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.     

Estimation and testing for a partially linear single-index spatial regression model

ABSTRACT

Observations recorded on ‘locations’ usually exhibit spatial dependence. In an effort to take into account both the spatial dependence and the possible underlying non-linear relationship, a partially linear single-index spatial regression model is proposed. This paper establishes the estimators of the unknowns. Moreover, it builds a generalized F-test to determine whether or not the data provide evidence on using linear settings in empirical studies. Their asymptotic properties are derived. Monte Carlo simulations indicate that the estimators and test statistic perform well. The analysis of Chinese house price data shows the existence of both spatial dependence and a non-linear relationship.     

Blockwise bootstrap wavelet in nonparametric regression model with weakly dependent processes

In this paper, we suggest a blockwise bootstrap wavelet to estimate the regression function in the nonparametric regression models with weakly dependent processes for both designs of fixed and random. We obtain the asymptotic orders of the biases and variances of the estimators and establish the asymptotic normality for a modified version of the estimators. We also introduce a principle to select the length of data block. These results show that the blockwise bootstrap wavelet is valid for general weakly dependent processes such as α-mixing, φ-mixing and ρ-mixing random variables.     

Specification testing for regression models with dependent data

We examine a consistent test for the correct specification of a regression function with dependent data. The test is based on the supremum of the difference between the parametric and nonparametric estimates of the regression model. Rather surprisingly, the behaviour of the test depends on whether the regressors are deterministic or stochastic. In the former situation, the normalization constants necessary to obtain the limiting Gumbel distribution are data dependent and difficult to estimate, so it may be difficult to obtain valid critical values, whereas, in the latter, the asymptotic distribution may not be even known. Because of that, under very mild regularity conditions, we describe a bootstrap analogue for the test, showing its asymptotic validity and finite sample behaviour in a small Monte-Carlo experiment.     

Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable

This paper presents a method for estimating the model Λ(Y)=min(β′X+U, C), where Y is a scalar, Λ is an unknown increasing function, X is a vector of explanatory variables, β is a vector of unknown parameters, U has unknown cumulative distribution function F, and C is a censoring threshold. It is not assumed that Λ and F belong to known parametric families; they are estimated nonparametrically. This model includes many widely used models as special cases, including the proportional hazards model with unobserved heterogeneity. The paper develops n^1/2-consistent, asymptotically normal estimators of Λ and F. Estimators of β that are n^1/2-consistent and asymptotically normal already exist. The results of Monte Carlo experiments illustrate the finite-sample behavior of the estimators.     

A solution to log of dependent variables with negative observations

Journal of Productivity Analysis - Negative observations pose a problem in econometric models that apply log-transformation to the data. We propose a simple yet effective solution to this problem...     

Extension of the Wald statistic to models with dependent observations

A generalization of the Wald statistic for testing composite hypotheses is suggested for dependent data from exponential models which include Lévy processes and diffusion fields. The generalized statistic is proved to be asymptotically chi-squared distributed under regular composite hypotheses. It is simpler and more easily available than the generalized likelihood ratio statistic. Simulations in an example where the latter statistic is available show that the generalized Wald test achieves higher average power than the generalized likelihood ratio test. Received: February 29, 2000     

A count-amount model with endogenous recording of observations

This paper discusses some of the problems which are encountered if an event ? is only recorded if its value satisfies a recording criterion A. It follows that we get an incorrect idea of the frequency of the events and of its true distribution. In order to solve these problems, an econometric model has been constructed by means of which consistent estimation of the true parameters is possible. The model is estimated on consumer purchases, where the number of purchases is assumed to be NEGBIN-distributed and the purchase amounts obey a lognormal distribution. Purchases are only recorded if their value exceeds Dfl. 10. It is shown that ignoring the recording condition will result in biased estimates and invalid predictions. Apart from this, the model is, among others, relevant for insurance problems, marketing surveys and criminological and epidemiological phenomena.     

Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors

In this paper, we analytically investigate three efficient estimators for cointegrating regression models: Phillips and Hansen’s [Phillips, P.C.B., Hansen, B.E., 1990. Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57, 99–125] fully modified OLS estimator, Park’s [Park, J.Y., 1992. Canonical cointegrating regressions. Econometrica 60, 119–143] canonical cointegrating regression estimator, and Saikkonen’s [Saikkonen, P., 1991. Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7, 1–21] dynamic OLS estimator. We consider the case where the regression errors are moderately serially correlated and the AR coefficient in the regression errors approaches 1 at a rate slower than 1/T$1/T$, where T$T$ represents the sample size. We derive the limiting distributions of the efficient estimators under this system and find that they depend on the approaching rate of the AR coefficient. If the rate is slow enough, efficiency is established for the three estimators; however, if the approaching rate is relatively faster, the estimators will have the same limiting distribution as the OLS estimator. For the intermediate case, the second-order bias of the OLS estimator is partially eliminated by the efficient methods. This result explains why, in finite samples, the effect of the efficient methods diminishes as the serial correlation in the regression errors becomes stronger. We also propose to modify the existing efficient estimators in order to eliminate the second-order bias, which possibly remains in the efficient estimators. Using Monte Carlo simulations, we demonstrate that our modification is effective when the regression errors are moderately serially correlated and the simultaneous correlation is relatively strong.     

