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Density Estimator (density + estimator)
Kinds of Density Estimator Selected AbstractsAllowing for redundancy and environmental effects in estimates of home range utilization distributionsENVIRONMETRICS, Issue 1 2005W. G. S. Hines Abstract Real location data for radio tagged animals can be challenging to analyze. They can be somewhat redundant, since successive observations of an animal slowly wandering through its environment may well show very similar locations. The data set can possess trends over time or be irregularly timed, and they can report locations in environments with features that should be incorporated to some degree. Also, the periods of observation may be too short to provide reliable estimates of characteristics such as inter-observation correlation levels that can be used in conventional time-series analyses. Moreover, stationarity (in the sense of the data being generated by a source that provides observations of constant mean, variance and correlation structure) may not be present. This article considers an adaptation of the kernel density estimator for estimating home ranges, an adaptation which allows for these various complications and which works well in the absence of exact (or precise) information about correlation structure and parameters. Modifications to allow for irregularly timed observations, non-stationarity and heterogeneous environments are discussed and illustrated. Copyright © 2004 John Wiley & Sons, Ltd. [source] A Streamflow Forecasting Framework using Multiple Climate and Hydrological Models,JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, Issue 4 2009Paul J. Block Abstract:, Water resources planning and management efficacy is subject to capturing inherent uncertainties stemming from climatic and hydrological inputs and models. Streamflow forecasts, critical in reservoir operation and water allocation decision making, fundamentally contain uncertainties arising from assumed initial conditions, model structure, and modeled processes. Accounting for these propagating uncertainties remains a formidable challenge. Recent enhancements in climate forecasting skill and hydrological modeling serve as an impetus for further pursuing models and model combinations capable of delivering improved streamflow forecasts. However, little consideration has been given to methodologies that include coupling both multiple climate and multiple hydrological models, increasing the pool of streamflow forecast ensemble members and accounting for cumulative sources of uncertainty. The framework presented here proposes integration and offline coupling of global climate models (GCMs), multiple regional climate models, and numerous water balance models to improve streamflow forecasting through generation of ensemble forecasts. For demonstration purposes, the framework is imposed on the Jaguaribe basin in northeastern Brazil for a hindcast of 1974-1996 monthly streamflow. The ECHAM 4.5 and the NCEP/MRF9 GCMs and regional models, including dynamical and statistical models, are integrated with the ABCD and Soil Moisture Accounting Procedure water balance models. Precipitation hindcasts from the GCMs are downscaled via the regional models and fed into the water balance models, producing streamflow hindcasts. Multi-model ensemble combination techniques include pooling, linear regression weighting, and a kernel density estimator to evaluate streamflow hindcasts; the latter technique exhibits superior skill compared with any single coupled model ensemble hindcast. [source] Central limit theorems for nonparametric estimators with real-time random variablesJOURNAL OF TIME SERIES ANALYSIS, Issue 5 2010Tae Yoon Kim Primary 62G07; 62F12; Secondary 62M05 C13; C14 In this article, asymptotic theories for nonparametric methods are studied when they are applied to real-time data. In particular, we derive central limit theorems for nonparametric density and regression estimators. For this we formally introduce a sequence of real-time random variables indexed by a parameter related to fine gridding of time domain (or fine discretization). Our results show that the impact of fine gridding is greater in the density estimation case in the sense that strong dependence due to fine gridding severely affects the major strength of nonparametric density estimator (or its data-adaptive property). In addition, we discuss some issues about nonparametric regression model with fine gridding of time domain. [source] A superharmonic prior for the autoregressive process of the second-orderJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2008Fuyuhiko Tanaka Abstract., The Bayesian estimation of the spectral density of the AR(2) process is considered. We propose a superharmonic prior on the model as a non-informative prior rather than the Jeffreys prior. Theoretically, the Bayesian spectral density estimator based on it dominates asymptotically the one based on the Jeffreys prior under the Kullback,Leibler divergence. In the present article, an explicit form of a superharmonic prior for the AR(2) process is presented and compared with the Jeffreys prior in computer simulation. [source] Minimum , -divergence estimation for arch modelsJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2006S. Ajay Chandra Abstract., This paper considers a minimum , -divergence estimation for a class of ARCH(p) models. For these models with unknown volatility parameters, the exact form of the innovation density is supposed to be unknown in detail but is thought to be close to members of some parametric family. To approximate such a density, we first construct an estimator for the unknown volatility parameters using the conditional least squares estimator given by Tjøstheim [Stochastic processes and their applications (1986) Vol. 21, pp. 251,273]. Then, a nonparametric kernel density estimator is constructed for the innovation density based on the estimated residuals. Using techniques of the minimum Hellinger distance estimation for stochastic models and residual empirical process from an ARCH(p) model given by Beran [Annals of Statistics (1977) Vol. 5, pp. 445,463] and Lee and Taniguchi [Statistica Sinica (2005) Vol. 15, pp. 215,234] respectively, it is shown that the proposed estimator is consistent and asymptotically normal. Moreover, a robustness measure for the score of the estimator is introduced. The asymptotic efficiency and robustness of the estimator are illustrated by simulations. The proposed estimator is also applied to daily stock returns of Dell Corporation. [source] Home-range overlap and spatial organization as indicators for territoriality among male bushbuck (Tragelaphus scriptus)JOURNAL OF ZOOLOGY, Issue 3 2005Torsten Wronski Abstract Many studies have concluded that territoriality is absent in male bushbuck Tragelaphus scriptus but a minority has suggested that some exclusive mechanisms act between adult males. This study provides indirect evidence for the existence of territorial structures between adult male bushbuck by comparing home-range overlap between adult and sub-adult males. The spatial organization of individuals in relation to each other was established by using numerical classification. Location fixes of 52 males, each individual distinguished by a characteristic coat pattern, were taken over a period of 3 years. Home ranges were estimated using the fixed kernel density estimator. Two indices (coefficient of overlap, index of overlap) were applied to compare home-range overlap between the different male age classes. There was a strong home-range overlap up to the 30% home-range core between sub-adult as well as between adult and sub-adult males, while adult male home ranges overlapped up to the 50% home-range core only. It could be shown that home ranges of adult males overlapped significantly less than those of sub-adult males and those between sub-adult and adult males indicating an exclusive use of central core areas (home sites). Sub-adult males form bachelor pools without being permanently associated. With increasing age, sub-adult males challenge territory holders and replace them in order to take over their exclusive areas. These maturing sub-adult males (young adults), often focused on a particular territory holder denoting the young adults as prospects or candidates. [source] On testing for multivariate ARCH effects in vector time series modelsTHE CANADIAN JOURNAL OF STATISTICS, Issue 3 2003Pierre Duchesne Abstract Using a spectral approach, the authors propose tests to detect multivariate ARCH effects in the residuals from a multivariate regression model. The tests are based on a comparison, via a quadratic norm, between the uniform density and a kernel-based spectral density estimator of the squared residuals and cross products of residuals. The proposed tests are consistent under an arbitrary fixed alternative. The authors present a new application of the test due to Hosking (1980) which is seen to be a special case of their approach involving the truncated uniform kernel. However, they typically obtain more powerful procedures when using a different weighting. The authors consider especially the procedure of Robinson (1991) for choosing the smoothing parameter of the spectral density estimator. They also introduce a generalized version of the test for ARCH effects due to Ling & Li (1997). They investigate the finite-sample performance of their tests and compare them to existing tests including those of Ling & Li (1997) and the residual-based diagnostics of Tse (2002).Finally, they present a financial application. Adoptant une approche spectrale, les auteurs proposent des tests permettant de détecter des effets ARCH multivariés dans les résidus d'un modèle de régression multivarié. Leurs tests reposent sur une comparaison en norme quadratique de la densité spectrale uniforme et d'un estimateur à noyau de la densité spectrale des résidus carrés et des produits croisés des résidus. Ces tests sont convergents sous une contre-hypothèse fixe quelconque. Les auteurs présentent une nouvelle application du test de Hosking (1980) qui correspond dans leur approche au choix particulier d'un noyau uniforme tronqué. Cependant, l'emploi d'autres pondérations leur permet d'obtenir des test encore plus puissants. Les auteurs étudient notamment la procédure de Robinson (1991) pour le choix du paramètre de lissage de l'estimateur de la densité spectrale. Os proposent aussi une version généralisée