Estimation in independent observer line transect surveys for clustered populations

This paper introduces a framework for animal abundance estimation in independent observer line transect surveys of clustered populations. The framework generalizes an approach given in Chen (1999, Environmental and Ecological Statistics 6, in press) to accommodate heterogeneity in detection caused by cluster size and other covariates. Both parametric and nonparametric estimators for the local effective search widths, given the covariates, can be derived from the framework. A nonparametric estimator based on conditional kernel density estimation is proposed and studied owing to its flexibility in modeling the detection functions. A real data set on harbor porpoise in the North Sea is analyzed.     

Local bandwidth selection for kernel estimation of population densities with line transect sampling

Seber (1986, Biometrics 42, 267-292) suggested an approach to biological population density estimation using kernel estimates of the probability density of detection distances in line transect sampling. Chen (1996a, Applied Statistics 45, 135-150) and others have employed cross validation to choose a global bandwidth for the kernel estimator or have suggested adaptive kernel estimation (Chen, 1996b, Biometrics 52, 1283-1294). Because estimation of the density is required at only a single point, we investigate a local bandwidth selection procedure that is a modification of the method of Schucany (1995, Journal of the American Statistical Association 90, 535-540) for nonparametric regression. We report on simulation results comparing the proposed method and a local normal scale rule with cross validation and adaptive estimation. The local bandwidths and normal scale rule produce estimates with mean squares that are half the size of the others in most cases. Consistency results are also provided.     

Nonparametric inverse-probability-weighted estimators based on the highly adaptive lasso

Inverse-probability-weighted estimators are the oldest and potentially most commonly used class of procedures for the estimation of causal effects. By adjusting for selection biases via a weighting mechanism, these procedures estimate an effect of interest by constructing a pseudopopulation in which selection biases are eliminated. Despite their ease of use, these estimators require the correct specification of a model for the weighting mechanism, are known to be inefficient, and suffer from the curse of dimensionality. We propose a class of nonparametric inverse-probability-weighted estimators in which the weighting mechanism is estimated via undersmoothing of the highly adaptive lasso, a nonparametric regression function proven to converge at nearly $n^{-1/3}$-rate to the true weighting mechanism. We demonstrate that our estimators are asymptotically linear with variance converging to the nonparametric efficiency bound. Unlike doubly robust estimators, our procedures require neither derivation of the efficient influence function nor specification of the conditional outcome model. Our theoretical developments have broad implications for the construction of efficient inverse-probability-weighted estimators in large statistical models and a variety of problem settings. We assess the practical performance of our estimators in simulation studies and demonstrate use of our proposed methodology with data from a large-scale epidemiologic study.     

Estimation of the Density of G Given Observations of Y=G+E

We study the problem of estimating the density of a random variable G, given observations of a random variable Y = G + E. The random variable E is independent of G and its probability distribution function is considered as known. We build a family of estimators of the density of G using characteristic functions. We then derive a family of estimators of the density of Y based on the model for Y. The estimators are shown to be asymptotically unbiased and consistent. Simulations show that these estimators are better, as measured by integrated squared error, than the standard kernel estimators. Finally, we give an example of the use of this method for the detection of major genes in animal populations.     

Simultaneous confidence bands in spectral density estimation

We propose a method for the construction of simultaneous confidencebands for a smoothed version of the spectral density of a Gaussianprocess based on nonparametric kernel estimators obtained bysmoothing the periodogram. A studentized statistic is used todetermine the width of the band at each frequency and a frequency-domainbootstrap approach is employed to estimate the distributionof the supremum of this statistic over all frequencies. We proveby means of strong approximations that the bootstrap estimatesconsistently the distribution of the supremum deviation of interestand, consequently, that the proposed confidence bands achieveasymptotically the desired simultaneous coverage probability.The behaviour of our method in finite-sample situations is investigatedby simulations and a real-life data example demonstrates itsapplicability in time series analysis.     

Nonparametric estimation for the three-stage irreversible illness-death model

In this paper, we present new nonparametric estimators of the stage-occupation probabilities in the three-stage irreversible illness-death model. These estimators use a fractional risk set and a reweighting approach and are valid under stage-dependent censoring. Using a simulated data set, we compare the behavior of our estimators with previously proposed estimators. We also apply our estimators to data on time to Pneumocystis pneumonia and death obtained from an AIDS cohort study.     

