On the use of the Box-Cox transformation in a linear regression with a lagged dependent variable

In this paper, we show a maximum likelihood estimation procedure in the Box-Cox model when a lagged dependent variable is included among explanatory variables and the first observation of the dependent variable is random. It is shown in a numerical example that a test of a coefficientof the lagged dependent variable is sensitive to whether the first observation of the dependentvariable is random or not.     

Indirect estimation of (latent) linear models with ordinal regressors A Monte Carlo study and some empirical illustrations

Summary This paper investigates the effects of ordinal regressors in linear regression models and in limited dependent variable models. Each ordered categorical variable is interpreted as a rough measurement of an underlying continuous variable as it is often done in microeconometrics for the dependent variable. It is shown that using ordinal indicators only leads to correct answers in a few special cases. In most situations, the usual estimators are biased. In order to estimate the parameters of the model consistently, the indirect estimation procedure suggested by Gourieroux et al. (1993) is applied. To demonstrate this method, first a simulation study is performed and then in a second step, two real data sets are used. In the latter case, continuous regressors are transformed into categorical variables to study the behavior of the estimation procedure. The method is extended to the case of limited dependent variable models. In general, the indirect estimators lead to adequate results. Received: March 27, 2000; revised version: March 6, 2001     

A computational framework for variable selection in multivariate regression

Stepwise variable selection procedures are computationally inexpensive methods for constructing useful regression models for a single dependent variable. At each step a variable is entered into or deleted from the current model, based on the criterion of minimizing the error sum of squares (SSE). When there is more than one dependent variable, the situation is more complex. In this article we propose variable selection criteria for multivariate regression which generalize the univariate SSE criterion. Specifically, we suggest minimizing some function of the estimated error covariance matrix: the trace, the determinant, or the largest eigenvalue. The computations associated with these criteria may be burdensome. We develop a computational framework based on the use of the SWEEP operator which greatly reduces these calculations for stepwise variable selection in multivariate regression.     

Multiple dependent state repetitive sampling plans with or without auxiliary variable

In this article, a new variable acceptance sampling plan has been developed using the multiple dependent state repetitive sampling scheme for the normal distribution. The plan parameters have been determined so as to minimize the average sample number while satisfying the producer's and the consumer's risks under the operating characteristic function. The multiple dependent state repetitive sampling scheme has also been extended to the case of utilizing an auxiliary variable. The proposed sampling plans are compared with the existing sampling plans.     

Nonstationary regression models with a lagged dependent variable

This paper studies regression models with a lagged dependent variable when both the dependent and independent variables are nonstationary, and the regression model is misspecified in some dimension. In particular, we discuss the limiting properties of leastsquares estimates of the parameters in such regression models, and the limiting distributions of their test statistics. We show that the estimate of the lagged dependent variable tends to unity asymptotically independent of its true value, while the estimates of the independent variables tend to zero. The limiting distributions of their test statistics are shown to diverge with sample size.     

Consistency of l 1 estimates in censored linear regression models

In this paper, the regression model with a nonnegativity constraint on the dependent variable is considered. Under weak conditions, L ₁ estimates of the regression coefficients are shown to be consistent.     

Exact maximum likelihood for incomplete data from a correlated gaussian process

In many situations in which a variable is measured at locations in time or space the observed data can be regarded as incomplete, the missing data sites perhaps completing a regular pattern such as a rectangular grid. In this paper general methods not dependent on the sequential nature of time are considered for estimating the parameters of Gaussian processes. An example is given.     

Maximum likelihood estimation for outcome‐dependent samples

In outcome‐dependent sampling, the continuous or binary outcome variable in a regression model is available in advance to guide selection of a sample on which explanatory variables are then measured. Selection probabilities may either be a smooth function of the outcome variable or be based on a stratification of the outcome. In many cases, only data from the final sample is accessible to the analyst. A maximum likelihood approach for this data configuration is developed here for the first time. The likelihood for fully general outcome‐dependent designs is stated, then the special case of Poisson sampling is examined in more detail. The maximum likelihood estimator differs from the well‐known maximum sample likelihood estimator, and an information bound result shows that the former is asymptotically more efficient. A simulation study suggests that the efficiency difference is generally small. Maximum sample likelihood estimation is therefore recommended in practice when only sample data is available. Some new smooth sample designs show considerable promise.     

Demand Systems Estimation With Microdata: A Censored Regression Approach

Demand systems estimation increasingly makes use of household-level microdata, mainly to measure the effects of demographic variables. Data based on these household-expenditure surveys present a major estimation problem. For any given household, many of the goods have zero consumption, implying a censored dependent variable. Techniques which do not take this censored dependent variable into account will yield biased results. We utilize a censored regression approach that is computationally simple, consistent, and asymptotically efficient. The results are then presented and compared with those obtained using an uncensored technique.     

Categorical multiblock linear discriminant analysis

Techniques of credit scoring have been developed these last years in order to reduce the risk taken by banks and financial institutions in the loans that they are granting. Credit Scoring is a classification problem of individuals in one of the two following groups: defaulting borrowers or non-defaulting borrowers. The aim of this paper is to propose a new method of discrimination when the dependent variable is categorical and when a large number of categorical explanatory variables are retained. This method, Categorical Multiblock Linear Discriminant Analysis, computes components which take into account both relationships between explanatory categorical variables and canonical correlation between each explanatory categorical variable and the dependent variable. A comparison with three other techniques and an application on credit scoring data are provided.     