du test pour effets ARCH de Ling & Li (1997). Ils examinent le comportement de leurs tests dans de petits échantillons par voie de simulation et les comparent aux tests de Ling & Li (1997) et aux diagnostiques de Tse (2002) fondés sur les résidus, us présentent en outre une application financière. [source] Multivariate Statistical Process Monitoring Using Kernel Density EstimationASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 1-2 2005J. Liang In this paper, a general kernel density estimator has been introduced and discussed for multivariate processes in order to provide enhanced real-time performance monitoring. The proposed approach is based upon the concept of kernel density function, which is more appropriate to the underlying probability distribution of industrial process data in the development of a real-time monitoring scheme, to overcome the limitations of the conventional approach of defining the normal operating region based upon the assumption of normality. An optimal bandwidth selection rule is given based on the so-called mean integrated squared error index, and that is the normal operating region of process calculated using the optimal kernel density estimator before new process data are projected onto the normal operating region. The results of a case study of an industrial reheating furnace clearly demonstrates the power and advantages (e.g. decreasing the number of false alarms, identifying abnormal behaviour earlier, and reducing data sparsity) of the kernel density estimator-based approach over the conventional approach under the assumption of normality, which is still widely used. [source] Impact of the timing of stocking on growth and allometric index in aquaculture-based fisheriesFISHERIES MANAGEMENT & ECOLOGY, Issue 2 2004A. L. Ibáñez Abstract The impact of tilapia stocking on fisheries production in Lake Metztitlán was determined through progression analysis of modes obtained from (Gaussian) kernel density estimators (KDEs) of size frequency distributions of juvenile tilapia stocked after a period of total desiccation. The relationship between the allometric index of four cohorts and water temperature and variation in the volume of the basin was analysed. The use of KDEs was found to be a useful technique for the recognition and progression analysis of modes. The reasons for the low yields from the tilapia fishery of Lake Metztitlán are poor growth rate, low water temperature, which is manifest in low allometric indices, and the use of small mesh size nets. Yields can be sustained by improving fishery management; otherwise it is necessary to continue stocking. [source] The Impact of Industrial Restructuring on Earnings Inequality: The Decline of Steel and Earnings in PittsburghGROWTH AND CHANGE, Issue 1 2004Patricia Beeson ABSTRACT Inter-industry employment shifts were largely responsible for changes in the income distribution in the Pittsburgh region during the 1980s. Kernel density estimators were used, together with decomposition techniques developed by DiNardo et al. (1996) to show that industry shifts were responsible for over 90 percent of the earnings reductions at some points on the earnings distribution. Most of the losses at the lower end of the distribution occurred in the early 1980s as the economy plunged into a deep recession. The recovery in the later part of the decade brought little improvement as earnings in the lower part of the distribution continued to fall with the increase in employment of part-time workers in the low-wage trade and service sectors. [source] Empirical comparison of density estimators for large carnivoresJOURNAL OF APPLIED ECOLOGY, Issue 1 2010Martyn E. Obbard Summary 1. Population density is a critical ecological parameter informing effective wildlife management and conservation decisions. Density is often estimated by dividing capture,recapture (C,R) estimates of abundance () by size of the study area, but this relies on the assumption of geographic closure , a situation rarely achieved in studies of large carnivores. For geographically open populations is overestimated relative to the size of the study area because animals with only part of their home range on the study area are available for capture. This bias (,edge effect') is more severe when animals such as large carnivores range widely. To compensate for edge effect, a boundary strip around the trap array is commonly included when estimating the effective trap area (). Various methods for estimating the width of the boundary strip are proposed, but / estimates of large carnivore density are generally mistrusted unless concurrent telemetry data are available to define. Remote sampling by cameras or hair snags may reduce study costs and duration, yet without telemetry data inflated density estimates remain problematic. 2. We evaluated recently developed spatially explicit capture,recapture (SECR) models using data from a common large carnivore, the American black bear Ursus americanus, obtained by remote sampling of 11 geographically open populations. These models permit direct estimation of population density from C,R data without assuming geographic closure. We compared estimates derived using this approach to those derived using conventional approaches that estimate density as /. 