Semiparametric additive time-varying coefficients model for longitudinal data with censored time origin

Statistical analysis of longitudinal data often involves modeling treatment effects on clinically relevant longitudinal biomarkers since an initial event (the time origin). In some studies including preventive HIV vaccine efficacy trials, some participants have biomarkers measured starting at the time origin, whereas others have biomarkers measured starting later with the time origin unknown. The semiparametric additive time-varying coefficient model is investigated where the effects of some covariates vary nonparametrically with time while the effects of others remain constant. Weighted profile least squares estimators coupled with kernel smoothing are developed. The method uses the expectation maximization approach to deal with the censored time origin. The Kaplan–Meier estimator and other failure time regression models such as the Cox model can be utilized to estimate the distribution and the conditional distribution of left censored event time related to the censored time origin. Asymptotic properties of the parametric and nonparametric estimators and consistent asymptotic variance estimators are derived. A two-stage estimation procedure for choosing weight is proposed to improve estimation efficiency. Numerical simulations are conducted to examine finite sample properties of the proposed estimators. The simulation results show that the theory and methods work well. The efficiency gain of the two-stage estimation procedure depends on the distribution of the longitudinal error processes. The method is applied to analyze data from the Merck 023/HVTN 502 Step HIV vaccine study.     

Testing Linear Contrasts of Means in Experimental Design Without Assuming Normality and Homogeneity of Variances

We investigate the efficiencies of TIKU'S (1967, 1980) modified maximum likelihood (MML) estimators of location and scale parameters of symmetric distributions and show that they are remarkably efficient (jointly). We develop test statistics (based on MML estimators), analogous to the classical tests based on sample means and variances, for testing the equality of two means (the population variances not necessarily equal). We show that these tests are remarkably robust to distributional assumptions and generally more powerful than the well-known nonparametric tests (WILCOXON , normal-score, KOLMOGOROV -SMIRNOV ). We generalize the results to testing linear contrasts of means in experimental design (the error variances not necessarily equal). We show that the analogous tests based on ‘adaptive’ robust estimators (wave, bisquare, HAMPEL ,) etc., GROSS (1976, and other ‘adaptive’ robust estimators) give misleading Type I errors.     

两种珍稀植物群落物种多度分布的核方法研究

首次提出物种多度分布的非参数核密度估计方法,介绍了此方法的构造和主要性质。珍稀濒危植物观光木群落和长苞铁杉群落的乔木层、灌木层、所有木本植物物种多度分布实例拟合结果表明,核方法能很好地描述群落物种多度分布。非参数核估计方法是群落物种多度分布模拟的一种有效方法,它丰富了物种多度分布拟合方法,为珍稀濒危植物的管理与保护提供了理论参考。     

Nonparametric density estimation and regression achieved with topographic maps maximizing the information-theoretic entropy of their outputs

We introduce an unsupervised competitive learning rule, called the extended Maximum Entropy learning Rule (eMER), for topographic map formation. Unlike Kohonen's Self-Organizing Map (SOM) algorithm, the presence of a neighborhood function is not a prerequisite for achieving topology-preserving mappings, but instead it is intended: (1) to speed up the learning process and (2) to perform nonparametric regression. We show that, when the neighborhood function vanishes, the neural weigh t density at convergence approaches a linear function of the input density so that the map can be regarded as a nonparametric model of the input density. We apply eMER to density estimation and compare its performance with that of the SOM algorithm and the variable kernel method. Finally, we apply the ‘batch’ version of eMER to nonparametric projection pursuit regression and compare its performance with that of back-propagation learning, projection pursuit learning, constrained topolog ical mapping, and the Heskes and Kappen approach. Received: 12 August 1996 / Accepted in revised form: 9 April 1997     

Estimation for the distribution of BOD and DO

A nonparametric probability estimator, having a uniform kernel, is utilized to obtain the joint probability density function of BOD and DO along the stretch of a stream when the velocity is distance dependent. The stochastic model is used to obtain probabilistic confidence bounds for BOD and DO. An example and computations are presented which illustrate the usefulness of the model.     

Population intervention causal effects based on stochastic interventions

Estimating the causal effect of an intervention on a population typically involves defining parameters in a nonparametric structural equation model (Pearl, 2000, Causality: Models, Reasoning, and Inference) in which the treatment or exposure is deterministically assigned in a static or dynamic way. We define a new causal parameter that takes into account the fact that intervention policies can result in stochastically assigned exposures. The statistical parameter that identifies the causal parameter of interest is established. Inverse probability of treatment weighting (IPTW), augmented IPTW (A-IPTW), and targeted maximum likelihood estimators (TMLE) are developed. A simulation study is performed to demonstrate the properties of these estimators, which include the double robustness of the A-IPTW and the TMLE. An application example using physical activity data is presented.     

