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1.
We consider Grenander‐type estimators for a monotone function , obtained as the slope of a concave (convex) estimate of the primitive of λ. Our main result is a central limit theorem for the Hellinger loss, which applies to estimation of a probability density, a regression function or a failure rate. In the case of density estimation, the limiting variance of the Hellinger loss turns out to be independent of λ. 相似文献
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A note on the central limit theorem for the idleness process in a one‐sided reflected Ornstein–Uhlenbeck model
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In this short communication, we present a (functional) central limit theorem for the idleness process of a one‐sided reflected Ornstein–Uhlenbeck proces. 相似文献
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We provide a new central limit theorem (CLT) for spatial processes under weak conditions that are plausible for many economic applications in which location is endogenous. In particular, our CLT is designed for problems that have some, but not necessarily all, of the following features: (i) Agents choose the locations of observations to maximize profits, welfare, or some other objective. (ii) The objects that are chosen (e.g., stores or brands) interact with one another. For example, they can be substitutes or complements. (iii) Interaction can be complex. In particular, interaction between i and j need not depend only on the distance between the locations of i and j, but can also depend on distance to or location of other observations k, or possibly on the number of other such observations. 相似文献
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In this paper, we establish a convergence result for equilibria in systems of social interactions with many locally and globally interacting players. Assuming spacial homogeneity and that interactions between different agents are not too strong, we show that equilibria of systems with finitely many players converge to the unique equilibrium of a benchmark system with infinitely many agents. We prove convergence of individual actions and of average behavior. Our results also apply to a class of interaction games. 相似文献
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Let (X n ) be a sequence of i.i.d random variables and U n a U-statistic corresponding to a symmetric kernel function h, where h 1(x 1) = Eh(x 1, X 2, X 3, . . . , X m ), μ = E(h(X 1, X 2, . . . , X m )) and ? 1 = Var(h 1(X 1)). Denote \({\gamma=\sqrt{\varsigma_{1}}/\mu}\), the coefficient of variation. Assume that P(h(X 1, X 2, . . . , X m ) > 0) = 1, ? 1 > 0 and E|h(X 1, X 2, . . . , X m )|3 < ∞. We give herein the conditions under which for a certain family of unbounded measurable functions g, where F(·) is the distribution function of the random variable \({\exp(\sqrt{2} \xi)}\) and ξ is a standard normal random variable.
相似文献
$\lim_{N\rightarrow\infty}\frac{1}{\log N}\sum_{n=1}^{N}\frac{1}{n}g\left(\left(\prod_{k=m}^{n}\frac{U_{k}}{\mu}\right)^{\frac{1}{m\gamma\sqrt{n}}}\right) =\int\limits_{-\infty}^{\infty}g(x)dF(x)\quad {\rm a.s.}$
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The product of partial sums of linear positive (negative) quadrant dependent, positive random variables is asymptotically
lognormal. This extends the earlier work on independent, positive random variables [see Rempala and Wegolowski Elect Comm
Probab 7:47–54, 2002].
Research supported by National Natural Science Foundation of China (No. 10471126); Research supported by Science Foundation
of Zhejiang Provincial Education (No. 20060122). 相似文献
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A general class of fluctuation tests for parameter instability in an M-estimation framework is suggested. Tests from this framework can be constructed by first choosing an appropriate estimation technique, deriving a partial sum process of the estimation scores that captures instabilities over time, and aggregating this process to a test statistic by using a suitable scalar functional. Inference for these tests is based on functional central limit theorems, which are derived under the null hypothesis of parameter stability and local alternatives. For (generalized) linear regression models, concrete tests are derived, which cover several known tests for (approximately) normal data but also allow for testing for parameter instability in regressions with binary or count data. The usefulness of the test procedures—complemented by powerful visualizations derived from these—is illustrated using Dow Jones industrial average stock returns, youth homicides in Boston, USA, and illegitimate births in Grossarl, Austria. 相似文献
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A random walk { Sn } with Sn = (Xl - Yl ) +…+ ( Xn - Yn ) is considered where the Xn Yn are non-negative random variables, the Yn are exponentially distributed with rate δ and the Xn have common distribution function B . It is shown that the expression δ(1 - S (x)) for the density of the ascending ladder height distribution of (Sn ), which is well-known for i.i.d. Xn , holds also when the Xn form a stationary sequence of not necessarily independent random variables. 相似文献
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P. Janssen 《Metrika》1981,28(1):35-46
This paper provides the rate of convergence in the central limit theorem and in the strong law of large numbers forvon Mises statistics
, based on i.i.d. random variablesX
1
,..., X
N
.The proofs rely on a decomposition ofvon Mises statistics into a linear combination ofU-statistics and then use (generalized) results on the convergence rates forU-statistics obtained byGrams/Serfling [1973] andCallaert/Janssen [1978]. 相似文献
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The paper derives a general Central Limit Theorem (CLT) and asymptotic distributions for sample moments related to panel data models with large n. The results allow for the data to be cross sectionally dependent, while at the same time allowing the regressors to be only sequentially rather than strictly exogenous. The setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and/or from the presence of common factors. The latter leads to the need for random norming. The limit theorem for sample moments is derived by showing that the moment conditions can be recast such that a martingale difference array central limit theorem can be applied. We prove such a central limit theorem by first extending results for stable convergence in Hall and Heyde (1980) to non-nested martingale arrays relevant for our applications. We illustrate our result by establishing a generalized estimation theory for GMM estimators of a fixed effect panel model without imposing i.i.d. or strict exogeneity conditions. We also discuss a class of Maximum Likelihood (ML) estimators that can be analyzed using our CLT. 相似文献
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Antonio Quesada 《Journal of Mathematical Economics》2005,41(8):1053-1059
Arrow’s theorem is based on two “vertical” aggregation conditions expressed in terms of the relative positions of two alternatives in a preference ranking. This note obtains the same result for the strict preference case using instead two “horizontal” aggregation conditions expressed in terms of the absolute position of an alternative in a preference ranking. 相似文献
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The purpose of this paper is twofold: first, to provide a closed form expression for the median of the Poisson distribution and, second, to improve the known estimates of the difference between the median and the mean of the Poisson distribution. We use elementary techniques based on the monotonicity of certain sequences involving tail probabilities of the Poisson distribution and the Central Limit TheoremReceived November 2002 相似文献
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Robert E. Gaunt 《Statistica Neerlandica》2019,73(2):176-179
The problem of finding an explicit formula for the probability density function of two zero‐mean correlated normal random variables dates back to 1936. Perhaps, surprisingly, this problem was not resolved until 2016. This is all the more surprising given that a very simple proof is available, which is the subject of this note; we identify the product of two zero‐mean correlated normal random variables as a variance‐gamma random variable, from which an explicit formula for the probability density function is immediate. 相似文献
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The Hahn–Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using non-constructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn–Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented economics intrinsically computational. 相似文献
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In this note we show that the class of stepwise Bayes procedures, suitable defined, forms the minimal complete class for decision problems where the parameter contains only finitely many points. Beyond the assumption on the parameter space, the result is quite general and extends some earlier results.Research supported in part by NSF grant DMS-8911548-01 相似文献
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We consider the Cox regression model and study the asymptotic global behavior of the Grenander-type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for Lp-error of the Grenander-type estimator. As an illustration of application of our main result, we propose a test procedure for a Weibull baseline distribution, based on the Lp-distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test. 相似文献
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