Linear Combination Of Estimators Research Articles

Reduced variance analysis of molecular dynamics simulations by linear combination of estimators.

Building upon recent developments of force-based estimators with a reduced variance for the computation of densities, radial distribution functions, or local transport properties from molecular simulations, we show that the variance can be further reduced by considering optimal linear combinations of such estimators. This control variates approach, well known in statistics and already used in other branches of computational physics, has been comparatively much less exploited in molecular simulations. We illustrate this idea on the radial distribution function and the one-dimensional density of a bulk and confined Lennard-Jones fluid, where the optimal combination of estimators is determined for each distance or position, respectively. In addition to reducing the variance everywhere at virtually no additional cost, this approach cures an artifact of the initial force-based estimators, namely, small but non-zero values of the quantities in regions where they should vanish. Beyond the examples considered here, the present work highlights, more generally, the underexplored potential of control variates to estimate observables from molecular simulations.

Combining Environmental Area Frame Surveys of a Finite Population

New ways to combine data from multiple environmental area frame surveys of a finite population are being introduced. Environmental surveys often sample finite populations through area frames. However, to combine multiple surveys without risking bias, design components (inclusion probabilities, etc.) are needed at unit level of the finite population. We show how to derive the design components and exemplify this for three commonly used area frame sampling designs. We show how to produce an unbiased estimator using data from multiple surveys, and how to reduce the risk of introducing significant bias in linear combinations of estimators from multiple surveys. If separate estimators and variance estimators are used in linear combinations, there’s a risk of introducing negative bias. By using pooled variance estimators, the bias of a linear combination estimator can be reduced. National environmental surveys often provide good estimators at national level, while being too sparse to provide sufficiently good estimators for some domains. With the proposed methods, one can plan extra sampling efforts for such domains, without discarding readily available information from the aggregate/national survey. Through simulation, we show that the proposed methods are either unbiased, or yield low variance with small bias, compared to traditionally used methods.

Smoothness adaptive average derivative estimation

Many important models utilize estimation of average derivatives of the conditional mean function. Asymptotic results in the literature on density weighted average derivative estimators (ADE) focus on convergence at parametric rates; this requires making stringent assumptions on smoothness of the underlying density; here we derive asymptotic properties under relaxed smoothness assumptions. We adapt to the unknown smoothness in the model by consistently estimating the optimal bandwidth rate and using linear combinations of ADE estimators for different kernels and bandwidths. Linear combinations of estimators (i) can have smaller asymptotic mean squared error (AMSE) than an estimator with an optimal bandwidth and (ii) when based on estimated optimal rate bandwidth can adapt to unknown smoothness and achieve rate optimality. Our combined estimator minimizes the trace of estimated MSE of linear combinations. Monte Carlo results for ADE confirm good performance of the combined estimator.

Linear combination of estimators in probability proportional to sizes sampling to estimate the population

In this paper we have studied the gain of efficiency and the relative bias of linear weighted estimators over conventional estimators under probability proportional to size with replacement (ppswr) sampling for a wide variety of populations. The five number summary statistics for the relative bias and the relative efficiency over conventional estimators is given for different magnitude of correlation coefficients. The computational study shows that there is a considerable gain in the efficiency of linear weighted estimators over conventional estimators. To develop the confidence of survey practitioners on linear weighted estimator, the computational study is extended to see the robustness of the linear weighted estimator by deviating the optimum value of the weight up to 50% on either side.

Weighted linear cue combination with possibly correlated error

We test hypotheses concerning human cue combination in a slant estimation task. Observers repeatedly adjusted the slant of a plane to 75°. Feedback was provided after each setting and the observers trained extensively until their setting error stabilized. The slant of the plane was defined by either linear perspective alone (a grid of lines) or texture gradient alone (diamond-shaped texture elements) or the two cues together. We chose a High and Low variance version of each cue type and measured setting variability in four single-cue conditions (Low, High for each cue) and in the four possible combined-cue conditions (Low–Low, Low–High, etc.). We compared performance in the combined-cue conditions to predictions based on single-cue performance. The results were consistent with a linear combination of estimates from cues. Six out of eight observers did better with combined cues than with either cue alone. For three observers, performance was consistent with optimal combination of uncorrelated cues. Three other observers’ results were also consistent with optimal combination, but with the assumption that internal cue estimates were correlated. The remaining two observers were consistent with sub-optimal cue combination.