We present a broad literature survey of parameter and state estimation for queueing systems. Our approach is based on various inference activities, queueing models, observations schemes, and statistical methods. We categorize these into branches of research that we call estimation paradigms. These include: the classical sampling approach, inverse problems, inference for non-interacting systems, inference with discrete sampling, inference with queueing fundamentals, queue inference engine problems, Bayesian approaches, online prediction, implicit models, and control, design, and uncertainty quantification. For each of these estimation paradigms, we outline the principles and ideas, while surveying key references. We also present various simple numerical experiments. In addition to some key references mentioned here, a periodically-updated comprehensive list of references dealing with parameter and state estimation of queues will be kept in an accompanying annotated bibliography.
Dynamic queueing networks (DQN) model queueing systems where demand varies strongly with time, such as airport terminals. With rapidly rising global air passenger traffic placing increasing pressure on airport terminals, efficient allocation of resources is more important than ever. Parameter inference and quantification of uncertainty are key challenges for developing decision support tools. The DQN likelihood function is, in general, intractable and current approaches to simulation make likelihood-free parameter inference methods, such as approximate Bayesian computation (ABC), infeasible si…
In this article we describe a method for carrying out Bayesian estimation for the double Pareto lognormal (dPlN) distribution which has been proposed as a model for heavy-tailed phenomena. We apply our approach to estimate the $\mathit{dPlN}/M/1$ and $M/\mathit{dPlN}/1$ queueing systems. These systems cannot be analyzed using standard techniques due to the fact that the dPlN distribution does not possess a Laplace transform in closed form. This difficulty is overcome using some recent approximations for the Laplace transform of the interarrival distribution for the $\mathit{Pareto}/M/1$ system…
In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all inputs. We develop a Bayesian approach to Gaussian process modelling capable of incorporating monotonicity information for computer model emulation. Markov chain Monte Carlo methods are used to sample from the posterior distribution of the process given the simulator output and monotonicity information. The performance of the proposed approach in terms of pr…
This note considers the problem of statistical inference of the parameters of the input process to a queue from periodic workload observations. The main focus is the open problem of constructing statistically efficient estimators for a given observation scheme, in the sense of minimizing the asymptotic variance of the estimation error.
Model-assisted estimation with complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting significant variables associated with the study variable would be necessary to achieve efficient estimation of population parameters of interest. In this paper, we formulate a regularized regression estimator in the framework of Bayesian inference using the penalty function as the shrinkage prior for model selection. The proposed Bayesian approach enables us to get not only efficient point estimates but also reasonable credible intervals. R…
Bayesian hierarchical methods implemented for small area estimation focus on reducing the noise variation in published government official statistics by borrowing information among dependent response values. Even the most flexible models confine parameters defined at the finest scale to link to each data observation in a one-to-one construction. We propose a Bayesian multiresolution formulation that utilizes an ensemble of observations at a variety of coarse scales in space and time to additively nest parameters we define at a finer scale, which serve as our focus for estimation. Our construct…
Traffic state estimation plays an important role in facilitating effective traffic management. This study develops a combinatorial approach for nonparametric short-term queue length estimation in terms of cycle-by-cycle partially observed queues from probe vehicles. The method does not assume random arrivals and does not assume any primary parameters or estimation of any parameters but uses simple algebraic expressions that only depend on signal timing. For an approach lane at a traffic intersection, the conditional queue lengths given probe vehicle location, count, time, and analysis interval…
Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in m…
Many countries conduct a full census survey to report official population statistics. As no census survey ever achieves 100 per cent response rate, a post-enumeration survey (PES) is usually conducted and analysed to assess census coverage and produce official population estimates by geographic area and demographic attributes. Considering the usually small size of PES, direct estimation at the desired level of disaggregation is not feasible. Design-based estimation with sampling weight adjustment is a commonly used method but is difficult to implement when survey non-response patterns cannot b…
We present a review of some recent results on estimation of location parameter for several models of observations with cusp-type singularity at the change point. We suppose that the cusp-type models fit better to the real phenomena described usually by change point models. The list of models includes Gaussian, inhomogeneous Poisson, ergodic diffusion processes, time series and the classical case of i.i.d. observations. We describe the properties of the maximum likelihood and Bayes estimators under some asymptotic assumptions. The asymptotic efficiency of estimators are discussed as well and th…
Nearest neighbor imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the nearest neighbor imputation estimator for general population parameters, including population means, proportions and quantiles. For variance estimation, the conventional bootstrap inference for matching estimators with fixed number of matches has been shown to be invalid due to the nonsmoothness nature of the matching estimator. We propose asymptotically valid replication variance estimation. The key strategy is to construct replicates of the estim…
The Future Elderly Model and related microsimulations are modeled as Markov chains. These simulations rely on longitudinal survey data to estimate their transition models. The use of survey data presents several incomplete data problems, including coarse and irregular spacing of interviews, data collection from subsamples, and structural changes to surveys over time. The Expectation-Maximization algorithm is adapted to create a method for maximum likelihood estimation of Markov chain transition models using incomplete data. The method is demonstrated on a simplified version of the Future Elder…