Analysis of interval‐grouped data in weed science: The binnednp Rcpp package

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Nonparametric estimation of stage occupation probabilities in a multistage model with current status data

Multistage models are used to describe individuals (or experimental units) moving through a succession of "stages" corresponding to distinct states (e.g., healthy, diseased, diseased with complications, dead). The resulting data can be considered to be a form of multivariate survival data containing information about the transition times and the stages occupied. Traditional survival analysis is the simplest example of a multistage model, where individuals begin in an initial stage (say, alive) and move irreversibly to a second stage (death). In this article, we consider general multistage models with a directed tree structure (progressive models) in which individuals traverse through stages in a possibly non-Markovian manner. We construct nonparametric estimators of stage occupation probabilities and marginal cumulative transition hazards. Empirical calculations of these quantities are not possible due to the lack of complete data. We consider current status information which represents a more severe form of censoring than the commonly used right censoring. Asymptotic validity of our estimators can be justified using consistency results for nonparametric regression estimators. Finite-sample behavior of our estimators is studied by simulation, in which we show that our estimators based on these limited data compare well with those based on complete data. We also apply our method to a real-life data set arising from a cardiovascular diseases study in Taiwan.     

Semiparametric frailty models for clustered failure time data

We consider frailty models with additive semiparametric covariate effects for clustered failure time data. We propose a doubly penalized partial likelihood (DPPL) procedure to estimate the nonparametric functions using smoothing splines. We show that the DPPL estimators could be obtained from fitting an augmented working frailty model with parametric covariate effects, whereas the nonparametric functions being estimated as linear combinations of fixed and random effects, and the smoothing parameters being estimated as extra variance components. This approach allows us to conveniently estimate all model components within a unified frailty model framework. We evaluate the finite sample performance of the proposed method via a simulation study, and apply the method to analyze data from a study of sexually transmitted infections (STI).     

THE TEMPO AND MODE OF EVOLUTION OF TRANSPOSABLE ELEMENTS AS REVEALED BY MOLECULAR PHYLOGENIES RECONSTRUCTED FROM MOSQUITO GENOMES

Although many mathematical models exist predicting the dynamics of transposable elements (TEs), there is a lack of available empirical data to validate these models and inherent assumptions. Genomes can provide a snapshot of several TE families in a single organism, and these could have their demographics inferred by coalescent analysis, allowing for the testing of theories on TE amplification dynamics. Using the available genomes of the mosquitoes Aedes aegypti and Anopheles gambiae, we indicate that such an approach is feasible. Our analysis follows four steps: (1) mining the two mosquito genomes currently available in search of TE families; (2) fitting, to selected families found in (1), a phylogeny tree under the general time‐reversible (GTR) nucleotide substitution model with an uncorrelated lognormal (UCLN) relaxed clock and a nonparametric demographic model; (3) fitting a nonparametric coalescent model to the tree generated in (2); and (4) fitting parametric models motivated by ecological theories to the curve generated in (3).     

Kernel estimates of dose response

A nonparametric method for analyzing quantal response data from an indirect bioassay experiment is proposed. Kernel estimates of the dose-response curve are used to develop approximate confidence intervals for (i) the optimal combination dose of a drug with therapeutic effects at low doses and toxic effects at high doses, and (ii) the lethal dose levels of a toxic chemical. This nonparametric procedure was implemented on real and simulated data. The confidence interval for problem (i) has high coverage probabilities when the dose-response curve is symmetric about the optima. However, the coverage probabilities are adversely affected by asymmetry about the optima and consequently are not reliable unless the sample sizes are large. The use of kernel estimators with higher-order kernels may alleviate this sensitivity to asymmetry. The confidence interval for problem (ii) has high coverage probabilities robust with respect to the shape or symmetry of the underlying dose-response curve.     

Interspecific variation in tephritid fruit fly larvae surface hydrocarbons

Hydrocarbons extracted from seven species of tephritid fruit fly larvae were analyzed using capillary column gas-liquid chromatography and gas-liquid chromatography/mass spectrometry. Interspecific variation in hydrocarbon patterns was evaluated using both classical and nonparametric discriminant analysis for four of the seven Anastrepha taxa; A. acris, A. Fraterculus, A. suspensa and A. obliqua. Three of the four taxa, excluding A. acris, were correctly classified using a linear discriminant model at 72–83% and a nonparametric kernel density discriminant model at 87–92%. © 1993 Wiley-Liss. Inc.     

Quantile Inference with Multivariate Failure Time Data

Quantiles, especially the medians, of survival times are often used as summary statistics to compare the survival experiences between different groups. Quantiles are robust against outliers and preferred over the mean. Multivariate failure time data often arise in biomedical research. For example, in clinical trials, each patient in the study may experience multiple events which may be of the same type or distinct types, while in family studies of genetic diseases or litter matched mice studies, failure times for subjects in the same cluster may be correlated. In this article, we propose nonparametric procedures for the estimation of quantiles with multivariate failure time data. We show that the proposed estimators asymptotically follow a multivariate normal distribution. The asymptotic variance‐covariance matrix of the estimated quantiles is estimated based on the kernel smoothing and bootstrap techniques. Simulation results show that the proposed estimators perform well in finite samples. The methods are illustrated with the burn‐wound infection data and the Diabetic Retinopathy Study (DRS) data.