Elasticity of Factor Substitution in Police Agencies Evidence From Florida

A multiproduct translog cost function is estimated and used to calculate elasticities of factor substitution in the production of police services. The data come from Florida's municipal police departments and are for 1982–1983. It is found that substitution elasticities between any pair of inputs in police production are significantly different from unity. This result is inconsistent with the Cobb–Douglas production function—a functional form that has been extensively employed in empirical studies of police production.     

Forecasting With Judgment

This article shows how to account for nonsample information in the classical forecasting framework. We explicitly incorporate two elements: a default decision and a probability reflecting the confidence associated with it. Starting from the default decision, the new estimator increases the objective function only as long as its first derivatives are statistically different from zero. It includes as a special case the classical estimator and has clear analogies with Bayesian estimators. The properties of the new estimator are studied with a detailed risk analysis. Finally, we illustrate its performance with applications to mean-variance portfolio selection and to GDP forecast.     

Tests of specification in econometrics

This survey of recent developments in testing for misspecification of econometric models reviews procedures based on a method due to Hausman. Particular attention is given to alternative forms of the test, its relationship to classical test procedures, and its role in pre-test estimation.     

Joint estimation of the mean and dispersion parameters in the analysis of proportions: A comparison of efficiency and bias

This paper deals with joint estimation of the mean and dispersion parameters in the analysis of proportions. We consider a parametric model, namely the extended beta-binomial model, and several semiparametric procedures. We study large-sample efficiency and small-sample bias and efficiency properties of the estimates of the mean and intraclass correlation parameters. Estimation and efficiency calculations are présentés for the regression model. However, for simplicity, numerical large-sample efficiency and small-sample bias and efficiency calculations are performed for the two-parameter model only. Numerical efficiency results are présentés in terms of graphs. Estimated asymptotic efficiencies of various estimates are also compared for two data sets. Our findings suggest that for the estimation of the mean (regression) parameters the quasilikelihood procedure performs best. However, for the joint estimation, the Gaussian likelihood estimates perform best.     

Detecting possibly non-consecutive outliers in industrial time series

A method for robust estimation and multiple outlier detection in time series generated by autoregressive integrated moving average processes in industrial environments is developed. The procedure is based on reweighted maximum likelihood estimation using Huber or redescending weights and, therefore, generalizes the well-established robust M -estimation procedures used in the regression framework. When the scalar process is non-stationary, the computations required can be performed equally well using either rhe original undifferenced series or auxiliary differenced series. Whereas the latter alternative may be preferred for scalar series, the former might be extended to cope with vector partially non-stationary time series without differencing the series, thus avoiding non-invertibility and parameter identifiability problems caused by overdifferencing. The overall strategy is applied in two real industrial data sets.     

Corrected likelihood ratio and score tests for the beta distribution

We present correction formulae to improve likelihood ratio and score teats for testing simple and composite hypotheses on the parameters of the beta distribution. As a special case of our results we obtain improved tests for the hypothesis that a sample is drawn from a uniform distribution on (0, 1). We present some Monte Carlo investigations to show that both corrected tests have better performances than the classical likelihood ratio and score tests at least for small sample sizes.     

Bayesian estimation on semiparametric models with shape restricted B-splines

In this paper, we develop a Bayesian estimation procedure for semiparametric models under shape constrains. The approach uses a hierarchical Bayes framework and characterizations of shape-constrained B-splines. We employ Markov chain Monte Carlo methods for model fitting, using a truncated normal distribution as the prior for the coefficients of basis functions to ensure the desired shape constraints. The small sample properties of the function estimators are provided via simulation and compared with existing methods. A real data analysis is conducted to illustrate the application of the proposed method.     

Penalized empirical likelihood for quantile regression with missing covariates and auxiliary information

Based on the inverse probability weight method, we, in this article, construct the empirical likelihood (EL) and penalized empirical likelihood (PEL) ratios of the parameter in the linear quantile regression model when the covariates are missing at random, in the presence and absence of auxiliary information, respectively. It is proved that the EL ratio admits a limiting Chi-square distribution. At the same time, the asymptotic normality of the maximum EL and PEL estimators of the parameter is established. Also, the variable selection of the model in the presence and absence of auxiliary information, respectively, is discussed. Simulation study and a real data analysis are done to evaluate the performance of the proposed methods.     

Marginalized lasso in sparse regression

We propose marginalized lasso, a new nonconvex penalization for variable selection in regression problem. The marginalized lasso penalty is motivated from integrating out the penalty parameter in the original lasso penalty with a gamma prior distribution. This study provides a thresholding rule and a lasso-based iterative algorithm for parameter estimation in the marginalized lasso. We also provide a coordinate descent algorithm to efficiently optimize the marginalized lasso penalized regression. Numerical comparison studies are provided to demonstrate its competitiveness over the existing sparsity-inducing penalizations and suggest some guideline for tuning parameter selection.     

Sample Size Determination for Logistic Regression: A Simulation Study

This article considers the different methods for determining sample sizes for Wald, likelihood ratio, and score tests for logistic regression. We review some recent methods, report the results of a simulation study comparing each of the methods for each of the three types of test, and provide Mathematica code for calculating sample size. We consider a variety of covariate distributions, and find that a calculation method based on a first order expansion of the likelihood ratio test statistic performs consistently well in achieving a target level of power for each of the three types of test.