An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well known Horvitz-Thompson estimators by combining the spline and local polynomial smoothing methods. These estimators are calibrated, asymptotically design-unbiased, consistent, normal and robust in the sense of asymptotically attaining the Godambe-Joshi lower bound to the anticipated variance. A consistent model selection procedure is further developed to select…
The odds ratio measure is used in health and social surveys where the odds of a certain event is to be compared between two populations. It is defined using logistic regression, and requires that data from surveys are accompanied by their weights. A nonparametric estimation method that incorporates survey weights and auxiliary information may improve the precision of the odds ratio estimator. It consists in $B$-spline calibration which can handle the nonlinear structure of the parameter. The variance is estimated through linearization. Implementation is possible through standard survey softwar…
Model-based small area estimation is frequently used in conjunction with survey data in order to establish estimates for under-sampled or unsampled geographies. These models can be specified at either the area-level, or the unit-level, but unit-level models often offer potential advantages such as more precise estimates and easy spatial aggregation. Nevertheless, relative to area-level models, literature on unit-level models is less prevalent. In modeling small areas at the unit level, challenges often arise as a consequence of the informative sampling mechanism used to collect the survey data…
Survey statisticians make use of the available auxiliary information to improve estimates. One important example is given by calibration estimation, that seeks for new weights that are close (in some sense) to the basic design weights and that, at the same time, match benchmark constraints on available auxiliary information. Recently, multiple frame surveys have gained much attention and became largely used by statistical agencies and private organizations to decrease sampling costs or to reduce frame undercoverage errors that could occur with the use of only a single sampling frame. Much atte…
We propose an orthogonal series density estimator for complex surveys, where samples are neither independent nor identically distributed. The proposed estimator is proved to be design-unbiased and asymptotically design-consistent. The asymptotic normality is proved under both design and combined spaces. Two data driven estimators are proposed based on the proposed oracle estimator. We show the efficiency of the proposed estimators in simulation studies. A real survey data example is provided for an illustration.
Calibration methods have been widely studied in survey sampling over the last decades. Viewing calibration as an inverse problem, we extend the calibration technique by using a maximum entropy method. Finding the optimal weights is achieved by considering random weights and looking for a discrete distribution which maximizes an entropy under the calibration constraint. This method points a new frame for the computation of such estimates and the investigation of its statistical properties.
Small area (or small domain) estimation is still rarely applied in business statistics, because of challenges arising from the skewness and variability of variables such as turnover. We examine a range of small area estimation methods as the basis for estimating the activity of industries within the retail sector in the Netherlands. We use tax register data and a sampling procedure which replicates the sampling for the retail sector of Statistics Netherlands' Structural Business Survey as a basis for investigating the properties of small area estimators. In particular, we consider the use of t…
We consider an empirical likelihood framework for inference for a statistical model based on an informative sampling design. Covariate information is incorporated both through the weights and the estimating equations. The estimator is based on conditional weights. We show that under usual conditions, with population size increasing unbounded, the estimates are strongly consistent, asymptotically unbiased and normally distributed. Our framework provides additional justification for inverse probability weighted score estimators in terms of conditional empirical likelihood. In doing so, it bridge…
A model-assisted semiparametric method of estimating finite population totals is investigated to improve the precision of survey estimators by incorporating multivariate auxiliary information. The proposed superpopulation model is a single-index model which has proven to be a simple and efficient semiparametric tool in multivariate regression. A class of estimators based on polynomial spline regression is proposed. These estimators are robust against deviation from single-index models. Under standard design conditions, the proposed estimators are asymptotically design-unbiased, consistent and …
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；The University of Chicago Booth School of Business（芝加哥大学布斯商学院）
Graphs from complex systems often share a partial underlying structure across domains while retaining individual features. Thus, identifying common structures can shed light on the underlying signal, for instance, when applied to scientific discoveries or clinical diagnoses. Furthermore, growing evidence shows that the shared structure across domains boosts the estimation power of graphs, particularly for high-dimensional data. However, building a joint estimator to extract the common structure may be more complicated than it seems, most often due to data heterogeneity across sources. This man…
The cross-classified sampling design consists in drawing samples from a two-dimension population, independently in each dimension. Such design is commonly used in consumer price index surveys and has been recently applied to draw a sample of babies in the French ELFE survey, by crossing a sample of maternity units and a sample of days. We propose to derive a general theory of estimation for this sampling design. We consider the Horvitz-Thompson estimator for a total, and show that the cross-classified design will usually result in a loss of efficiency as compared to the widespread two-stage de…
Model-assisted estimators have attracted a lot of attention in the last three decades. These estimators attempt to make an efficient use of auxiliary information available at the estimation stage. A working model linking the survey variable to the auxiliary variables is specified and fitted on the sample data to obtain a set of predictions, which are then incorporated in the estimation procedures. A nice feature of model-assisted procedures is that they maintain important design properties such as consistency and asymptotic unbiasedness irrespective of whether or not the working model is corre…
