This paper develops methods of inference for nonparametric and semiparametric parameters de…ned by conditional moment inequalities and/or equalities. The parameters need not be identi…ed. Con…dence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS’s and tests are established for …xed altern...

This paper analyses how outliers affect the identification of conditional heteroscedasticity and the estimation of generalized autoregressive conditionally heteroscedastic (GARCH) models. First, we derive the asymptotic biases of the sample autocorrelations of squared observations generated by stationary processes and show that the properties of some conditional homoscedasticity tests can be di...

In this paper, we present a statistical framework for modeling conditional quantiles of spatial processes assumed to be strongly mixing in space. We establish the L1 consistency and the asymptotic normality of the kernel conditional quantile estimator in the case of random fields. We also define a nonparametric spatial predictor and illustrate the methodology used with some simulations.

Abstract: Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are established. Kernel estimators of the noise’s density and its derivatives are defined and shown to be uniformly consistent. A simulation experiment conduct...

Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum withgeneral stochasticpartition is studied. Effectivediscretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective d...

Abstract: We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to spectral domain bootstrap are made. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) mom...

We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) moments,...

Value-at-risk (VaR) and conditional value-at-risk (CVaR) are important risk measures. They are often estimated by using importance sampling (IS) techniques. In this paper, we derive the asymptotic representations for IS estimators of VaR and CVaR. Based on these representations, we are able to prove the consistency and asymptotic normality of the estimators and to provide simple conditions unde...

This note pursues the techniques of modified psi classes on the stack of stable maps (cf. [Graber-Kock-Pandharipande]) to give concise solutions to the characteristic number problem of rational curves in P2 or P1×P1 with a cusp or a prescribed triple contact. The classes of such loci are computed in terms of modified psi classes, diagonal classes, and certain codimension-2 boundary classes. Via...