A simple ordered data estimator for inverse density weighted expectations

We consider estimation of means of functions that are scaled by an unknown density, or equivalently, integrals of conditional expectations. The “ordered data” estimator we provide is root n$n$ consistent, asymptotically normal, and is numerically extremely simple, involving little more than ordering the data and summing the results. No sample-size-dependent smoothing is required. A similarly simple estimator is provided for the limiting variance. The proofs include new limiting distribution results for functions of nearest-neighbor spacings. Potential applications include endogenous binary choice, willingness to pay, selection, and treatment models.     

A simple estimator for nonlinear error in variable models

We propose a simple estimator for nonlinear method of moment models with measurement error of the classical type when no additional data, such as validation data or double measurements, are available. We assume that the marginal distributions of the measurement errors are Laplace (double exponential) with zero means and unknown variances and the measurement errors are independent of the latent variables and are independent of each other. Under these assumptions, we derive simple revised moment conditions in terms of the observed variables. They are used to make inference about the model parameters and the variance of the measurement error. The results of this paper show that the distributional assumption on the measurement errors can be used to point identify the parameters of interest. Our estimator is a parametric method of moments estimator that uses the revised moment conditions and hence is simple to compute. Our estimation method is particularly useful in situations where no additional data are available, which is the case in many economic data sets. Simulation study demonstrates good finite sample properties of our proposed estimator. We also examine the performance of the estimator in the case where the error distribution is misspecified.     

Approximate confidence and tolerance limits for the discrete Pareto distribution for characterizing extremes in count data

Statistical tolerance intervals for discrete distributions are widely employed for assessing the magnitude of discrete characteristics of interest in applications like quality control, environmental monitoring, and the validation of medical devices. For such data problems, characterizing extreme counts or outliers is also of considerable interest. These applications typically use traditional discrete distributions, like the Poisson, binomial, and negative binomial. The discrete Pareto distribution is an alternative yet flexible model for count data that are heavily right‐skewed. Our contribution is the development of statistical tolerance limits for the discrete Pareto distribution as a strategy for characterizing the extremeness of observed counts in the tail. We discuss the coverage probabilities of our procedure in the broader context of known coverage issues for statistical intervals for discrete distributions. We address this issue by applying a bootstrap calibration to the confidence level of the asymptotic confidence interval for the discrete Pareto distribution's parameter. We illustrate our procedure on a dataset involving cyst formation in mice kidneys.     

A bivariate count data model for household tourism demand

Households' choice of the number of leisure trips and the total number of overnight stays is empirically studied using Swedish tourism data. A bivariate hurdle approach separating the participation (to travel and stay the night or not) from the quantity (the number of trips and nights) decision is employed. The quantity decision is modelled with a bivariate mixed Poisson lognormal model allowing for both positive as well as negative correlation between count variables. The observed endogenous variables are drawn from a truncated density and estimation is pursued by simulated maximum likelihood. The estimation results indicate a negative correlation between the number of trips and nights. In most cases own price effects are as expected negative, while estimates of cross‐price effects vary between samples. Copyright © 2005 John Wiley & Sons, Ltd.     

Selection correction and sensitivity analysis for ordered treatment effect on count response

In estimating the effect of an ordered treatment τ on a count response y with an observational data where τ is self‐selected (not randomized), observed variables x and unobserved variables ε can be unbalanced across the control group (τ = 0) and the treatment groups (τ = 1, …, J). While the imbalance in x causes ‘overt bias’ which can be removed by controlling for x, the imbalance in ε causes ‘covert (hidden or selection) bias’ which cannot be easily removed. This paper makes three contributions. First, a proper counter‐factual causal framework for ordered treatment effect on count response is set up. Second, with no plausible instrument available for τ, a selection correction approach is proposed for the hidden bias. Third, a nonparametric sensitivity analysis is proposed where the treatment effect is nonparametrically estimated under no hidden bias first, and then a sensitivity analysis is conducted to see how sensitive the nonparametric estimate is to the assumption of no hidden bias. The analytic framework is applied to data from the Health and Retirement Study: the treatment is ordered exercise levels in five categories and the response is doctor office visits per year. The selection correction approach yields very large effects, which are however ruled out by the nonparametric sensitivity analysis. This finding suggests a good deal of caution in using selection correction approaches. Copyright © 2004 John Wiley & Sons, Ltd.     

