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Item nonresponse is a common issue in surveys. Because unadjusted estimators may be biased in the presence of nonresponse, it is common practice to impute the missing values with the objective of reducing the nonresponse bias as much as possible. However, commonly used imputation procedures may lead to unstable estimators of population totals/means when influential units are present in the set of respondents. In this article, we consider the class of multiply robust imputation procedures that provide some protection against the failure of underlying model assumptions. We develop an efficient version of multiply robust estimators based on the concept of conditional bias, a measure of influence. We present the results of a simulation study to show the benefits of our proposed method in terms of bias and efficiency. [ABSTRACT FROM AUTHOR]

Accurate spatial estimation of extremes is an increasingly important topic in environmental research and risk assessment. Conditional bias (CB)-penalized kriging (CBPK) improves such estimation by minimizing linearly weighted sum of error variance and variance of Type-II error. However, CBPK requires skillful prescription of the weight for the CB penalty which is a significant challenge in practice. In this paper, we describe an extension of CBPK, referred to herein as adaptive conditional bias-penalized kriging (ACBPK), which objectively prescribes the weight for improved estimation of extremes without deteriorating performance in the unconditional mean squared error sense. For comparative evaluation in the real world, cross validation experiments were carried out for precipitation estimation using hourly rain gauge data in the Arkansas-Red River Basin (AB), central Texas (TX) and southeastern US (SE) areas. The results show that CB is detected for about 26, 24 and 25% of all data points in the AB, TX and SE cases, respectively, and that, given detection of CB, ACBPK reduces root mean square error of hourly precipitation exceeding 12.7 mm by 15, 21 and 9% and hourly precipitation exceeding 25.4 mm by 14, 26 and 10% relative to ordinary kriging (OK) for the AB, TX and SE cases, respectively. The overall findings indicate that, if accurate spatial estimation in the tails of the distribution is important or accurate modeling of spatiotemporally-varying correlation structure is a challenge, ACBPK should be favored over OK. [ABSTRACT FROM AUTHOR]

In adaptive clinical trials, the conventional end‐of‐trial point estimate of a treatment effect is prone to bias, that is, a systematic tendency to deviate from its true value. As stated in recent FDA guidance on adaptive designs, it is desirable to report estimates of treatment effects that reduce or remove this bias. However, it may be unclear which of the available estimators are preferable, and their use remains rare in practice. This article is the second in a two‐part series that studies the issue of bias in point estimation for adaptive trials. Part I provided a methodological review of approaches to remove or reduce the potential bias in point estimation for adaptive designs. In part II, we discuss how bias can affect standard estimators and assess the negative impact this can have. We review current practice for reporting point estimates and illustrate the computation of different estimators using a real adaptive trial example (including code), which we use as a basis for a simulation study. We show that while on average the values of these estimators can be similar, for a particular trial realization they can give noticeably different values for the estimated treatment effect. Finally, we propose guidelines for researchers around the choice of estimators and the reporting of estimates following an adaptive design. The issue of bias should be considered throughout the whole lifecycle of an adaptive design, with the estimation strategy prespecified in the statistical analysis plan. When available, unbiased or bias‐reduced estimates are to be preferred. [ABSTRACT FROM AUTHOR]

In sample surveys that collect information on skewed variables, it is often desirable to assess the influence of sample units on the sampling error of survey-weighted estimators of finite population parameters. The conditional bias is an attractive measure of influence that accounts for the sampling design and the estimation method. It is defined as the design expectation of the sampling error conditional on a given unit being selected in the sample. The estimation of the conditional bias is relatively straightforward for simple sampling designs and estimators. However, for complex designs or complex estimators, it may be tedious to derive an explicit expression for the conditional bias. In those complex surveys, variance estimation is often achieved through replication methods such as the bootstrap. Bootstrap methods of variance estimation are typically implemented by producing a set of bootstrap weights that is provided to users along with the survey data. In this article, we show how to use these bootstrap weights to obtain an estimator of the conditional bias. Our bootstrap estimator is evaluated in a simulation study and illustrated using data from the Canadian Survey of Household Spending. [ABSTRACT FROM AUTHOR]

This paper presents a comparative geometric analysis of the conditional bias (CB)-informed Kalman filter (KF) with the Kalman filter (KF) in the Euclidean space. The CB-informed KFs considered include the CB-penalized KF (CBPKF) and its ensemble extension, the CB-penalized Ensemble KF (CBEnKF). The geometric illustration for the CBPKF is given for the bi-state model, composed of an observable state and an unobservable state. The CBPKF co-minimizes the error variance and the variance of the Type-II error. As such, CBPKF-updated state error vectors are larger than the KF-updated, the latter of which is based on minimizing the error variance only. Different error vectors in the Euclidean space imply different eigenvectors and covariance ellipses in the state space. To characterize the differences in geometric attributes between the two filters, numerical experiments were carried out using the Lorenz 63 model. The results show that the CBEnKF yields more accurate confidence regions for encompassing the truth, smaller errors in the ensemble mean, and larger norms for Kalman gain and error covariance matrices than the EnKF, particularly when assimilating highly uncertain observations. [ABSTRACT FROM AUTHOR]

