共查询到20条相似文献,搜索用时 31 毫秒
1.
John Kornak Mark E. Irwin Noel Cressie 《Statistical Inference for Stochastic Processes》2006,9(1):31-46
The study of stochastic processes can take many forms. Theoretical properties are important to ensure consistent model definition.
Statistical inference on unknown parameters is equally important but can be difficult. This is principally because many of
the standard assumptions for proving consistency and asymptotic normality of estimators involve independence and homogeneity.
In the case where inference is concerned with detecting change in a spatial process from one time point to another, a statistical-computing
approach can be rewarding. Regardless of the complexity of the stochastic process, if simulating from it is relatively easy,
then detecting change is possible using a Monte Carlo approach. The methodology is applied in a military scenario, where a
country’s defensive posture changes as a function of its perceived threat. For tactical-decision purposes, it is extremely
important to know whether the country’s perceived threat level has changed. 相似文献
2.
K. Muralidharan 《商业与工业应用随机模型》2001,17(4):331-343
The modulated power law process (MPLP) is often used to model failure data from repairable system, when both renewal type behaviour and time trends are present. The MPLP allows for the failure rate of a system to be affected by the failure and repair. Since the MLEs of the estimates do not have closed form expressions, they have to be approximated, and hence deriving a test procedure will be difficult. Black and Rigdon (1996) have proposed asymptotic MLEs and asymptotic likelihood ratio tests for the parameters which also do not have closed form expressions and hence are not easy for application. In this paper, we derive a closed form expression for the test statistics which is simple and easy to apply for testing (i) H0: β=1 versus H1: β≠1 when κ is known and (ii) H0: (β=1 and κ=1) versus H1: (β≠1 or κ≠1). The simulation study for percentiles and powers are given. We also compare the performance of the test with that of Black and Rigdon's (1996) test. Some numerical examples are also provided to illustrate the testing procedures. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
3.
Nonhomogeneous Poisson processes (NHPPs) are often used to model failure data from repairable systems, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness‐of‐fit tests for parametric NHPPs. The idea is to use conditional tests given a sufficient statistic under the null hypothesis model. The tests are performed by simulating conditional samples given the sufficient statistic. Algorithms are presented for testing goodness‐of‐fit for the power law and the log‐linear law NHPP models. It is noted that while exact algorithms for the power law case are well known in the literature, the availability of such algorithms for the log‐linear case seems to be less known. A data example, as well as simulations, are considered. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
4.
In this paper, we establish oracle inequalities for penalized projection estimators of the intensity of an inhomogeneous
Poisson process. We study consequently the adaptive properties of penalized projection estimators. At first we provide lower
bounds for the minimax risk over various sets of smoothness for the intensity and then we prove that our estimators achieve
these lower bounds up to some constants. The crucial tools to obtain the oracle inequalities are new concentration inequalities
for suprema of integral functionals of Poisson processes which are analogous to Talagrand's inequalities for empirical processes.
Received: 24 April 2001 / Revised version: 9 October 2002 /
Published online: 15 April 2003
Mathematics Subject Classification (2000): 60E15, 62G05, 62G07
Key words or phrases: Inhomogeneous Poisson process – Concentration inequalities – Model selection – Penalized projection estimator – Adaptive
estimation 相似文献
5.
Y. A. Kutoyants 《Journal of Mathematical Sciences》2009,163(3):213-226
We consider the problem of parameter estimation by observations of an inhomogeneous Poisson process. It is well known that
if regularity conditions are fulfilled, then the maximum likelihood and Bayesian estimators are consistent, asymptotically
normal, and asymptotically efficient. These regularity conditions can be roughly presented as follows: (a) the intensity function of the observed process belongs to a known parametric family of functions, (b) the model is identifiable, (c) the Fisher information is a positive continuous function, (d) the intensity function is sufficiently smooth with respect to the unknown parameter, and (e) this parameter is an interior point of the interval. We are interested in properties of estimators for which these regularity
conditions are not fulfilled. More precisely, we present a review of results which correspond to the rejection of these conditions
one by one and show how properties of the MLE and Bayesian estimators change. The proofs of these results are essentially
based on some general results by Ibragimov and Khasminskii. Bibliography: 9 titles. 相似文献
6.
S. Juneja 《Queueing Systems》2007,57(2-3):115-127
Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems
in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient
algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such
tail probabilities are developed and it is proved that these estimators are asymptotically efficient or even possess the desirable
bounded relative error property. In this paper, as an illustration, we consider a simple tail probability involving geometric
sums of heavy tailed random variables. This is useful in estimating the probability of large delays in M/G/1 queues. In this setting we develop an unbiased estimator whose relative error decreases to zero asymptotically. The key
idea is to decompose the probability of interest into a known dominant component and an unknown small component. Simulation
then focuses on estimating the latter ‘residual’ probability. Here we show that the existing conditioning methods or importance
sampling methods are not effective in estimating the residual probability while an appropriate combination of the two estimates
it with bounded relative error. As a further illustration of the proposed ideas, we apply them to develop an estimator for
the probability of large delays in stochastic activity networks that has an asymptotically zero relative error.
相似文献
7.