A latent class poisson regression model for heterogeneous count data

In this paper an approach is developed that accommodates heterogeneity in Poisson regression models for count data. The model developed assumes that heterogeneity arises from a distribution of both the intercept and the coefficients of the explanatory variables. We assume that the mixing distribution is discrete, resulting in a finite mixture model formulation. An EM algorithm for estimation is described, and the algorithm is applied to data on customer purchases of books offered through direct mail. Our model is compared empirically to a number of other approaches that deal with heterogeneity in Poisson regression models.     

A simple,flexible distributed lag technique: The polynomial inverse lag

This paper presents a new distributed lag technique, the polynomial inverse lag, which has two useful characteristics. It has a flexible shape, allowing both humped and monotonically declining lag weight distributions; and it can be easily implemented with a small number of nested OLS regressions. The lag is similar in spirit to the Almon lag, but it is an infinite lag and thus does not require specification of a fixed lag length. Experiments with simulated data show a good ability to replicate the true lag structure even in the face of lag structure misspecifition. The technique is also demonstrated using the well-known St. Louis equation.     

A more flexible joint latent model for longitudinal and survival time data

In this article, a more flexible and easily explained joint latent model with time-varying coefficients is used to characterize time-dependent responses and a failure time. The dependence within time-dependent responses and between time-dependent responses and a failure time, and the heterogeneity in both processes are established through partially non-parametric latent variables. Based on longitudinal and survival time data, an estimation procedure is proposed for the parameter functions of the joint latent model. In our estimation, the approximated likelihood is constructed via substituting the basis function expansions for parameter functions. The expectation and maximization (EM) algorithm is then implemented to obtain the maximizer of the approximated likelihood function, and, hence, the estimated parameter functions. The validity of the considered joint latent model enables us to derive the asymptotic properties of the estimated functions. Moreover, the corresponding finite sample properties and the usefulness of our methods are demonstrated through a Monte Carlo simulation and the AIDS Clinical Trials Group (ACTG) 175 data. A possible extension of our joint latent model and some additional topics of interest are also discussed herein.     

A bivariate Poisson count data model using conditional probabilities

The applied econometrics of bivariate count data predominantly focus on a bivariate Poisson density with a correlation structure that is very restrictive. The main limitation is that this bivariate distribution excludes zero and negative correlation. This paper introduces a new model which allows for a more flexible correlation structure. To this end the joint density is decomposed by means of the multiplication rule in marginal and conditional densities. Simulation experiments and an application of the model to recreational data are presented.     

Statistical properties of the total variation estimator for compositional data

The sample space of compositional data, a simplex, induces a different kind of geometry, known as Aitchison geometry, with the Euclidean space property. For this reason, the standard statistical analysis is not meaningful here, and this is also true for measures of location and covariance. The measure of location, called centre, is the best linear unbiased estimator of the central tendency of the distribution of a random composition with respect to the geometry on the simplex (Pawlowsky-Glahn and Egozcue in Stoch Envir Res Risk Ass, 15:384–398, 2001; Math Geol, 34:259–274, 2002). Its covariance structure is described through a variation matrix, which induces the so called total variation as a measure of dispersion. The aim of the paper is to show that its sample counterpart has theoretical properties, corresponding to the standard multivariate case, like unbiasedness and convergence in probability. Moreover, its distribution in the case of normality on the simplex is developed.     

Strong representation of the presmoothed quantile function estimator for censored data

We consider lifetime data subject to right random censorship. In this context, this paper deals with the topic of estimating the distribution function of the lifetime and the corresponding quantile function. As it has been shown that the classical Kaplan–Meier estimator of the distribution function can be improved by means of presmoothing ideas, we introduce a quantile function estimator via the presmoothed distribution function estimator studied by Cao et al. [Journal of Nonparametric statistics, Vol. 17 (2005) pp. 31–56.] The main result of this paper is an almost sure representation of this presmoothed estimator. As a consequence, its strong consistency and asymptotic normality are established. The performance of this new quantile estimator is analyzed in a simulation study and applied to a real data example.     

A flexible lattice framework for valuing options on assets paying discrete dividends and variable annuities embedding GMWB riders

In a market where a stochastic interest rate component characterizes asset dynamics, we propose a flexible lattice framework to evaluate and manage options on equities paying discrete dividends and variable annuities presenting some provisions, like a guaranteed minimum withdrawal benefit. The framework is flexible in that it allows to combine financial and demographic risk, to embed in the contract early exercise features, and to choose the dynamics for interest rates and traded assets. A computational problem arises when each dividend (when valuing an option) or withdrawal (when valuing a variable annuity) is paid, because the lattice lacks its recombining structure. The proposed model overcomes this problem associating with each node of the lattice a set of representative values of the underlying asset (when valuing an option) or of the personal subaccount (when valuing a variable annuity) chosen among all the possible ones realized at that node. Extensive numerical experiments confirm the model accuracy and efficiency.

