841 research outputs found
Discretisation of Stochastic Control Problems for Continuous Time Dynamics with Delay
As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretizing time and space. A new feature in this context is to allow for delay in the dynamics. The existence of an optimal strategy with respect to the cost functional can be guaranteed in the class of relaxed controls. Weak convergence of the approximating extended Markov chains to the original process together with convergence of the associated optimal strategies is established.Markov, Markov chain, time dynamics, stochastic control problem
On rate optimality for ill-posed inverse problems in econometrics
In this paper, we clarify the relations between the existing sets of
regularity conditions for convergence rates of nonparametric indirect
regression (NPIR) and nonparametric instrumental variables (NPIV) regression
models. We establish minimax risk lower bounds in mean integrated squared error
loss for the NPIR and the NPIV models under two basic regularity conditions
that allow for both mildly ill-posed and severely ill-posed cases. We show that
both a simple projection estimator for the NPIR model, and a sieve minimum
distance estimator for the NPIV model, can achieve the minimax risk lower
bounds, and are rate-optimal uniformly over a large class of structure
functions, allowing for mildly ill-posed and severely ill-posed cases.Comment: 27 page
Exact and Asymptotic Tests on a Factor Model in Low and Large Dimensions with Applications
In the paper, we suggest three tests on the validity of a factor model which
can be applied for both small dimensional and large dimensional data. Both the
exact and asymptotic distributions of the resulting test statistics are derived
under classical and high-dimensional asymptotic regimes. It is shown that the
critical values of the proposed tests can be calibrated empirically by
generating a sample from the inverse Wishart distribution with identity
parameter matrix. The powers of the suggested tests are investigated by means
of simulations. The results of the simulation study are consistent with the
theoretical findings and provide general recommendations about the application
of each of the three tests. Finally, the theoretical results are applied to two
real data sets, which consist of returns on stocks from the DAX index and on
stocks from the S&P 500 index. Our empirical results do not support the
hypothesis that all linear dependencies between the returns can be entirely
captured by the factors considered in the paper
Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case
Asymptotic local equivalence in the sense of Le Cam is established for
inference on the drift in multidimensional ergodic diffusions and an
accompanying sequence of Gaussian shift experiments. The nonparametric local
neighbourhoods can be attained for any dimension, provided the regularity of
the drift is sufficiently large. In addition, a heteroskedastic Gaussian
regression experiment is given, which is also locally asymptotically equivalent
and which does not depend on the centre of localisation. For one direction of
the equivalence an explicit Markov kernel is constructed.Comment: 03 May 2005, 23 page
Nonlinear estimation for linear inverse problems with error in the operator
We study two nonlinear methods for statistical linear inverse problems when
the operator is not known. The two constructions combine Galerkin
regularization and wavelet thresholding. Their performances depend on the
underlying structure of the operator, quantified by an index of sparsity. We
prove their rate-optimality and adaptivity properties over Besov classes.Comment: Published in at http://dx.doi.org/10.1214/009053607000000721 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Posterior contraction rates for support boundary recovery
Given a sample of a Poisson point process with intensity we study recovery of the boundary function from a
nonparametric Bayes perspective. Because of the irregularity of this model, the
analysis is non-standard. We establish a general result for the posterior
contraction rate with respect to the -norm based on entropy and one-sided
small probability bounds. From this, specific posterior contraction results are
derived for Gaussian process priors and priors based on random wavelet series
On rate optimality for ill-posed inverse problems in econometrics
In this paper, we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models. We establish minimax risk lower bounds in mean integrated squared error loss for the NPIR and the NPIV models under two basic regularity conditions that allow for both mildly ill-posed and severely ill-posed cases.We show that both a simple projection estimator for the NPIR model, and a sieve minimum distance estimator for the NPIV model,can achieve the minimax risk lower bounds, and are rate-optimal uniformly over a large class of structure functions, allowing for mildly ill-posed and severely ill-posed cases.
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