Complexity regularization via localized random penalties

In this article, model selection via penalized empirical loss minimization in nonparametric classification problems is studied. Data-dependent penalties are constructed, which are based on estimates of the complexity of a small subclass of each model class, containing only those functions with small empirical loss. The penalties are novel since those considered in the literature are typically based on the entire model class. Oracle inequalities using these penalties are established, and the advantage of the new penalties over those based on the complexity of the whole model class is demonstrated.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000046

DESIGNING FOOD SAFETY REGULATIONS: THE EFFECT OF INSPECTION POLICY AND PENALTIES FOR NONCOMPLIANCE ON FOOD PROCESSOR BEHAVIOR

In the United States, federal, state, and local governments are involved with the regulation of the safety of the food supply. Food safety regulations that set standards for food processors usually include inspection policies for monitoring performance and penalties for processors who do not comply with regulatory standards. In this analysis, we examine how penalties and inspection policies interact to influence processor behavior. We distinguish between internal penalties (imposed by the regulator) and external penalties (imposed by the market or by the court). Using a model of the processor's expected annual cost, we find that under a given inspection policy internal penalties are only relevant under specific conditions. For cases in which internal and external penalties can be influenced, we use comparative statics to discover that internal penalties are more economically efficient for motivating processors than external penalties. These results imply that regulators should utilize internal penalties for noncompliance rather that rely on market or court-imposed penalties.Food Consumption/Nutrition/Food Safety,

Collective penalties and inducement of self-reporting

Random accidents can be contained by collective penalties. These penalties are not likely to be enforced but rather induce self-reporting that enhances welfare due to early containment. Self-reporting under collective penalties increases overall welfare, but may increase expected environmental cost. Even when regulation is constrained by an upper limit on the acceptable collective penalty, the threat of collective penalties can induce an incentive-compatible mutual insurance scheme under which a side-payment is made to the agent that self-reports an accident. This self-reporting mechanism is welfare-improving, but first-best outcomes can only be obtained when the collective penalty is unconstrained, or when an honor system applies. In cases when there is a new externality that requires fast response (avian flu), collective penalties can compliment or substitute for monitoring.Ambient tax, collective penalties, enforcement, self-reporting.

Likelihood Adaptively Modified Penalties

A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study stability properties of the penalized maximum likelihood estimator, two types of asymptotic stability are defined. Theoretical properties, including the parameter estimation consistency, model selection consistency, and asymptotic stability, are established under suitable regularity conditions. An efficient coordinate-descent algorithm is proposed. Simulation results and real data analysis show that the proposed method has competitive performance in comparison with existing ones.Comment: 42 pages, 4 figure

For Better and Worse: The Differing Income Tax Treatments of Marriage at Different Income Levels

Although both marriage penalties and marriage bonuses exist at all income levels under the federal income tax, the system is tilted toward penalties for lower-income couples, toward bonuses for middle-income couples, and back toward penalties for upper income couples. This Article begins by explaining how the tax rules produce these differing treatments of marriage at different points in the income distribution. It then argues that the increase in recent decades in the social acceptability and prevalence of cohabitation makes tax marriage effects a more serious concern--in terms of both behavioral, effects and fairness-than in earlier decades. After demonstrating that Congress has never offered any justification for the differing tax treatments of marriage at different income levels, and that no plausible defense exists for the current distribution of penalties and bonuses, the Article offers several policy recommendations. The most basic and most important recommendation is simply that, whatever Congress does in this area, it should make conscious decisions about the appropriate distributions of penalties and bonuses at various income levels, instead of following its current practice of stumbling into a set of poorly understood and almost-impossible-to-defend effects

Optimal Penalties in Contracts

Contract law's liquidated damage rules prevent enforcement of contractual damage measures that require the promisor, if it breaches, to transfer to the promisee a sum that exceeds the net gain the promisee expected to make from performance; but these rules permit the promisor to transfer less than the promisee's expectation. We define a contractual damage multiplier as any number between zero and infinity by which the promisee's expected gain -- its expectation interest -- is multiplied. Multipliers of one or less thus comply with the liquidated damage rules while multipliers that exceed one do not; the high multipliers are unenforceable penalties. This paper shows that multipliers of any size can be efficient or inefficient, depending on the parties' purposes in creating them. For example, a multiplier that exceeds one will decrease welfare if used by a seller with market power to deter entry; but will increase welfare if used by parties to induce efficient relation specific investment. As a consequence, a court should inquire, not into the size of the multiplier, but into the purpose the multiplier serves for the parties.