This study shows the benefits of doing a probability transform of kriging estimates, into the sample data distribution, to improve the selection of spatial locations with values higher than a given threshold. The probability transform restores the data variance in the kriging estimates, which increases the conditional bias but reduces the bias for the expected true values when selection is done on the basis of the transformed estimates. [ABSTRACT FROM AUTHOR]

Objective merging of multiple forecasts to improve forecast accuracy is of large interest in many disciplines. Multiple linear regression (MLR) is an extremely attractive technique for this purpose because of its simplicity and interpretability. For modeling and prediction of extremes such as floods using MLR, however, attenuation bias is a very serious issue as it results in systematic under- and over-prediction in the upper and lower tails of the predictand, respectively. In this work, we introduce conditional bias-penalized multiple linear regression (CBP-MLR) which reduces attenuation bias by jointly minimizing mean squared error (MSE) and Type-II error squared. Whereas CBP-MLR improves prediction over tails, it degrades the performance near median. To retain MLR-like performance near median while exploiting the ability of CBP-MLR to improve prediction over tails, we employ composite MLR (CompMLR) which linearly weight-averages the MLR and CBP-MLR estimates. For comparative evaluation, we apply the proposed technique to multi-model streamflow prediction using several operationally produced streamflow forecasts as predictors. The results for multiple forecast groups in the US National Weather Service Middle Atlantic River Forecast Center's service area show that the relative performance among different input forecasts varies most significantly with the range of the verifying observed streamflow, and that CompMLR is generally superior to the best performing forecasts in the mean squared error sense under widely varying conditions of predictability and predictive skill. [ABSTRACT FROM AUTHOR]

Many variables encountered in practice have skewed distributions. While the sample mean is unbiased for the true mean regardless of the underlying distribution that generated the sample observations, it can be highly unstable in the context of skewed distributions. To cope with this problem, we propose an efficient estimator of the population mean based on the concept of conditional bias of a unit, which can be viewed as a measure of its influence. The idea is to reduce the impact of the sample units that have a large influence. The resulting estimator depends on a cut‐off value. We suggest selecting the cut‐off value that minimizes the maximum absolute estimated conditional bias with respect to the proposed estimator. An estimator of the mean square error is also presented. An empirical investigation comparing several estimators in terms of relative bias and relative efficiency suggests that the proposed estimator and the estimator of its mean square error perform well for a wide class of distributions. [ABSTRACT FROM AUTHOR]

This study revisits the conditional bias that can be observed with spatial estimators such as kriging. In the geostatistical literature, the term "conditional bias" has been used to describe two different effects: underestimation of high values and overestimation of low values, or the opposite, viz. overestimation of high values and underestimation of low values. To add to the confusion, the smoothing effect of the estimator is always indicated to be the culprit. It seems that geostatisticians have been debating conditional bias since the birth of geostatistics. Is less or more smoothing required to alleviate conditional bias, and which one? This paradox is actually resolved when one considers the different distribution partitions on which conditional expectation can be calculated. Depending on the partitions of the bivariate distribution of true versus estimated values, conditional expectation can be calculated on conditional or marginal distributions. These lead to different types of conditional bias, and smoothing affects them differently. The type based on conditional distributions is smoothing friendly, while the type based on marginal distributions is smoothing adverse. The same estimator can display under- and overestimation, depending on whether a conditional or marginal distribution is considered. It is also observed that all conditional biases, regardless of the bivariate distribution partitions, are greatly affected by the variance of the conditioning data and vary with the sampling. A simple estimator correction can be applied to exactly remove the smoothing-friendly conditional bias in the sample as measured by the slope of the linear regression between the true and estimated values in cross-validation. Over many samplings, it is observed that this cross-validation measure is itself conditionally biased, depending on the variance of the data. On the other hand, the smoothing-adverse type of conditional bias can be corrected by conditional simulation that reproduces the distribution of the data. The results are also biased, depending on the variance of the conditioning data. Correcting for the smoothing-adverse type will worsen the smoothing-friendly type, and vice versa. Both types of conditional bias can be corrected by averaging statistics, or averaging estimates, over multiple samplings. [ABSTRACT FROM AUTHOR]

