels required only 5–10 years of data. Increasing the sample size to 15 years provided estimates with up to a 25% error rate, and 25 or more years of data were required to provide estimates with less than a 20% error. These are simply the results of a case study, and could be applied to similar catchments. However, the methodology can be applied to any stream.

Precision of different methods used for estimating the abundance of the nitrogen-fixing marine cyanobacterium, Trichodesmium Ehrenberg.

Variances involved in estimating the abundance of the nitrogen-fixing marine cyanobacterium, Trichodesmium Ehrenberg, were evaluated by repeated sampling using bottle casts and plankton net tows at two stations in the southern East China Sea. The variance among individual samples and the variance arising from subsampling processes were separated by the method of analysis of variance, and the coefficient of variation (C.V.) of an abundance estimate based on a single subsample was calculated. For bottle-collected samples, the major source of variation came from taking subsamples from a water bottle. The C.V. of a single subsample estimate ranged from 57% to 184%. For net-collected samples, variance in abundance estimation was mainly caused by distinctive net tows, and when distributing materials in the receiving bucket into smaller containers. The C.V.s of single subsample estimates were 34% and 40%, respectively. Trichodesmium abundance estimated with bottle- and net-collected samples were further compared using data obtained from 17 stations in the East China Sea. Although a general distribution pattern was supported by both methods, the correlation coefficient between them was 0.461, not significantly different from 0.

On Subsampling Estimators with Unknown Rate of Convergence

Politis and Romano have put forth a general subsampling methodology for the construction of large-sample confidence regions for a general unknown parameter θ associated with the probability distribution generating the stationary sequence X 1,…,X n . The subsampling methodology hinges on approximating the large-sample distribution of a statistic T n = T n (X 1,…, X n ) that is consistent for θ at some known rate τ n . Although subsampling has been shown to yield confidence regions for θ of asymptotically correct coverage under very weak assumptions, the applicability of the methodology as it has been presented so far is limited if the rate of convergence τ n happens to be unknown or intractable in a particular setting. In this article we show how it is possible to circumvent this limitation by (a) using the subsampling methodology to derive a consistent estimator of the rate τ n , and (b) using the estimated rate to construct asymptotically correct confidence regions for θ based on subsampling.

On Subsampling Estimators with Unknown Rate of Convergence

On Subsampling Estimators with Unknown Rate of Convergence

Capture-Recapture Analysis of Batterer Reassaults: An Epidemiological Innovation for Batterer Program Evaluation

Capture-recapture analysis is an analytical tool being used in epidemiological research to estimate incidence rates for missing cases and unreliable reporting. Its contribution to batterer program evaluations is examined through a capture-recapture analysis of a multisite evaluation of batterer programs (n = 853). Capture-recapture analysis is applied to various subsamples of the multisite study and to different outcomes (i.e., any reassault, "severe" reassault) to explore the utility of capture-recapture. Finally, the capture-recapture estimates are compared to only the women's reports and to adjusted women's reports (women's reports supplemented with arrest records and men's reports), which are the basis of existing batterer program evaluation. The capture-recapture reassault estimate for the 15-month follow-up is equal to the adjusted women's reports (39%), but is 7% greater than the women reports. The subsample estimates for the individual sites appear to vary as a result of unreliable or unavailable arrest records.

Common Stochastic Trends and Predictability of International Stock Prices

This paper investigates comovements and predictability of aggregate stock prices in Japan, Germany, the United Kingdom and the United States for the period from January 1975 to December 1990. The paper finds that the unit root nonstationary stock prices in the four countries are cointegrated with a single cointegrating vector, and share a long-run equilibrium relationship. Since each national stock price series contains information on the common stochastic trends, the predictability of one country′s stock prices can be enhanced significantly by utilizing information on other countries′ stock prices and on world common stochastic trends. It is found that U.S. stock prices contain substantial information on future movements of other countries′ stock prices. The subsample estimation results provide evidence of increasing comovements of stock prices and of the increasing importance of U.S. and Japanese stock prices in the major world stock markets during the 1980s. J. Japan. Int. Econ., September 1995, 9(3), pp.245–277. Carlson School of Management, University of Minnesota, Minneapolis, MN 55455; and Department of Economics, Drexel University, Philadelphia, Pennsylvania 19104

A system of stock prices in world stock exchanges: Common stochastic trends for 1975–1990

This article reports an investigation of the behavior of stock prices in major world stock exchanges based on univariate and multivariate approaches. The evidence shows that each series of stock prices in the New York, London, Tokyo, and Frankfurt stock exchanges during the period from January 1975 through March 1990 has a unit root. The multivariate tests for unit roots, however, show that there are three unit roots in a system of stock prices in the world's four largest stock exchanges, suggesting the existance of a common stochastic trend in the system. The subsample estimation results are consistent with greater globalization of world stock markets during the 1980s.

PRICE FORMATION AND MARKET STRUCTURE: THE CASE OF THE INTER‐WAR COAL INDUSTRY

This paper is concerned with the question of whether changes in market structure affect pricing behavior, in the context of the interwar U.K. coal-mining industry. In contrast to previous U.K. studies, the authors use time-series data, allowing them to model the dynamics of price adjustment. The problem of measuring market structure is avoided in this case since legislation in the 1930s established cartels and effectively transformed the coal industry from an atomistic to a monopolistic structure. Subsample estimates are presented for the 1920s and 1930s and it is found that, after controlling for other influences, the price-cost mark-up rises on average by around 12 percentage points as a result of cartelization. Copyright 1988 by Blackwell Publishing Ltd

The Forward Rate as a Predictor of the Future Spot Rate--A Stochastic Coefficient Approach

This paper develops a stochastic coefficient model to examine the unbiased forward rate hypothesis for the period January 1974 to August 1983. Tests from the full-sample estimations confirm the null hypothesis. However, the re sults from the Brown-Durbin-Evans (1975) test and the Chow test indic ate that the exchange-rate behavior departs from parameter constancy. Using joint-rolling regressions for the subsample estimations, the a uthor finds evidence that the unbiasedness hypothesis in most cases s hould be rejected and that the estimated parameters, sensitive to new information, vary through different subsample periods. The out-of-sa mple test concludes that incorporation of the stochastic properties o f the parameters into the model improves accuracy of exchange-rate pr edictions. Copyright 1988 by Ohio State University Press.