Marzia Marcheselli

A three-phase sampling strategy for large-scale multiresource forest inventories

This article considers a two-phase estimation for the areal extent of K land categories partitioning a study region and a three-phase estimation for the biomass of W forest categories out of the K. In the first phase, a sample of N points is selected according to the unaligned systematic sampling. In the second phase, the selected points are partitioned into L strata on the basis of aerial photos. Then, a total sample of n < N points is selected by stratified sampling and the selected points are visited on the ground and correctly classified into one of K categories. The information achieved in the second phase is sufficient for obtaining an unbiased estimator of the areal extent vector together with a conservative estimator of its variance-covariance matrix. As to the estimation of the biomass of the W forest categories, in the third phase the second-phase sample is further partitioned into substrata on the basis of ground information. Finally, a total sample of m < n points is selected by stratified sampling. Then a plot of adequate radius centered at each point is considered and the biomass is recorded within. An unbiased estimator of the biomass vector is derived together with a conservative estimator of its variance-covariance matrix. The proposed strategy also makes it possible to obtain the calibrated estimator of the areal extent vector as well as estimators for the sums or ratios of the areal extents and biomasses. The application of the strategy in the Italian National Forest Inventory is considered.

Statistical Analysis of the Hirsch Index

The Hirsch index (commonly referred to as h-index) is a bibliometric indicator which is widely recognized as effective for measuring the scientific production of a scholar since it summarizes size and impact of the research output. In a formal setting, the h-index is actually an empirical functional of the distribution of the citation counts received by the scholar. Under this approach, the asymptotic theory for the empirical h-index has been recently exploited when the citation counts follow a continuous distribution and, in particular, variance estimation has been considered for the Pareto-type and the Weibull-type distribution families. However, in bibliometric applications, citation counts display a distribution supported by the integers. Thus, we provide general properties for the empirical h-index under the small- and large-sample settings. In addition, we also introduce consistent nonparametric variance estimation, which allows for the implemention of large-sample set estimation for the theoretical h-index.

Parameter Estimation for the Discrete Stable Family

The discrete stable family constitutes an interesting two-parameter model of distributions on the non-negative integers with a Paretian tail. The practical use of the discrete stable distribution is inhibited by the lack of an explicit expression for its probability function. Moreover, the distribution does not possess moments of any order. Therefore, the usual tools—such as the maximum-likelihood method or even the moment method—are not feasible for parameter estimation. However, the probability generating function of the discrete stable distribution is available in a simple form. Hence, we initially explore the application of some existing estimation procedures based on the empirical probability generating function. Subsequently, we propose a new estimation method by minimizing a suitable weighted L 2-distance between the empirical and the theoretical probability generating functions. In addition, we provide a goodness-of-fit statistic based on the same distance.

Improved strategies for coverage estimation by using replicated line-intercept sampling

Coverage, i.e., the area covered by the target attribute in the study region, is a key parameter in many surveys. Coverage estimation is usually performed by adopting a replicated protocol based on line-intercept sampling coupled with a suitable linear homogeneous estimator. Since coverage is a parameter which may be interestingly represented as the integral of a suitable function, improved Monte Carlo strategies for implementing the replicated protocol are introduced in order to achieve estimators with small variance rates. In addition, new specific theoretical results on Monte Carlo integration methods are given to deal with the integrand functions arising in the special coverage estimation setting.

Design-based ranked set sampling using auxiliary variables

A ranked set sampling protocol is proposed when an auxiliary variable is available in addition to the target variable in sample surveys. The protocol may be practically carried out without additional sampling effort or costs. Under the suggested sampling scheme, the estimators usually adopted in surveys with auxiliary information - such as the ratio estimator or the regression estimator - display surprising theoretical properties as well as high performance in practice.

Statistical inference on the h-index with an application to top-scientist performance

Despite the huge amount of literature concerning the h-index, few papers have been devoted to its statistical analysis when a probabilistic distribution is assumed for citation counts. The present contribution mainly aims to divulge the inferential techniques recently introduced by Pratelli et al. (2012), by explaining the details for proper point and set estimation of the theoretical h-index. Moreover, some new achievements on simultaneous inference – addressed to produce suitable scholar comparisons – are carried out. Finally, the analysis of the citation dataset for the Nobel Laureates (in the last five years) and for the Fields medallists (from 2002 onward) is considered in order to exemplify the theoretical issues.

Design-based asymptotics for two-phase sampling strategies in environmental surveys

&NA; We analyse design‐based properties of two‐phase strategies for estimating totals and nonlinear functions of totals for environmental populations when the sampling schemes are uniquely determined by points placed in the study region. In the first phase, points are located using tessellation stratified sampling, whereas in the second phase a finite population sampling scheme is adopted. We give sufficient conditions on second‐phase designs that ensure consistency, and we investigate the variance convergence rate for some familiar schemes.

Species abundance estimation using point-to-plant sampling in a design-based setting

A new species abundance estimator is proposed when point-to-plant sampling is adopted in a design-based framework. The method is based on the relationship between each species abundance and the probability density function of the relative squared point-to-plant distance. Using this result, a kernel estimator for species abundance is provided and the nearest neighbor method is suggested for bandwidth selection. The proposed estimator requires no assumptions about the species point patterns nor corrections for sampling near the edges of the study region. Moreover, the estimator shows suitable statistical properties as well as good practical performance as is shown in a simulation study.

Design-Based Maps for Finite Populations of Spatial Units

ABSTRACT The estimation of the values of a survey variable in finite populations of spatial units is considered for making maps when samples of spatial units are selected by probabilistic sampling schemes. The single values are estimated by means of an inverse distance weighting predictor. The design-based asymptotic properties of the resulting maps, referred to as the design-based maps, are considered when the study area remains fixed and the sizes of the spatial units tend to zero. Conditions ensuring design-based asymptotic unbiasedness and consistency are derived. They essentially require the existence of a pointwise or uniformly continuous density function of the survey variable onto the study area, some regularities in the size and shape of the units, and the use of spatially balanced designs to select units. The continuity assumption can be relaxed into a Riemann integrability assumption when estimation is performed at a sufficiently small spatial grain and the estimates are subsequently aggregated at a greater grain. A computationally simple mean squared error estimator is proposed. A simulation study is performed to assess the theoretical results. An application to estimate the map of wine cultivations in Tuscany (Central Italy) is considered. Supplementary materials for this article are available online.

Parameter estimation in the classical occupancy model

Under the classical occupancy model, balls are randomly and independently allocated into cells (by assuming that each arrangement of balls is equally probable) in such a way that the random variable of interest is the empty cell number. In some practical applications the total cell number is known and the target parameter turns out to be the number of balls which is estimated on the basis of the observed empty cell count. For instance, the classical occupancy model is commonly adopted for airborne-microorganism abundance estimation, a topic of central importance in environmental microbiology, in aerobiology and in occupational medicine. The classical occupancy model is also applied to the analysis of US National AIDS surveillance data (which are inflated by duplicate reporting) in order to estimate the true population size of AIDS cases. Since many inaccuracies and misunderstandings are present in applied literature, the aim of the present paper is to introduce a formal analysis of the inferential issues connected with the estimation of the number of balls.