This paper presents a comparative geometric analysis of the conditional bias (CB)-informed Kalman filter (KF) with the Kalman filter (KF) in the Euclidean space. The CB-informed KFs considered include the CB-penalized KF (CBPKF) and its ensemble extension, the CB-penalized Ensemble KF (CBEnKF). The geometric illustration for the CBPKF is given for the bi-state model, composed of an observable state and an unobservable state. The CBPKF co-minimizes the error variance and the variance of the Type-II error. As such, CBPKF-updated state error vectors are larger than the KF-updated, the latter of which is based on minimizing the error variance only. Different error vectors in the Euclidean space imply different eigenvectors and covariance ellipses in the state space. To characterize the differences in geometric attributes between the two filters, numerical experiments were carried out using the Lorenz 63 model. The results show that the CBEnKF yields more accurate confidence regions for encompassing the truth, smaller errors in the ensemble mean, and larger norms for Kalman gain and error covariance matrices than the EnKF, particularly when assimilating highly uncertain observations.

Kalman filter (KF) and its variants and extensions are wildly used for hydrologic prediction in environmental science and engineering. In many data assimilation applications of Kalman filter (KF) and its variants and extensions, accurate estimation of extreme states is often of great importance. When the observations used are uncertain, however, KF suffers from conditional bias (CB) which results in consistent under- and overestimation of extremes in the right and left tails, respectively. Recently, CB-penalized KF, or CBPKF, has been developed to address CB. In this paper, we present an alternative formulation based on variance-inflated KF to reduce computation and algorithmic complexity, and describe adaptive implementation to improve unconditional performance. For theoretical basis and context, we also provide a complete self-contained description of CB-penalized Fisher-like estimation and CBPKF. The results from one-dimensional synthetic experiments for a linear system with varying degrees of nonstationarity show that adaptive CBPKF reduces the root-mean-square error at the extreme tail ends by 20 to 30% over KF while performing comparably to KF in the unconditional sense. The alternative formulation is found to approximate the original formulation very closely while reducing computing time to 1.5 to 3.5 times of that for KF depending on the dimensionality of the problem. Hence, adaptive CBPKF offers a significant addition to the dynamic filtering methods for general application in data assimilation when the accurate estimation of extremes is of importance.

• Conditional Bias-Penalized EnKF (CBEnKF) has been developed. • CBEnKF significantly outperforms EnKF for high flow events. • CRPSS of CBEnKF in reference to EnKF is larger for larger flows. We present a novel ensemble extension of the conditional bias-penalized Kalman filter, referred to herein as the conditional bias-penalized ensemble Kalman filter (CBEnKF), and apply it to flood forecasting. The CBEnKF differs from most data assimilation (DA) techniques in that it minimizes a weighted sum of the error variance and the expected value of the Type-II conditional bias squared for improved estimation and prediction of extremes. To assess the ability of the CBEnKF to improve flood prediction, we carried out real-world DA experiments in which the CBEnKF and the EnKF were applied under identical conditions for assimilation of hourly streamflow observations into the lumped Sacramento soil moisture accounting and unit hydrograph models. Ten headwater basins in Texas, whose drainage areas and times-to-peak range from 137 to 1037 km2 and from 3 to 21 hrs, respectively, were used in the twin experiments. All events in a 10-yr period with peak flow exceeding 100 m3/s were used. Verification of the ensemble mean predictions indicates that the CBEnKF improves the multi-basin mean of the mean square error skill score over the EnKF by about 0.15 over lead times of up to the time-to-peak of the basin. Verification of the ensemble predictions indicates that the CBEnKF improves the mean continuous ranked probability skill score by about 0.2 on average over the EnKF for all ranges of flow within the significant events, and by about 0.3 for flows exceeding the 95th percentile in those events. That the gain in skill is larger for larger flows makes the CBEnKF very appealing despite the significantly higher computational cost. [ABSTRACT FROM AUTHOR]

Background Baseline covariate imbalance (between treatment groups) is a common problem in randomized clinical trials which often raises questions about the validity of trial results. Answering these questions requires careful consideration of the statistical implications of covariate imbalance. The possibil ity of having covariate imbalance contributes to the marginal variance of an unadjusted treatment difference estimator, which can be reduced by making appropriate adjustments. Actual observed imbalance introduces a conditional bias into an unadjusted estimator, which may increase the conditional size of an unadjusted test. Methods This article provides conditional estimation and inference procedures to address the conditional bias due to observed imbalance. Interestingly, it is possible to use the same adjusted treatment difference estimator to address the marginal variance issue and the conditional bias issue associated with covariate imbalance. Its marginal variance estimator tends to be conservative for conditional inference, and we propose a conditionally appropriate variance estimator. We also provide an estimator of the conditional bias in an unadjusted treatment difference estimator, together with a conditional variance estimator. Results The proposed methodology is illustrated with real data from a stroke trial and evaluated in simulation experiments based on the same trial. The simulation results show that covariate imbalance can result in a substantial conditional bias and that the proposed methods deal with the conditional bias quite effectively. Discussion We recommend that the proposed methodology be used routinely to address the observed covariate imbalance in randomized clinical trials. [ABSTRACT FROM AUTHOR]

