The relation between unemployment and interest rate:

In bierens (1987) a granger casual relation was found between unemployment and the interest rate for the netherlands. In the present paper we will investigate whether there exists a similar granger casual relation between unemployment and interest rate for a number of other countries. It appears that, with our ARMAX modeling approach, this relationship is not confined to the netherlands, but also holds for the USA, Canada, Japan, Germany, the UK and France. For these countries the interest rate is the main explanatory variable, together with industrial production (the latter with one exception), whereas for most countries the wage rate is of minor or no importance as a determinant of unemployment. A number of economic theories can explain these phenomena of which the revenue maximization theory of baumol (1959) augmented with a flexible labor effort rate seems quite realistic     

Fraction of design space plots for generalized linear models

The use of graphical methods for comparing the quality of prediction throughout the design space of an experiment has been explored extensively for responses modeled with standard linear models. In this paper, fraction of design space (FDS) plots are adapted to evaluate designs for generalized linear models (GLMs). Since the quality of designs for GLMs depends on the model parameters, initial parameter estimates need to be provided by the experimenter. Consequently, an important question to consider is the design's robustness to user misspecification of the initial parameter estimates. FDS plots provide a graphical way of assessing the relative merits of different designs under a variety of types of parameter misspecification. Examples using logistic and Poisson regression models with their canonical links are used to demonstrate the benefits of the FDS plots.     

Semiparametric Inference for the Two‐way Layout Under Order Restrictions

There are many situations in which a researcher would like to analyse data from a two‐way layout. Often, the assumptions of linearity and normality may not hold. To address such situations, we introduce a semiparametric model. The model extends the well‐known density ratio model from the one‐way to the two‐way layout and provides a useful framework for semiparametric analysis of variance type problems under order restrictions. In particular, the likelihood ratio order is emphasized. The model enables highly efficient inference without resorting to fully parametric assumptions or the use of transformations. Estimation and testing procedures under order restrictions are developed and investigated in detail. It is shown that the model is robust to misspecification, and several simulations suggest that it performs well in practice. The methodology is illustrated using two data examples; in the first, the response variable is discrete, whereas in the second, it is continuous.     

Higher-order asymptotics under model misspecification

Most of the higher-order asymptotic results in statistical inference available in the literature assume model correctness. The aim of this paper is to develop higher-order results under model misspecification. The density functions to O(n^?3/2) of the robust score test statistic and the robust Wald test statistic are derived under the null hypothesis, for the scalar as well as the multiparameter case. Alternate statistics which are robust to O(n^?3/2) are also proposed.     

Effect of Violation of the Normal Assumption on MI and ML Estimators in the Analysis of Incomplete Data

Asymptotic distributions of normal-theory-based ML/MI estimators are studied in a simple regression model under general distributions with MAR missing data. The asymptotic variance of the ML/MI estimator of residuals’ variance is explicitly derived, from which it follows that the kurtosis of the error distribution primarily affects the asymptotic variance. Results of numerical simulations conducted to study finite sample properties of the estimators, conformed largely to the asymptotic results, and they also indicated interesting findings particularly for small samples, which do not follow from the asymptotic property. It is concluded that the ML estimators perform best in the situation studied here.     

Asymptotic misspecification biases for heckman's two step estimator

Asymptotic bias formulae are obtained for Heckman's two step estimator under misspecification of the single equation Tobit modelj and the two equation sample selection model. Asymptotic biases are also obtained for the ordinary least squares estimator based on uncensored observations only. Omitted variables, errors in variables, and heteroskedasticity are considered as sources of misspecification. The biases are illustrated by numerical examples, in which the Tobit maximum likelihood estimator is also included. Severe consequences for the two step estimator are indicated.     

Estimation in Discretely Observed Diffusions Killed at a Threshold

Abstract. Parameter estimation in diffusion processes from discrete observations up to a first‐passage time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modelled as discretely observed diffusions which are killed when the threshold is reached. Statistical inference is often based on a misspecified likelihood ignoring the presence of the threshold causing severe bias, e.g. the bias incurred in the drift parameters of the Ornstein–Uhlenbeck model for biological relevant parameters can be up to 25–100 per cent. We compute or approximate the likelihood function of the killed process. When estimating from a single trajectory, considerable bias may still be present, and the distribution of the estimates can be heavily skewed and with a huge variance. Parametric bootstrap is effective in correcting the bias. Standard asymptotic results do not apply, but consistency and asymptotic normality may be recovered when multiple trajectories are observed, if the mean first‐passage time through the threshold is finite. Numerical examples illustrate the results and an experimental data set of intracellular recordings of the membrane potential of a motoneuron is analysed.     

Evaluating Statistical Hypotheses Using Weakly‐Identifiable Estimating Functions

Abstract. Many statistical models arising in applications contain non‐ and weakly‐identified parameters. Due to identifiability concerns, tests concerning the parameters of interest may not be able to use conventional theories and it may not be clear how to assess statistical significance. This paper extends the literature by developing a testing procedure that can be used to evaluate hypotheses under non‐ and weakly‐identifiable semiparametric models. The test statistic is constructed from a general estimating function of a finite dimensional parameter model representing the population characteristics of interest, but other characteristics which may be described by infinite dimensional parameters, and viewed as nuisance, are left completely unspecified. We derive the limiting distribution of this statistic and propose theoretically justified resampling approaches to approximate its asymptotic distribution. The methodology's practical utility is illustrated in simulations and an analysis of quality‐of‐life outcomes from a longitudinal study on breast cancer.