     

A consistent model specification test with mixed discrete and continuous data

In this paper we propose a nonparametric kernel-based model specification test that can be used when the regression model contains both discrete and continuous regressors. We employ discrete variable kernel functions and we smooth both the discrete and continuous regressors using least squares cross-validation (CV) methods. The test statistic is shown to have an asymptotic normal null distribution. We also prove the validity of using the wild bootstrap method to approximate the null distribution of the test statistic, the bootstrap being our preferred method for obtaining the null distribution in practice. Simulations show that the proposed test has significant power advantages over conventional kernel tests which rely upon frequency-based nonparametric estimators that require sample splitting to handle the presence of discrete regressors.     

离散制造车间的质量数据采集研究

在智能制造时代,质量数据具有数量大,结构模式复杂,变化多的特点,如果没有合理的质量数据采集方式,会造成质量管理的困难,增加质量管理成本。文章通过分析非关系型数据库特点,得到非关系型数据库是以后质量数据管理应用的重要工具的结论,最后介绍基于非关系型数据库的C/S架构的质量数据采集系统应用的实现。     

Individual effects and dynamics in count data models

In this paper we examine the panel data estimation of dynamic models for count data that include correlated fixed effects and predetermined variables. Use of a linear feedback model is proposed. A quasi-differenced GMM estimator is consistent for the parameters in the dynamic model, but when series are highly persistent, there is a problem of weak instrument bias. An estimator is proposed that utilises pre-sample information of the dependent count variable, which is shown in Monte Carlo simulations to possess desirable small sample properties. The models and estimators are applied to data on US patents and R&D expenditure.     

A consistent estimator for nonlinear regression models

In this paper an estimator for the general (nonlinear) regression model with random regressors is studied which is based on the Fourier transform of a certain weight function. Consistency and asymptotic normality of the estimator are established and simulation results are presented to illustrate the theoretical ones.Supported by the Hungarian National Science Foundation OTKA under Grants No. F 032060/2000 and F 046061/2004 and by the Bolyai Grant of the Hungarian Academy of Sciences.Received October 2003     

Inferring trader behavior from transaction data: A trade count model

We present a model that uses trade counts to infer the arrival of private news and the probability of informed trading (PIN). Although similar in approach, our model avoids problems with factor-driven biases and standard errors associated with estimating the buy-sell model of Easley et al. (1996). In particular, tests using the probability of informed trading may suffer from spurious correlations between the Easley et al. (1996) PIN and firm or market characteristics. Results for our model suggest that trade counts, independent of trade direction, are able to capture important features of a firm’s information environment. (JEL C51, D82)     

Using orthogonal trend contrasts for testing ranked data with ordered alternatives

In the analysis of variance (Anova ) the use of orthogonal contrasts is quite common and is a traditional topic in many basic Anova courses. Similar ideas apply to rank tests. In this paper we present a simple and general method that allows an orthogonal contrast decomposition of rank test statistics such as the Kruskal‐Wallis, Friedman and Durbin statistics. The components of the test statistics are informative, particularly when ordered alternatives are of interest. The method can handle ties, and null distributions are readily available. Most of the methods are not new, but the way we present them is. Moreover, our formulation makes it easier to better understand and interpret the tests when the traditional location‐shift assumption does not hold. The methods are illustrated using several data sets.     

Specification and testing of some modified count data models

This paper explores the specification and testing of some modified count data models. These alternatives permit more flexible specification of the data-generating process (dgp) than do familiar count data models (e.g., the Poisson), and provide a natural means for modeling data that are over- or underdispersed by the standards of the basic models. In the cases considered, the familiar forms of the distributions result as parameter-restricted versions of the proposed modified distributions. Accordingly, score tests of the restrictions that use only the easily-computed ML estimates of the standard models are proposed. The tests proposed by Hausman (1978) and White (1982) are also considered. The tests are then applied to count data models estimated using survey microdata on beverage consumption.     

A local maximum likelihood estimator for Poisson regression

A local maximum likelihood estimator based on Poisson regression is presented as well as its bias, variance and asymptotic distribution. This semiparametric estimator is intended to be an alternative to the Poisson, negative binomial and zero-inflated Poisson regression models that does not depend on regularity conditions and model specification accuracy. Some simulation results are presented. The use of the local maximum likelihood procedure is illustrated on one example from the literature. This procedure is found to perform well. This research was partially supported by Calouste Gulbenkian Foundation and PRODEP III.