One of the most crucial applications of radar-based precipitation nowcasting systems is the short-term forecast of extreme rainfall events such as flash floods and severe thunderstorms. While deep learning nowcasting models have recently shown to provide better overall skill than traditional echo extrapolation models, they suffer from conditional bias, sometimes reporting lower skill on extreme rain rates compared to Lagrangian persistence, due to excessive prediction smoothing. This work presents a novel method to improve deep learning prediction skills in particular for extreme rainfall regimes. The solution is based on model stacking, where a convolutional neural network is trained to combine an ensemble of deep learning models with orographic features, doubling the prediction skills with respect to the ensemble members and their average on extreme rain rates, and outperforming them on all rain regimes. The proposed architecture was applied on the recently released TAASRAD19 radar dataset: the initial ensemble was built by training four models with the same TrajGRU architecture over different rainfall thresholds on the first six years of the dataset, while the following three years of data were used for the stacked model. The stacked model can reach the same skill of Lagrangian persistence on extreme rain rates while retaining superior performance on lower rain regimes.

The uncertainty structure of satellite‐based passive infrared quantitative precipitation estimation (QPE) is largely unknown at fine spatio‐temporal scales, and requires more than just one deterministic "best estimate" to adequately cope with the intermittent, highly skewed distribution that characterizes precipitation. An investigation of this subject has been carried out within the framework of the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks‐Cloud Classification System (PERSIANN‐CCS). A new method, PIRSO (Probabilistic QPE using InfraRed Satellite Observations), is proposed to advance the use of uncertainty as an integral part of QPE. Probability distributions of precipitation rates are computed instead of deterministic values using a model quantifying the relation between satellite infrared brightness temperatures and the corresponding "true" precipitation rate. Ensembles of brightness temperatures‐to‐precipitation rate relationships are derived at a 30 min/0.04° scale. This approach conditions probabilistic quantitative precipitation estimates (PQPE) on the precipitation rate and typology. PIRSO's components were estimated based on a data sample covering two warm seasons over the conterminous USA. Precipitation probability maps outperform the deterministic PERSIANN‐CCS QPE. PIRSO is shown to mitigate systematic biases from deterministic retrievals, quantify uncertainty, and advance the monitoring of precipitation extremes. It also provides the basis for precipitation probability maps and satellite precipitation ensembles needed for satellite multi‐sensor merging of precipitation, early warning and mitigation of hydrometeorological hazards, and hydrological modelling. Satellite‐based quantitative precipitation estimation (QPE) requires more than just one deterministic "best estimate" to adequately cope with the intermittent, highly skewed precipitation distribution. A new approach called Probabilistic QPE using Infrared Satellite Observations (PIRSO) is proposed to advance the use of uncertainty as an integral part of QPE. PIRSO precipitation probability maps outperform conventional deterministic QPE by mitigating biases. PIRSO quantifies uncertainty needed for precipitation ensembles and multisensor merging, and advances the monitoring of precipitation extremes for hydrometeorological hazards. [ABSTRACT FROM AUTHOR]

Two‐stage designs are widely used to determine whether a clinical trial should be terminated early. In such trials, a maximum likelihood estimate is often adopted to describe the difference in efficacy between the experimental and reference treatments; however, this method is known to display conditional bias. To reduce such bias, a conditional mean‐adjusted estimator (CMAE) has been proposed, although the remaining bias may be nonnegligible when a trial is stopped for efficacy at the interim analysis. We propose a new estimator for adjusting the conditional bias of the treatment effect by extending the idea of the CMAE. This estimator is calculated by weighting the maximum likelihood estimate obtained at the interim analysis and the effect size prespecified when calculating the sample size. We evaluate the performance of the proposed estimator through analytical and simulation studies in various settings in which a trial is stopped for efficacy or futility at the interim analysis. We find that the conditional bias of the proposed estimator is smaller than that of the CMAE when the information time at the interim analysis is small. In addition, the mean‐squared error of the proposed estimator is also smaller than that of the CMAE. In conclusion, we recommend the use of the proposed estimator for trials that are terminated early for efficacy or futility. [ABSTRACT FROM AUTHOR]

We propose a method with better predictions at extreme values than the standard method of Kriging. We construct our predictor in two ways: by penalizing the mean squared error through conditional bias and by penalizing the conditional likelihood at the target function value. Our prediction exhibits robustness to the model mismatch in the covariance parameters, a desirable feature for computer simulations with a restricted number of data points. Applications on several functions show that our predictor is robust to the non-Gaussianity of the function. [ABSTRACT FROM AUTHOR]