The corrected VIF (CVIF)

In this paper, we propose a new corrected variance inflation factor (VIF) measure to evaluate the impact of the correlation among the explanatory variables in the variance of the ordinary least squares estimators. We show that the real impact on variance can be overestimated by the traditional VIF when the explanatory variables contain no redundant information about the dependent variable and a corrected version of this multicollinearity indicator becomes necessary.     

Model averaging for multivariate multiple regression models

The theories and applications of model averaging have been developed comprehensively in the past two decades. In this paper, we consider model averaging for multivariate multiple regression models. In order to make use of the correlation information of the dependent variables sufficiently, we propose a model averaging method based on Mahalanobis distance which is related to the correlation of the dependent variables. We prove the asymptotic optimality of the resulting Mahalanobis Mallows model averaging (MMMA) estimators under certain assumptions. In the simulation study, we show that the proposed MMMA estimators compare favourably with model averaging estimators based on AIC and BIC weights and the Mallows model averaging estimators from the single dependent variable regression models. We further apply our method to the real data on urbanization rate and the proportion of non-agricultural population in ethnic minority areas of China.     

A percentile regression model with an application to error frequency in group conversation tests

In many applications, estimates of percentile curves interest investigators more than the mean regression line. We consider the situation where the dependent variable is a compound Poisson variable. Explicit parametric assumptions are made using a linear model for scale and heterogeneous variance. The model is applied to the data on group conversation tests in spoken English.     

Bayesian predictive analysis of the linear regression model with an edgeworth series prior distribution

In this paper we obtain the Bayes forecasts for the future observations on the dependent variable in the linear regression model when the regression coefficients have an Edgeworth series prior distribution. Furthermore, we consider the effect of departure from normality of the prior distribution of regression coefficients on the Bayes forecasts.     

A coefficient of multiple association based on ranks

A generalization of Kendall's tau is formulated for describing the association between a dependent variable and a collection of independent variables. The coefficient may be defined in terms of the proportional reduction in prediction errors obtained by predicting the ordering of pairs of observations on the dependent variable based on orderings of the pairs on the independent variables. The coefficient is formulated both for continuous and discrete variables. Approximate large-sample distributions are considered for both cases. Some of the properties of this coefficient are discussed and compared with those of other multiple measures of association based on ranks.     

A Test For Heteroscedasticity in a Limited Dependent Variable Model

Limited Dependent Variable models arise, for example, when the dependent variable is necessarily non-negative. When these models are estimated under the incorrect assumption of homoscedasticity, serious consequences have been found. It is therefore important to test for its existence. In this paper, we make use of the Lagrange multiplier procedure to derive a test for heteroscedasticity in the Tobit model.     

Sampling design proportional to order statistic of auxiliary variable

The sampling designs dependent on sample moments of auxiliary variables are well known. Lahiri (Bull Int Stat Inst 33:133–140, 1951) considered a sampling design proportionate to a sample mean of an auxiliary variable. Sing and Srivastava (Biometrika 67(1):205–209, 1980) proposed the sampling design proportionate to a sample variance while Wywiał (J Indian Stat Assoc 37:73–87, 1999) a sampling design proportionate to a sample generalized variance of auxiliary variables. Some other sampling designs dependent on moments of an auxiliary variable were considered e.g. in Wywiał (Some contributions to multivariate methods in, survey sampling. Katowice University of Economics, Katowice, 2003a); Stat Transit 4(5):779–798, 2000) where accuracy of some sampling strategies were compared, too.These sampling designs cannot be useful in the case when there are some censored observations of the auxiliary variable. Moreover, they can be much too sensitive to outliers observations. In these cases the sampling design proportionate to the order statistic of an auxiliary variable can be more useful. That is why such an unequal probability sampling design is proposed here. Its particular cases as well as its conditional version are considered, too. The sampling scheme implementing this sampling design is proposed. The inclusion probabilities of the first and second orders were evaluated. The well known Horvitz–Thompson estimator is taken into account. A ratio estimator dependent on an order statistic is constructed. It is similar to the well known ratio estimator based on the population and sample means. Moreover, it is an unbiased estimator of the population mean when the sample is drawn according to the proposed sampling design dependent on the appropriate order statistic.     

基于路径分析的科技成果评价指标赋权方法研究

指标赋权是科技成果评价过程中的关键环节。通过建立路径模型，对科技成果评价指标进行路径分析，在消除其他因素影响的基础上，确定原因变量（指标）对结果变量（指标）的直接影响，并据此对指标进行赋权。实证分析表明，该赋权方法具有可操作性和实用性。     

The application of the durbin-watson test to the dynamic regression model under normal and non-normal errors

Until recently, a difficulty with applying the Durbin-Watson (DW) test to the dynamic linear regression model has been the lack of appropriate critical values. Inder (1986) used a modified small-disturbance distribution (SDD) to find approximate critical values. King and Wu (1991) showed that the exact SDD of the DW statistic is equivalent to the distribution of the DW statistic from the regression with the lagged dependent variables replaced by their means. Unfortunately, these means are unknown although they could be estimated by the actual variable values. This provides a justification for using the exact critical values of the DW statistic from the regression with the lagged dependent variables treated as non-stochastic regressors. Extensive Monte Carlo experiments are reported in this paper. They show that this approach leads to reasonably accurate critical values, particularly when two lags of the dependent variable are present. Robustness to non-normality is also investigated.