A multiple linear regression model for imprecise information

In standard regression analysis the relationship between the (response) variable and a set of (explanatory) variables is investigated. In the classical framework the response is affected by probabilistic uncertainty (randomness) and, thus, treated as a random variable. However, the data can also be subjected to other kinds of uncertainty such as imprecision. A possible way to manage all of these uncertainties is represented by the concept of fuzzy random variable (FRV). The most common class of FRVs is the LR family (LR FRV), which allows us to express every FRV in terms of three random variables, namely, the center, the left spread and the right spread. In this work, limiting our attention to the LR FRV class, we consider the linear regression problem in the presence of one or more imprecise random elements. The procedure for estimating the model parameters and the determination coefficient are discussed and the hypothesis testing problem is addressed following a bootstrap approach. Furthermore, in order to illustrate how the proposed model works in practice, the results of a real-life example are given together with a comparison with those obtained by applying classical regression analysis.     

A generalized non-linear forecasting model for limited overs international cricket

This paper proposes a generalized non-linear forecasting model (GNLM) for forecasting the number of runs remaining to be scored in an innings of cricket. The proposed model takes into account the numbers of overs left and wickets lost. The GNLFM can be used to build a model for any format of limited-overs international cricket. However, the purpose of its use in this paper is for building a forecasting model for projecting second innings total runs in Twenty-20 International cricket. Our model makes it possible to estimate the runs differential of the two competing teams whilst the match is in progress. The runs differential can be used not only to gauge the closeness of a game, but also to estimate the ratings of cricket teams that take into account the margin of victory. Furthermore, the well-known original Duckworth/Lewis (DL) model and the McHale/Asif version of it for revising targets in interrupted matches are special cases of our proposed generalized non-linear forecasting model.     

A non-linear model of the real US/UK exchange rate

This paper provides a framework for building and estimating non-linear real exchange rate models. The approach derives the stationary distribution from a continuous time error correction model and estimates this by MLE methods. The derived distribution exhibits a wide variety of distributional shapes including multimodality. The main result is that swings in the US/UK rate over the period 1973:3 to 1990:5 can be attributed to the distribution becoming bimodal with the rate switching between equilibria. By capturing these changes in the distribution, the non-linear model yields improvements over the random walk, the speculative efficiency model, and Hamilton's stochastic segmented trends model.     

A robust support vector regression model for electric load forecasting

Electric load forecasting is a crucial part of business operations in the energy industry. Various load forecasting methods and techniques have been proposed and tested. With growing concerns about cybersecurity and malicious data manipulations, an emerging topic is to develop robust load forecasting models. In this paper, we propose a robust support vector regression (SVR) model to forecast the electricity demand under data integrity attacks. We first introduce a weight function to calculate the relative importance of each observation in the load history. We then construct a weighted quadratic surface SVR model. Some theoretical properties of the proposed model are derived. Extensive computational experiments are based on the publicly available data from Global Energy Forecasting Competition 2012 and ISO New England. To imitate data integrity attacks, we have deliberately increased or decreased the historical load data. Finally, the computational results demonstrate better accuracy of the proposed robust model over other recently proposed robust models in the load forecasting literature.     

Use of minimum risk approach in the estimation of regression models with missing observations

This article considers a linear regression model with some missing observations on the response variable and presents two estimators of regression coefficients employing the approach of minimum risk estimation. Small disturbance asymptotic properties of these estimators along with the traditional unbiased estimator are analyzed and conditions, that are easy to check in practice, for the superiority of one estimator over the other are derived. Received May 2001     

A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model

Computationally efficient methods for Bayesian analysis of seemingly unrelated regression (SUR) models are described and applied that involve the use of a direct Monte Carlo (DMC) approach to calculate Bayesian estimation and prediction results using diffuse or informative priors. This DMC approach is employed to compute Bayesian marginal posterior densities, moments, intervals and other quantities, using data simulated from known models and also using data from an empirical example involving firms’ sales. The results obtained by the DMC approach are compared to those yielded by the use of a Markov Chain Monte Carlo (MCMC) approach. It is concluded from these comparisons that the DMC approach is worthwhile and applicable to many SUR and other problems.     

Estimating regression equations with common explanatory variables but unequal numbers of observations

It is well known that generalised least-squares estimators of a set of regression equations coincide with ordinary least-squares estimators when the explanatory variables are the same in all equations and there are equal numbers of observations. This paper is concerned with the case of unequal numbers of observations and it is shown that the above result no longer holds. Appropriate estimators are derived and their small-sample properties are investigated analytically. The results are of practical importance because the data patterns discussed can easily arise in econometric studies.     

Biased statistics with zero observations in multiple regression analysis of regional data

Observations containing zeroes as the values of all variables, and which are not meaningful, are shown to be likely in certain regional data sets which may be subjected to multiple regression analysis. The biasing effects of such observations on regression statistics are shown and illustrated with a small data set. It is recommended that such zero observation be identified and removed from regional data sets prior to analysis.