Kalman filter (KF) and its variants are widely used for real-time state updating and prediction in environmental science and engineering. Whereas in many applications the most important performance criterion may be the fraction of the times when the filter performs satisfactorily under different conditions, in many other applications estimation and prediction specifically of extremes, such as floods, droughts, algal blooms, etc., may be of primary importance. Because KF is essentially a least squares solution, it is subject to conditional biases (CB) which arise from the error-in-variable, or attenuation, effects when the model dynamics are highly uncertain, the observations have large errors and/or the system being modeled is not very predictable. In this work, we describe conditional bias-penalized KF, or CBPKF, based on CB-penalized linear estimation which minimizes a weighted sum of error variance and expectation of Type-II CB squared and comparatively evaluate with KF through a set of synthetic experiments for one-dimensional state estimation under the idealized conditions of normality and linearity. The results show that CBPKF reduces root mean square error (RMSE) over KF by 10-20% or more over the tails of the distribution of the true state. In the unconditional sense CBPKF performs comparably to KF for nonstationary cases in that CBPKF increases RMSE over all ranges of the true state only up to 3%. With the ability to reduce CB explicitly, CBPKF provides a significant new addition to the existing suite of filtering techniques for improved analysis and prediction of extreme states of uncertain environmental systems. [ABSTRACT FROM AUTHOR]

A new technique for merging radar precipitation estimates and rain gauge data is developed and evaluated to improve multisensor quantitative precipitation estimation (QPE), in particular, of heavy-to-extreme precipitation. Unlike the conventional cokriging methods which are susceptible to conditional bias (CB), the proposed technique, referred to herein as conditional bias-penalized cokriging (CBPCK), explicitly minimizes Type-II CB for improved quantitative estimation of heavy-to-extreme precipitation. CBPCK is a bivariate version of extended conditional bias-penalized kriging (ECBPK) developed for gauge-only analysis. To evaluate CBPCK, cross validation and visual examination are carried out using multi-year hourly radar and gauge data in the North Central Texas region in which CBPCK is compared with the variant of the ordinary cokriging (OCK) algorithm used operationally in the National Weather Service Multisensor Precipitation Estimator. The results show that CBPCK significantly reduces Type-II CB for estimation of heavy-to-extreme precipitation, and that the margin of improvement over OCK is larger in areas of higher fractional coverage (FC) of precipitation. When FC > 0.9 and hourly gauge precipitation is > 60 mm, the reduction in root mean squared error (RMSE) by CBPCK over radar-only (RO) is about 12 mm while the reduction in RMSE by OCK over RO is about 7 mm. CBPCK may be used in real-time analysis or in reanalysis of multisensor precipitation for which accurate estimation of heavy-to-extreme precipitation is of particular importance. [ABSTRACT FROM AUTHOR]

An adaptive cumulative sum (CUSUM) procedure is proposed to monitor parameter changes in a multiparameter exponential family where the change-point and postchange parameters are estimated adaptively. Approximations for average run lengths are derived. Monitoring changes in both mean and variance in the normal case is considered as an illustration. The conditional biases of the estimations for the change-point and postchange mean and variance is studied by simulation comparison with several other CUSUM procedures. An adaptive dam process by modifying the adaptive CUSUM process is used to detect and identify change points and change segments by using Citibank stock prices from 30 Dow Jones Industry Index. [ABSTRACT FROM PUBLISHER]

Influential units occur frequently in surveys, especially in business surveys that collect economic variables whose distributions are highly skewed. A unit is said to be influential when its inclusion or exclusion from the sample has an important impact on the sampling error of estimates. We extend the concept of conditional bias attached to a unit and propose a robust version of the double expansion estimator, which depends on a tuning constant. We determine the tuning constant that minimizes the maximum estimated conditional bias. Our results can be naturally extended to the case of unit nonresponse, the set of respondents often being viewed as a second-phase sample. A robust version of calibration estimators, based on auxiliary information available at both phases, is also constructed. [ABSTRACT FROM AUTHOR]

