An empirical likelihood goodness-of-fit test for time series

Summary. Standard goodness-of-fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model. When a parametric regression model is compared with a nonparametric model, goodness-of-fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework. We employ the empirical likelihood for an α -mixing process to formulate a test statistic that measures the goodness of fit of a parametric regression model. The technique is based on a comparison with kernel smoothing estimators. The empirical likelihood formulation of the test has two attractive features. One is its automatic consideration of the variation that is associated with the nonparametric fit due to empirical likelihood's ability to Studentize internally. The other is that the asymptotic distribution of the test statistic is free of unknown parameters, avoiding plug-in estimation. We apply the test to a discretized diffusion model which has recently been considered in financial market analysis.     

Diagnosis and therapy of male gamblers in a university psychiatric hospital

From 1980 to mid-1990 fifty-one gamblers were evaluated and treated at the psychiatric university hospital of Homburg/Saar in Germany. All were men with a mean age of 33.7 years. Gambling had lasted 5.2 years on average. Most patients were motivated to undergo therapy by members of their family. The majority of them had been in psychotherapeutic treatment before. Thirty-six of the 51 patients had committed punishable acts including fraud and embezzlement and, in 7 cases, robbery. The sample could be divided into three clinical subgroups. The first group consisted of patients with severe psychiatric diseases such as schizophrenia, manic-depressive illness or organic brain disorder. Patients of the second group suffered from serious personality disorders. Those of the third group showed deep-rooted problems in their current relationships.This article is an extension of the special issue on Gambling in Europe edited by Iver Hand, M.D.     

Public pensions in transition

The main purpose of this paper is to analyze problems of financing an old-age insurance when birth rates are low and population declines or fertility fluctuates with time. A government then searches for optimal policies to cope with such problems. A first criterion could be seen in the Pareto principle. But we all know that there is no way out of PAYG unless at least one generation has to pay for the transition. Therefore an optimal policy is concerned with intergenerational redistribution and optimal growth.In the absence of public pensions the economy will in the long run converge to a steady state which is not optimal in the sense of a golden rule. This dynamic in-efficiency results from the decentralized decision making by the consumers and the firms. If the PAYG system influences the savings ratio of the economy, public pensions can be seen as an instrument to implement a modified golden rule.Paper presented at the ISPE-conference on The Fiscal Implications of an Ageing Population, Vaalsbroek, The Netherlands, May 30–June 1, 1990. I am obliged to Dieter Bös, Friedrich Breyer, Christian Keuschnigg, Wolfgang Kitterer, and an anonymous referee for helpful comments on an earlier draft of this paper. Financial support through Deutsche Forschungsgemeinschaft, SFB 303 is gratefully acknowledged.     

GM Foods and the Misperception of Risk Perception

Public opposition to genetically modified (GM) food and crops is widely interpreted as the result of the public's misperception of the risks. With scientific assessment pointing to no unique risks from GM crops and foods, a strategy of accurate risk communication from trusted sources has been advocated. This is based on the assumption that the benefits of GM crops and foods are self-evident. Informed by the interpretation of some qualitative interviews with lay people, we use data from the Eurobarometer survey on biotechnology to explore the hypothesis that it is not so much the perception of risks as the absence of benefits that is the basis of the widespread rejection of GM foods and crops by the European public. Some respondents perceive both risks and benefits, and may be trading off these attributes along the lines of a rational choice model. However, for others, one attribute-benefit-appears to dominate their judgments: the lexicographic heuristic. For these respondents, their perception of risk is of limited importance in the formation of attitudes toward GM food and crops. The implication is that the absence of perceived benefits from GM foods and crops calls into question the relevance of risk communication strategies for bringing about change in public opinion.     

Bayesian estimation of the efficient frontier

In this paper, we consider the estimation of the three determining parameters of the efficient frontier, the expected return, and the variance of the global minimum variance portfolio and the slope parameter, from a Bayesian perspective. Their posterior distribution is derived by assigning the diffuse and the conjugate priors to the mean vector and the covariance matrix of the asset returns and is presented in terms of a stochastic representation. Furthermore, Bayesian estimates together with the standard uncertainties for all three parameters are provided, and their asymptotic distributions are established. All obtained findings are applied to real data, consisting of the returns on assets included into the S&P 500. The empirical properties of the efficient frontier are then examined in detail.     

An Extended Single‐index Model with Missing Response at Random

An extended single‐index model is considered when responses are missing at random. A three‐step estimation procedure is developed to define an estimator for the single‐index parameter vector by a joint estimating equation. The proposed estimator is shown to be asymptotically normal. An algorithm for computing this estimator is proposed. This algorithm only involves one‐dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Some simulation studies are conducted to investigate the finite sample performances of the proposed estimators.