17,908 research outputs found
Minimax estimation of linear and quadratic functionals on sparsity classes
For the Gaussian sequence model, we obtain non-asymptotic minimax rates of
estimation of the linear, quadratic and the L2-norm functionals on classes of
sparse vectors and construct optimal estimators that attain these rates. The
main object of interest is the class s-sparse vectors for which we also provide
completely adaptive estimators (independent of s and of the noise variance)
having only logarithmically slower rates than the minimax ones. Furthermore, we
obtain the minimax rates on the Lq-balls where 0 < q < 2. This analysis shows
that there are, in general, three zones in the rates of convergence that we
call the sparse zone, the dense zone and the degenerate zone, while a fourth
zone appears for estimation of the quadratic functional. We show that, as
opposed to estimation of the vector, the correct logarithmic terms in the
optimal rates for the sparse zone scale as log(d/s^2) and not as log(d/s). For
the sparse class, the rates of estimation of the linear functional and of the
L2-norm have a simple elbow at s = sqrt(d) (boundary between the sparse and the
dense zones) and exhibit similar performances, whereas the estimation of the
quadratic functional reveals more complex effects and is not possible only on
the basis of sparsity described by the sparsity condition on the vector.
Finally, we apply our results on estimation of the L2-norm to the problem of
testing against sparse alternatives. In particular, we obtain a non-asymptotic
analog of the Ingster-Donoho-Jin theory revealing some effects that were not
captured by the previous asymptotic analysis.Comment: 32 page
The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance
For two decades, the Colless index has been the most frequently used
statistic for assessing the balance of phylogenetic trees. In this article,
this statistic is studied under the Yule and uniform model of phylogenetic
trees. The main tool of analysis is a coupling argument with another well-known
index called the Sackin statistic. Asymptotics for the mean, variance and
covariance of these two statistics are obtained, as well as their limiting
joint distribution for large phylogenies. Under the Yule model, the limiting
distribution arises as a solution of a functional fixed point equation. Under
the uniform model, the limiting distribution is the Airy distribution. The
cornerstone of this study is the fact that the probabilistic models for
phylogenetic trees are strongly related to the random permutation and the
Catalan models for binary search trees.Comment: Published at http://dx.doi.org/10.1214/105051606000000547 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Investment and Sales: Some Empirical Evidence
This paper attempts to give a structural interpretation to the distributed lag of sales on investment at the two-digit level in US manufacturing. It first presents a simple model which captures the various sources of lags and their respective implications. It then estimates the model, using both data on investment and sales as well as direct evidence on the sources of lags. The spirit of the paper is exploratory ; the model is used mainly as a vehicle to construct, present and interpret the data. We find that the following model can roughly generate the distributed lag structure found in the data. Firms face delivery lags of 3 quarters. They also face adjustment costs, which lead them to take into account expected future sales, with discount factor -9 when constructing the desired capital stock, and to close about 5% of the gap between actual and desired capital per quarter. They pay for orders at a constant rate between the time of order and that of delivery. The model is however not very successful in explaining differences in dynamics across sectors.
An Intertemporal Model of Saving and Investment
The standard model of optimal growth, interpreted as a model of a market economy with infinitely long-lived agents, does not allow separation of the savings decisions of agents from the investment decisions of firms. Investment is essentially passive: the "one good" assumption leads to a perfectly elastic investment supply; the absence of installation costs for investment leads to a perfectly elastic investment demand. On the other hand, the standard model of temporary equilibrium used in macroeconomics characterizes both the savings-consumption decision and the investment decision, or, equivalently, derives a well-behaved aggregate demand which, in equilibrium, must be equal to aggregate supply. Often, however, we want to study the movement of the temporary equilibrium over time in response to a particular shock or policy. The discrepancy between the treatment of investment in the two models makes imbedding the temporary equilibrium model in the growth model difficult. This paper characterizes the dynamic behavior of the optimal growth model with adjustment costs. It shows the similarity between the temporary equilibrium of the corresponding market economy and the short-run equilibrium of standard macroeconomic models: consumption depends on wealth, investment on Tobin's q. Equilibrium is maintained by the endogenous adjustment of the term structure of interest rates. It then shows how the equivalence can be used to study the dynamic effects of policies; it considers various fiscal policies and exploits their equivalence to technological shifts in the optimal growth problem.