Summary The high spatio-temporal resolutions of radar-based multi-sensor Quantitative Precipitation Estimates (QPEs) makes them a potential complement to the gauge records for engineering design purposes, such as precipitation frequency analysis. The current study investigates three fundamental issues that arise when radar-based QPE products are used in frequency analysis: (a) Effect of sample size due to the typically short records of radar products; (b) Effect of uncertainties present in radar-rainfall estimation algorithms; and (c) Effect of the frequency estimation approach adopted. The study uses a 13-year dataset of hourly, 4 × 4 km 2 radar-based over a domain that covers Louisiana, USA. Data-based investigations, as well as synthetic simulations, are performed to quantify the uncertainties associated with the radar-based derived frequencies, and to gain insight into the relative contributions of short record lengths and those from conditional biases in the radar product. Three regional estimation procedures were tested and the results indicate the sensitivity of the radar frequency estimates to the selection of the estimation approach and the impact on the uncertainties of the derived extreme quantiles. The simulation experiments revealed that the relatively short radar records explained the majority of the uncertainty associated with the radar-based quantiles; however, they did not account for any tangible contribution to the systematic underestimation observed between radar- and gauge-based frequency estimates. This underestimation was mostly attributable to the conditional bias inherent in the radar product. Addressing such key outstanding problems in radar-rainfall products is necessary before they can be fully and reliably used for frequency analysis applications. [ABSTRACT FROM AUTHOR]

Rain intensity spectra as seen by space sensors feed numerous applications at global scales ranging from water budget studies to forecasting natural hazards related to extreme rainfall events. Rainfall variability at scales finer than what is resolved by current space sensors affects their detection capabilities, the characterization of rainfall types, as well as the quantification of rainfall rates. A high-resolution surface rainfall product is used to evaluate the impact of rainfall variability within the field of view (FOV) of the Tropical Rainfall Measurement Mission (TRMM) Precipitation Radar (PR) quantitative precipitation estimation (QPE) at ground. The primary contribution of this study is to assess the impact of rainfall variability in terms of occurrence, types and rate at PR's pixel resolution on PR precipitation detection, classification and quantification. Several aspects of PR errors are revealed and quantified including sensitivity to non-uniform beam filling. While the error structure of the PR is complicated because of the interaction of these factors, simple error models are developed to describe the PR performances. The methodology and framework developed herein applies more generally to rainfall rate estimates from other sensors on board low Earth-orbiting satellites such as microwave imagers and dual-frequency radars such as with the Global Precipitation Measurement (GPM) mission. [ABSTRACT FROM AUTHOR]

The uncertainty structure of radar quantitative precipitation estimation (QPE) is largely unknown at fine spatiotemporal scales near the radar measurement scale. By using the WSR-88D radar network and gauge data sets across the conterminous US, an investigation of this subject has been carried out within the framework of the NOAA/NSSL ground radar-based Multi-Radar Multi-Sensor (MRMS) QPE system. A new method is proposed and called PRORATE for probabilistic QPE using radar observations of rate and typology estimates. Probability distributions of precipitation rates are computed instead of deterministic values using a model quantifying the relation between radar reflectivity and the corresponding 'true' precipitation. The model acknowledges the uncertainty arising from many factors operative at the radar measurement scale and from the correction algorithm. Ensembles of reflectivity-to-precipitation rate relationships accounting explicitly for precipitation typology were derived at a 5 min/1 km scale. This approach conditions probabilistic quantitative precipitation estimates (PQPE) on the precipitation rate and type. The model components were estimated on the basis of a 1 year long data sample over the CONUS. This PQPE model provides the basis for precipitation probability maps and the generation of radar precipitation ensembles. Maps of the precipitation exceedance probability for specific thresholds (e.g., precipitation return periods) are computed. Precipitation probability maps are accumulated to the hourly time scale and compare favorably to the deterministic QPE. As an essential property of precipitation, the impact of the temporal correlation on the hourly accumulation is examined. This approach to PQPE can readily apply to other systems including space-based passive and active sensor algorithms. [ABSTRACT FROM AUTHOR]

We describe adaptive conditional bias (CB)-penalized ensemble Kalman filter (AEnKF) to improve estimation and prediction of extremes. Environmental variables are generally observed with significant uncertainties. Geoscientific data assimilation (DA) is hence often subject to CB which adversely impacts estimation of extremes. A generalization of EnKF, AEnKF accounts for CB by dynamically reflecting the flow-dependent information content in the model prediction relative to that in the observation via a scaler weight. The implicit dependence of the weight on the posterior state renders the AEnKF solution nonlinear for superior performance over the tails of the predictand as well as in the (unconditional) mean sense. AEnKF prescribes the weight in real time by minimizing the degrees of freedom for noise. Real-time optimization of the weight also means that AEnKF obviates or reduces the need for calibration of uncertainty parameters which is often subjective and expensive. Comparative evaluation for flood prediction shows that AEnKF outperforms EnKF by a very significant margin but is about two to three times more expensive computationally. Because AEnKF uses the EnKF solution, it can be easily implemented in any EnKF code with the addition of the weight optimization module. Given superior performance and relative ease of implementation, AEnKF should be favored over KF in a wide range of geoscientific DA, particularly when performance over tails is important. • AEnKF improves state estimation in the presence conditional bias. • AEnKF maximizes flow-dependent information content via a scaler weight. • Simplicity of solution allows closed-form expressions for parameter optimization. • AEnKF easily outperforms EnKF for flood prediction for headwater basins in the US. [ABSTRACT FROM AUTHOR]