3. Spatially explicit C,R estimates were 20,200% lower than densities estimated as /. AICc supported individual heterogeneity in capture probabilities and home range sizes. Variable home range size could not be accounted for when estimating density as /. 4.Synthesis and applications. We conclude that the higher densities estimated as / compared to estimates from SECR models are consistent with positive bias due to edge effects in the former. Inflated density estimates could lead to management decisions placing threatened or endangered large carnivores at greater risk. Such decisions could be avoided by estimating density by SECR when bias due to geographic closure violation cannot be minimized by study design. [source] A semiparametric model for binary response and continuous outcomes under index heteroscedasticityJOURNAL OF APPLIED ECONOMETRICS, Issue 5 2009Roger Klein This paper formulates a likelihood-based estimator for a double-index, semiparametric binary response equation. A novel feature of this estimator is that it is based on density estimation under local smoothing. While the proofs differ from those based on alternative density estimators, the finite sample performance of the estimator is significantly improved. As binary responses often appear as endogenous regressors in continuous outcome equations, we also develop an optimal instrumental variables estimator in this context. For this purpose, we specialize the double-index model for binary response to one with heteroscedasticity that depends on an index different from that underlying the ,mean response'. We show that such (multiplicative) heteroscedasticity, whose form is not parametrically specified, effectively induces exclusion restrictions on the outcomes equation. The estimator developed exploits such identifying information. We provide simulation evidence on the favorable performance of the estimators and illustrate their use through an empirical application on the determinants, and affect, of attendance at a government-financed school. Copyright © 2009 John Wiley & Sons, Ltd. [source] Evaluating capture,recapture population and density estimation of tigers in a population with known parametersANIMAL CONSERVATION, Issue 1 2010R. K. Sharma Abstract Conservation strategies for endangered species require accurate and precise estimates of abundance. Unfortunately, obtaining unbiased estimates can be difficult due to inappropriate estimator models and study design. We evaluate population,density estimators for tigers Panthera tigris in Kanha Tiger Reserve, India, using camera traps in conjunction with telemetry (n=6) in a known minimum population of 14 tigers. An effort of 462 trap nights over 42 days yielded 44 photographs of 12 adult tigers. Using closed population estimators, the best-fit model (program capture) accounted for individual heterogeneity (Mh). The least biased and precise population estimate ( (SE) []) was obtained by the Mh Jackknife 1 (JK1) [14 (1.89)] in program care -2. Tiger density ( (SE) []) per 100 km2 was estimated at 13 (2.08) when the effective trapping area was estimated using the half mean maximum distance moved (1/2 MMDM), 8.1 (2.08), using the home-range radius, 7.8 (1.59), with the full MMDM and 8.0 (3.0) with the spatial likelihood method in program density 4.1. The actual density of collared tigers (3.27 per 100 km2) was closely estimated by home-range radius at 3.9 (0.76), full MMDM at 3.48 (0.81) and spatial likelihood at 3.78 (1.54), but overestimated by 1/2 MMDM at 6 (0.81) tigers per 100 km2. Sampling costs (Rs. 450 per camera day) increased linearly with camera density, while the precision of population estimates leveled off at 25 cameras per 100 km2. At simulated low tiger densities, a camera density of 50 per 100 km2 with an effort of 8 trap nights km,2 provided 95% confidence coverage, but estimates lacked precision. [source] Variable kernel density estimationAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2003Martin L. Hazelton Summary This paper considers the problem of selecting optimal bandwidths for variable (sample-point adaptive) kernel density estimation. A data-driven variable bandwidth selector is proposed, based on the idea of approximating the log-bandwidth function by a cubic spline. This cubic spline is optimized with respect to a cross-validation criterion. The proposed method can be interpreted as a selector for either integrated squared error (ISE) or mean integrated squared error (MISE) optimal bandwidths. This leads to reflection upon some of the differences between ISE and MISE as error criteria for variable kernel estimation. Results from simulation studies indicate that the proposed method outperforms a fixed kernel estimator (in terms of ISE) when the target density has a combination of sharp modes and regions of smooth undulation. Moreover, some detailed data analyses suggest that the gains in ISE may understate the improvements in visual appeal obtained using the proposed variable kernel estimator. These numerical studies also show that the proposed estimator outperforms existing variable kernel density estimators implemented using piecewise constant bandwidth functions. [source] | |||||||||||||