A flexible point and variance estimator to assess bird/bat fatality from carcass searches

Estimation of bird and bat fatalities due to collision with anthropogenic structures (such as power lines or wind turbines) is an important ecological issue. However, searching for collision victims usually only detects a proportion of the true number of collided individuals. Various mortality estimators have previously been proposed to correct for this incomplete detection, based on regular carcass searches and additional field experiments. However, each estimator implies specific assumptions/restrictions, which may easily be violated in practice. In this study, we extended previous approaches and developed a versatile algorithm to compute point and variance estimates for true carcass numbers. The presented method allows for maximal flexibility in the data structure. Using simulated data, we showed that our point and variance estimators ensured unbiased estimates under various challenging data conditions. The presented method may improve the estimation of true collision numbers, as an important pre-condition for calculating collision rates and evaluating measures to reduce collision risks, and may thus provide a basis for management decisions and/or compensation actions with regard to planned or existing wind turbines and power lines.

Evaluation of mapped-plot variance estimators across a range of partial nonresponse in a post-stratified national forest inventory

When conducting a forest inventory, sometimes portions of plots cannot be measured due to inaccessibility. Two primary methods have been presented to account for partial nonresponse in the estimation phase: 1) use a ratio-to-size estimator, or 2) apply an adjustment factor to all plot observations in proportion to the missing area. Both approaches provide identical estimates of the population mean, but the estimates of variance differ when partial nonresponse is present. Variance estimator performance was examined for a range of population forest area and partial nonresponse proportions in the sample. The ratio-to-size variance estimator performed unbiasedly with respect to simulation results, but the adjustment factor variance estimates were biased with the magnitude and direction dependent upon the forest area proportion and amount of partial nonresponse. The bias is relatively small when the partial nonresponse is small, which is often the case; however, the ratio-to-size method is preferred to ensure accurate variance estimation for a wide range of circumstances.

Checking for model consistency in optimal fingerprinting: a comment

Allen and Tett (1999, herein AT99) introduced a Generalized Least Squares (GLS) regression methodology for decomposing patterns of climate change for attribution purposes and proposed the “Residual Consistency Test” (RCT) to check the GLS specification. Their methodology has been widely used and highly influential ever since, in part because subsequent authors have relied upon their claim that their GLS model satisfies the conditions of the Gauss-Markov (GM) Theorem, thereby yielding unbiased and efficient estimators. But AT99 stated the GM Theorem incorrectly, omitting a critical condition altogether, their GLS method cannot satisfy the GM conditions, and their variance estimator is inconsistent by construction. Additionally, they did not formally state the null hypothesis of the RCT nor identify which of the GM conditions it tests, nor did they prove its distribution and critical values, rendering it uninformative as a specification test. The continuing influence of AT99 two decades later means these issues should be corrected. I identify 6 conditions needing to be shown for the AT99 method to be valid.

Error Propagation of Capon’s Minimum Variance Estimator

The error propagation of Capon’s minimum variance estimator resulting from measurement errors and position errors is derived within a linear approximation. It turns out, that Capon’s estimator provides the same error propagation as the conventionally used least square fit method. The shape matrix which describes the location depence of the measurement positions is the key parameter for the error propagation, since the condition number of the shape matrix determines how the errors are amplified. Furthermore, the error resulting from a finite number of data samples is derived by regarding Capon’s estimator as a special case of the maximum likelihood estimator.

An approximate point-based alternative for the estimation of variance under big BAF sampling

Background A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. Methods The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula. Results Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas. Conclusions A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of $\frac {1}{n}$ 1 n where n is the number of sample points.

The Estimation of Residual Variance in Nonparametric Regression

Given a nonparametric regression model Yi = g(xi) + ei, i = 1, 2, …, n, where Y is a dependent variable, x is an independent variable, g is an unknown function and e is an error assumed to be an independent, identical, and is distributed with mean 0 and variance σ2. In this research Rice estimator is used to determine the biased value of a residual variance estimator. The Rice estimator is given as follows: . The biased value of residual variance estimator of the Rice method is: , where and. Using the Rice estimator, the Tong-Wang residual variance estimator is obtained, that is: , Where , , , , , k = 1, 2, … , m. Based upon the data simulation by considering the exponential, arithmetical, and trigonometrical models, it is found that the MSE value of the Tong-Wang estimator tends to be less compared to those of the Rice estimator as well as the GSJ (Gasser, Sroka, and Jennen) estimator.

On the Impact and Mitigation of Signal Crosstalk in Ground-Based and Low Altitude Airborne GNSS-R

Global Navigation Satellite System Reflectometry (GNSS-R) is a powerful way to retrieve information from a reflecting surface by exploiting GNSS as signals of opportunity. In dual antenna conventional GNSS-R architectures, the reflected signal is correlated with a clean replica to obtain the specular reflection point delay and Doppler estimates, which are further processed to obtain the GNSS-R product of interest. An important problem that may appear for low elevation satellites is signal crosstalk, that is the direct line-of-sight signal leaks into the antenna dedicated to the reflected signal. Such crosstalk may degrade the overall system performance if both signals are very close in time, similar to multipath in standard GNSS receivers, the reason why mitigation strategies must be accounted for. In this article: (i) we first provide a geometrical analysis to justify that the estimation performance is only affected for low height receivers; (ii) then, we analyze the impact of crosstalk if not taken into account, by comparing the single source conditional maximum likelihood estimator (CMLE) performance in a dual source context with the corresponding Cramér–Rao bound (CRB); (iii) we discuss dual source estimators as a possible mitigation strategy; and (iv) we investigate the performance of the so-called variance estimator, which is designed to eliminate the coherent signal part, compared to both the CRB and non-coherent dual source estimators. Simulation results are provided for representative GNSS signals to support the discussion. From this analysis, it is found that: (i) for low enough reflected-to-direct signal amplitude ratios (RDR), the crosstalk has no impact on standard single source CMLEs; (ii) for high enough signal-to-noise ratios (SNR), the dual source estimators are efficient irrespective of the RDR, then being a promising solution for any reflected signal scenario; (iii) non-coherent dual source estimators are also efficient at high SNR; and (iv) the variance estimator is efficient as long as the non-coherent part of the signal is dominant.

Nonignorable Attrition in Pairwise Randomized Experiments

In pairwise randomized experiments, what if the outcomes of some units are missing? One solution is to delete missing units (the unitwise deletion estimator, UDE). If attrition is nonignorable, however, the UDE is biased. Instead, scholars might employ the pairwise deletion estimator (PDE), which deletes the pairmates of missing units as well. This study proves that the PDE can be biased but more efficient than the UDE and, surprisingly, the conventional variance estimator of the PDE is unbiased in a super-population. I also propose a new variance estimator for the UDE and argue that it is easier to interpret the PDE as a causal effect than the UDE. To conclude, I recommend the PDE rather than the UDE.