For a fallback randomized clinical trial design with a marker, Choai and Matsui (2015, Biometrics 71, 25-32) estimate the bias of the estimator of the treatment effect in the marker-positive subgroup conditional on the treatment effect not being statistically significant in the overall population. This is used to construct and examine conditionally bias-corrected estimators of the treatment effect for the marker-positive subgroup. We argue that it may not be appropriate to correct for conditional bias in this setting. Instead, we consider the unconditional bias of estimators of the treatment effect for marker-positive patients. [ABSTRACT FROM AUTHOR]

Summary A new technique for gauge-only precipitation analysis for improved estimation of heavy-to-extreme precipitation is described and evaluated. The technique is based on a novel extension of classical optimal linear estimation theory in which, in addition to error variance, Type-II conditional bias (CB) is explicitly minimized. When cast in the form of well-known kriging, the methodology yields a new kriging estimator, referred to as CB-penalized kriging (CBPK). CBPK, however, tends to yield negative estimates in areas of no or light precipitation. To address this, an extension of CBPK, referred to herein as extended conditional bias penalized kriging (ECBPK), has been developed which combines the CBPK estimate with a trivial estimate of zero precipitation. To evaluate ECBPK, we carried out real-world and synthetic experiments in which ECBPK and the gauge-only precipitation analysis procedure used in the NWS’s Multisensor Precipitation Estimator (MPE) were compared for estimation of point precipitation and mean areal precipitation (MAP), respectively. The results indicate that ECBPK improves hourly gauge-only estimation of heavy-to-extreme precipitation significantly. The improvement is particularly large for estimation of MAP for a range of combinations of basin size and rain gauge network density. This paper describes the technique, summarizes the results and shares ideas for future research. [ABSTRACT FROM AUTHOR]

Sinha & Rao (2009) proposed estimation procedures designed for small-area means, based on robustified maximum likelihood estimators and robust empirical best linear unbiased predictors. Their methods are of the plug-in type and may be biased. Bias-corrected estimators have been proposed by Chambers et al. (2013). Here, we investigate two new approaches: one relying on the work of Chambers (1986), and the second using the concept of conditional bias to measure the influence of units in the population. These two classes of estimators also include correction terms for the bias but are both fully bias-corrected, in the sense that the corrections account for the potential impact of the other domains on the small area of interest. Monte Carlo simulations suggest that the Sinha–Rao method and the bias-adjusted estimator of Chambers et al. (2013) may exhibit a large bias, while the new procedures often offer lower bias and mean squared error. A parametric bootstrap procedure is considered for constructing confidence intervals. [ABSTRACT FROM AUTHOR]

We argue that the conditional bias associated with a sample unit can be a useful measure of influence in finite population sampling. We use the conditional bias to derive robust estimators that are obtained by downweighting the most influential sample units. Under the model-based approach to inference, our proposed robust estimator is closely related to the well-known estimator of Chambers (1986). Under the design-based approach, it possesses the desirable feature of being applicable with most sampling designs used in practice. For stratified simple random sampling, it is essentially equivalent to the estimator of Kokic & Bell (1994). The proposed robust estimator depends on a tuning constant. In this paper, we propose a method for determining the tuning constant and show that the resulting estimator is consistent. Results from a simulation study suggest that our approach improves the efficiency of standard nonrobust estimators when the population contains units that may be influential if selected in the sample. [ABSTRACT FROM AUTHOR]

Characterising the error associated with satellite rainfall estimates based on space-borne passive and active microwave measurements is a major issue for many applications, such as water budget studies or assessment of natural hazards caused by extreme rainfall events. We focus here on the error structure of the Bayesian Rain retrieval Algorithm Including Neural Network (BRAIN), the algorithm that provides instantaneous quantitative precipitation estimates at the surface based on the MADRAS radiometer on board the Megha-Tropiques satellite. A version of BRAIN using data from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) has been compared to reference values derived either from TRMM Precipitation Radar (PR) or from a ground validation (GV) dataset. The ground-based measurements were provided by two densified rain-gauge networks in West Africa, using a geostatistical framework. The comparisons were carried out at the BRAIN retrieval scale for TMI (instantaneous and 12.5 km) and over a ten-year-long period. The primary contribution of this study is to provide some insight into the most significant error sources of satellite rainfall retrieval. This involves comparisons of rainfall detectability, distributions and spatial representativeness, as well as separation of systematic biases and random errors using Generalized Additive Models for Location, Scale and Shape. In spite of their different sampling properties, the three rain estimates were found to detect rainfall consistently. The most important BRAIN-TMI error is due to the rain/no-rain delimitation which causes about 20% of volume rainfall loss relative to PR and GV. BRAIN-TMI presents a narrow PDF relative to GV and catches the spatial structure of the most active part of rain fields. The conditional bias is significant (e.g. +2 mm h−1 for light-moderate rain rates, −2 mm h−1 for rain rates greater than 8 mm h−1) and the overall bias is within 10%. The PR shows a significant underestimation for high rain rates with respect to GV. The proposed framework could be applied to the evaluation of other passive microwave sensors (SSMI, AMSR-E or MADRAS) or rainfall satellite products. Copyright © 2012 Royal Meteorological Society [ABSTRACT FROM AUTHOR]