Measurement of thermal conductance of silicon nanowires at low temperature
We have performed thermal conductance measurements on individual single
crystalline silicon suspended nanowires. The nanowires (130 nm thick and 200 nm
wide) are fabricated by e-beam lithography and suspended between two separated
pads on Silicon On Insulator (SOI) substrate. We measure the thermal
conductance of the phonon wave guide by the 3 method. The cross-section
of the nanowire approaches the dominant phonon wavelength in silicon which is
of the order of 100 nm at 1K. Above 1.3K the conductance behaves as T3, but a
deviation is measured at the lowest temperature which can be attributed to the
reduced geometry
American Options with Stochastic Dividends and Volatility: A Nonparametric Investigation
In this paper, we consider American option contracts when the underlying asset has stochastic dividends and stochastic volatility. We provide a full discussion of the theoretical foundations of American option valuation and exercise boundaries. We show how they depend on the various sources of uncertainty which drive dividend rates and volatility, and derive equilibrium asset prices, derivative prices and optimal exercise boundaries in a general equilibrium model. The theoretical models yield fairly complex expressions which are difficult to estimate. We therefore adopt a nonparametric approach which enables us to investigate reduced forms. Indeed, we use nonparametric methods to estimate call prices and exercise boundaries conditional on dividends and volatility. Since the latter is a latent process, we propose several approaches, notably using EGARCH filtered estimates, implied and historical volatilities. The nonparametric approach allows us to test whether call prices and exercise decisions are primarily driven by dividends, as has been advocated by Harvey and Whaley (1992a,b) and Fleming and Whaley (1994) for the OEX contract, or whether stochastic volatility complements dividend uncertainty. We find that dividends alone do not account for all aspects of call option pricing and exercise decisions, suggesting a need to include stochastic volatility.
Cet article examine les contrats optionnels de type américain lorsque l'actif sous-jacent paie des dividendes et a une volatilité stochastiques. Nous présentons une discussion complète des fondations théoriques de l'évaluation des options américaines et de leurs frontières d'exercice. Nous démontrons leur dépendance par rapport aux diverses sources d'incertitude qui déterminent le taux de dividendes et la volatilité, et dérivons les prix d'équilibre des actifs, titres dérivés ainsi que les politiques optimales d'exercice dans un modèle d'équilibre général. Les modèles théoriques conduisent à des expressions complexes qui sont difficiles à estimer. C'est pourquoi nous adoptons une approche non-paramétrique qui permet d'examiner des formes réduites. Nous utilisons des méthodes non-paramétriques pour estimer les prix d'options à l'achat et les frontières d'exercice conditionnelles aux dividendes et à la volatilité. Puisque cette dernière est un processus latent nous proposons plusieurs approches, fondées en particulier sur des estimateurs-filtres EGARCH, des volatilités implicites et historiques. L'approche non-paramétrique nous permet de tester si les prix d'options et les décisions d'exercice sont principalement déterminés par les dividendes, comme suggéré par Harvey et Whaley (1992a, b) et Fleming et Whaley (1994) pour le contrat OEX, ou si la volatilité stochastique complémente l'incertitude sur les dividendes. Nous établissons que les dividendes seuls ne rendent pas compte de tous les aspects de l'évaluation de ces options et des décisions d'exercice, ce qui suggère la nécessité d'inclure la volatilité stochastique.Option Pricing, Derivative Securities, OEX Contract, Kernel Estimation, Prix d'options, titres dérivés, contrat OEX, estimation par méthode de noyau
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