Reputation for Quality

We propose a model of firm reputation in which a firm can invest or disinvest in product quality and the firm's reputation is defined as the market's belief about this quality. We analyze the relationship between a firm's reputation and its investment incentives, and derive implications for reputational dynamics. Reputational incentives depend on the specification of market learning. When consumers learn about quality through perfect good news signals, incentives decrease in reputation and there is a unique work–shirk equilibrium with ergodic dynamics. When learning is through perfect bad news signals, incentives increase in reputation and there is a continuum of shirk–work equilibria with path‐dependent dynamics. For a class of imperfect Poisson learning processes and low investment costs, we show that there exists a work–shirk equilibrium with ergodic dynamics. For a subclass of these learning processes, any equilibrium must feature working at all low and intermediate levels of reputation and shirking at the top.     

Rényi statistics for testing composite hypotheses in general exponential models

We introduce a family of Rényi statistics of orders r?∈?R for testing composite hypotheses in general exponential models, as alternatives to the previously considered generalized likelihood ratio (GLR) statistic and generalized Wald statistic. If appropriately normalized exponential models converge in a specific sense when the sample size (observation window) tends to infinity, and if the hypothesis is regular, then these statistics are shown to be χ²-distributed under the hypothesis. The corresponding Rényi tests are shown to be consistent. The exact sizes and powers of asymptotically α-size Rényi, GLR and generalized Wald tests are evaluated for a concrete hypothesis about a bivariate Lévy process and moderate observation windows. In this concrete situation the exact sizes of the Rényi test of the order r?=?2 practically coincide with those of the GLR and generalized Wald tests but the exact powers of the Rényi test are on average somewhat better.     

Nonlinear programming solutions to the nonstationary markov model

A nonstationary Markov process model with embedded explanatory variables offers a means to account for underlying causal factors while retaining unrestrictive assumptions and the predictive ability of a stochastic framework. We find that a direct search algorithm requiring minimal user preparation is a feasible computational procedure for estimating such a model. We compare this method with several others using factorially designed Monte Carlo simulations and find evidence that a small state space and a long time series lead to better algorithmic performance.     

A Pointwise Estimator for the k-Fold Convolution of a Distribution Function

ABSTRACT

This article is concerned with some parametric and nonparametric estimators for the k-fold convolution of a distribution function. An alternative estimator is proposed and its unbiasedness, asymptotic unbiasedness, and consistency properties are investigated. The asymptotic normality of this estimator is established. Some applications of the estimator are given in renewal processes. Finally, the computational procedures are described and the relative performance of these estimators for small sample sizes is investigated by a simulation study.     

Forward Moving Average Representation in Multivariate MA(1) Processes

Forward-moving average coefficients are in general different from their corresponding backward-moving average coefficients in multivariate stationary time series. There is lack of practical methods to derive forward-moving average coefficients from the backward ones. In this article, we establish a new practical approach for obtaining the forward-moving average coefficients for multivariate moving average processes of order one.     

Nonparametric Testing of an Exclusion Restriction in Quantile Regression

Using the framework proposed by Bickel et al. (2006 Bickel , P. J. , Ritov , Y. , Stoker , T. ( 2006 ). Tailor-made tests for goodness-of-fit to semiparametric hypotheses . Ann. Stat. 34 ( 2 ): 721 – 741 . [Google Scholar]), we provide a score-based testing method to check the exclusion restriction in quantile regression, i.e., H: ν_α(Y|U, V) = ν_α(Y|U) w.p.1, where ν_α denotes the αth (0 < α < 1) quantile. A subsampling method is suggested to acquire the critical values and justified. The tests are all found to be consistent against fixed alternatives and have discriminating power against local alternatives at root-n scale. We address this particular problem as a representative among a wide family of semiparametric model checking problems. The methodology can be carried over to other goodness-of-fit testing of semiparametric models, possibly involve non smooth functions.     

Additive Regression Model for Continuous Time Processes

In the setting of additive regression model for continuous time process, we establish the optimal uniform convergence rates and optimal asymptotic quadratic error of additive regression. To build our estimate, we use the marginal integration method.     

Clinical Trials with Exponential Survival Times

We consider a bandit process with delayed responses which are exponentially distributed survival times. The objective is to maximize the expected value of the total response from all selections. We formulate the problem and show that the optimal strategy is characterized by a sequence of break-even values. A monotonicity property of this sequence is derived, which implies the non-optimality of the myopic strategy and a special optimal stopping solution. An example is included to illustrate a possible application of the main results.     

The Augmented Semi-Markov System in Continuous Time

This article proposes a continuous time semi-Markov hierarchical manpower planning model that incorporates the need of the employees to attend seminars, so as to enhance their prospects, as well as the organizations' intention to avoid situations concerning unavailability in skilled personnel when needed. At large, we study a hierarchical system where the workforce demand at each time period can be met via internal mobility and two streams of recruitment; one from the outside environment and another from a supplementary auxiliary system. For the suggested model, namely the Continuous Time Augmented Semi-Markov System, we examine initially its dynamic behavior by deriving the equations reflecting the expected number of persons in each grade. In the sequel, we probe its limiting population structure and it is found that under a set of conditions this structure exists and is specified. Finally, we present a real case which demonstrates the practical motivation of the subject under study.     

Extremes Values of Discrete and Continuous Time Strongly Dependent Gaussian Processes

The joint limit distribution of the maximum of a continuous, strongly dependent stationary Gaussian process and the maximum of this process sampled at discrete time points is studied. It is shown that these two extreme values are asymptotically totally dependent if the grid of the discrete time points is sufficiently dense, and asymptotically dependent if the the grid points are sparse or Pickands grids. Our results are motivated by the deep contributions Piterbarg (2004 Piterbarg , V. I. ( 2004 ). Discrete and continuous time extremes of Gaussian processes . Extremes 7 : 161 – 177 .[Crossref] , [Google Scholar]) and Hüsler (2004 Hüsler , J. ( 2004 ). Dependence between extreme values of discrete and continuous time locally stationary Gaussian processes . Extremes 7 : 179 – 190 .[Crossref] , [Google Scholar]).