Simple and ordinary kriging, or SK and OK, respectively, represent the best linear unbiased estimator in the unconditional sense in that they minimize the unconditional (on the unknown truth) error variance and are unbiased in the unconditional mean. However, because the above properties hold only in the unconditional sense, kriging estimates are generally subject to conditional biases that, depending on the application, may be unacceptably large. For example, when used for precipitation estimation using rain gauge data, kriging tends to significantly underestimate large precipitation and, albeit less consequentially, overestimate small precipitation. In this work, we describe an extremely simple extension to SK or OK, referred to herein as conditional bias-penalized kriging (CBPK), which minimizes conditional bias in addition to unconditional error variance. For comparative evaluation of CBPK, we carried out numerical experiments in which normal and lognormal random fields of varying spatial correlation scale and rain gauge network density are synthetically generated, and the kriging estimates are cross-validated. For generalization and potential application in other optimal estimation techniques, we also derive CBPK in the framework of classical optimal linear estimation theory. [ABSTRACT FROM AUTHOR]

Linear models constitute the primary statistical technique for any experimental science. A major topic in this area is the detection of influential subsets of data, that is, of observations that are influential in terms of their effect on the estimation of parameters in linear regression or of the total population parameters. Numerous studies exist on radiocarbon dating which propose a value consensus and remove possible outliers after the corresponding testing. An influence analysis for the value consensus from a Bayesian perspective is developed in this article. [ABSTRACT FROM AUTHOR]

This paper evaluates a nonparametric technique for estimating the conditional probability distribution of a predictand given a vector of predictors. In the current application, the predictors are formed from a multimodel ensemble of simulated streamflows, such that the hydrologic uncertainties are modelled independently of any forcing uncertainties. The technique is based on Bayesian optimal linear estimation of indicator variables and is analogous to indicator cokriging (ICK) in geostatistics. By developing linear estimators for the conditional probability that the observed variable does not exceed several thresholds, ICK provides a discrete approximation of the full conditional probability distribution. The weights of the predictors can be chosen to minimize the expected error variance at each threshold (the Brier score) or, without loss of analytical tractability, a combination of the error variance and the expected square bias conditional upon the observation, i.e. the Type-II conditional bias (CB). The latter is referred to as CB-penalized ICK (CBP-ICK) and is an important enhancement to ICK. Indeed, the biases in atmospheric and hydrologic predictions generally increase towards the tails of their probability distributions. The performance of CBP-ICK is evaluated for selected basins in the eastern USA using a range of probabilistic verification metrics and associated confidence intervals for the sampling uncertainties. Overall, CBP-ICK produces unbiased and skillful estimates of the hydrologic uncertainties, with some sensitivity to the calibration data period at high flow thresholds. More generally, we argue that the common aim in statistical post-processing of 'maximizing sharpness subject to reliability (Type-I CB)' should be recast to accommodate both the Type-I and Type-II CBs, as both are important for practical applications of hydrologic predictions. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Influence Analysis in Principal Component Analysis has usually been tackled using the influence function or local influence approaches. The main objective of this paper is that of proposing influence diagnostics for the eigenvalues of the covariance matrix, that is, for the variance explained by the principal components, from a different angle: that of the conditional bias . An approximation of the conditional bias of the simple eigenvalues of the sample covariance matrix is calculated under normality and some influence diagnostics are proposed. The study is carried by considering joint influence. [Copyright &y& Elsevier]

Abstract: Conditional bias and asymptotic mean sensitivity curve (AMSC) are useful measures to assess the possible effect of an observation on an estimator when sampling from a parametric model. In this paper we obtain expressions for these measures in truncated distributions and study their theoretical properties. Specific results are given for the UMVUE of a parametric function. We note that the AMSC for the UMVUE in truncated distributions verifies some of the most relevant properties we got in a previous paper for the AMSC of UMVUE in the NEF-QVF case, main differences are also established. As for the conditional bias, since it is a finite sample measure, we include some practical examples to illustrate its behaviour when the sample size increases. [ABSTRACT FROM AUTHOR]