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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]

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]

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]

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]

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]

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]

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]

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]