Recently, the PASTA (Poisson Arrivals See Time Averages) property has been extended to ASTA (Arrivals See Time Averages) by eliminating the need for Poisson arrivals and weakening the LAA (Lack of Anticipation Assumption). This paper presents a strengthening of ASTA under the original LAA of Wolff. We consider a stochastic processX with an associated point processN that admits a stochastic intensity and satisfies LAA. Various authors have noted in various contexts that ASTA holds if and only if the arrival intensity is state independent. For a class of point processes that includes doubly stochastic as well as ordinary Poisson processes, we prove that the point process obtained by restricting the processX to any given set of states not only has the same intensity but also the same probabilistic structure as the original point process. In particular, if the original point process is Poisson, the new point process is still Poisson with the same parameter as the original point process. For a discrete-time version, of interest in its own right, we provide a simple proof of a strengthened version of ASTA in discrete time. Unlike other discrete-time versions of ASTA, ours is valid for point processes with stationary but not necessarily independent increments. The continuous-time results are obtained using martingale theory. A corollary is a simple proof of PASTA under conditions that require only that the relevant limits exist. Our results may also provide some insight into characterizing Poisson flows in queueing systems.The research of this author was partially supported by the National Science Foundation under Grant No. DDM-8719825. The Government has certain rights in this material. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. 相似文献
8.
In the estimation problem of the mean function of an inhomogeneous Poisson process there is a class of kernel type estimators that are asymptotically efficient alongside with the empirical mean function. We start by describing such a class of estimators which we call first order efficient estimators. To choose the best one among them we prove a lower bound that compares the second order term of the mean integrated square error of all estimators. The proof is carried out under the assumption on the mean function Λ(·) that Λ(τ) = S, where S is a known positive number. In the end, we discuss the possibility of the construction of an estimator which attains this lower bound, thus, is asymptotically second order efficient. 相似文献
9.
A. S. Dabye A. A. Gounoung Yu. A. Kutoyants 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2018,53(4):237-246
We introduce two types of estimators of the finite–dimensional parameters in the case of observations of inhomogeneous Poisson processes. These are the estimators of the method of moments and Multi–step MLE. It is shown that the estimators of the method of moments are consistent and asymptotically normal and the Multi–step MLE are consistent and asymptotically efficient. The construction of Multi–step MLE–process is done in two steps. First we construct a consistent estimator by the observations on some learning interval and then this estimator is used for construction of One–step and Two–step MLEs. The main advantage of the proposed approach is its computational simplicity. 相似文献
10.
S. Dachian 《Statistical Inference for Stochastic Processes》2003,6(1):1-14
We consider an inhomogeneous Poisson process X on [0, T]. The intensity function of X is supposed to be regular on [0, T] except at the point , in which it has a singularity (a cusp) of order p. We suppose that we know the shape of the intensity function, but not the location (given by the parameter ) of the point of cusp. We consider the problem of estimation of this location (shift) parameter based on n observations of the process X. We study the maximum likelihood estimator and the Bayesian estimators. We show that these estimators are consistent, their rate of convergence is n
1/(2p+1), they have different limit distributions, and the Bayesian estimators are asymptotically efficient. 相似文献
11.
Yasutaka Shimizu 《Statistical Inference for Stochastic Processes》2006,9(2):179-225
We study parametric inference for multidimensional stochastic differential equations with jumps from some discrete observations.
We consider a case where the structure of jumps is mainly controlled by a random measure which is generated by a Lévy process
with a Lévy measure fθ(z)dz, and we admit the case ∫ fθ(z)dz = ∞ in which infinitely many small jumps occur even in any finite time intervals. We propose an estimating function under
this complicated situation and show the consistency and the asymptotic normality. Although the estimators in this paper are
not completely efficient, the method can be applied to comparatively wide class of stochastic differential equations, and
it is easy to compute the estimating equations. Therefore, it may be useful in applications. We also present some simulation
results for some simple models.
Final version 25 December 2004 相似文献
12.
Denis Bosq 《Statistical Inference for Stochastic Processes》2002,5(3):287-306
The autoregressive model in a Banach space (ARB) contains many continuous time processes used in practice, for example, processes that satisfy linear stochastic differential
equations of order k, a very particular case being the Ornstein–Uhlenbeck process. In this paper we study empirical estimators for ARB processes. In particular we show that, under some regularity conditions, the empirical mean is asymptotically optimal with
respect to a.s. convergence and convergence of order 2. Limit in distribution and the law of the iterated logarithm are also
presented. Concerning the empirical covariance operator we note that, if (X
n, n ∈ ℤ) is ARB then (X
n ⊗ X
n, n ∈ ℤ) is AR in a suitable space of linear operators. This fact allows us to interpret the empirical covariance operator as a sample mean
of an AR and to derive similar results for it.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
13.
The focus of this article is on the analysis of repairable systems that are subject to multiple sources of recurrence. The event of interest at the system level is assumed to be caused by the earliest occurrence of a source, thereby conforming to a series system competing risks framework. Parametric inference is carried out under the power law process model that has found significant attention in industrial applications. Dependence among the cause‐specific recurrent processes is induced via a shared frailty structure. The theoretical inference results are implemented to a warranty database for a fleet of automobiles, for which the warranty repair is triggered by the failure of one of many components. Extensive finite‐sample simulation is carried out to supplement the asymptotic findings. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
14.
A. D. Dharmadhikari U. V. Naik-Nimbalkar S. Bhyri 《Annals of the Institute of Statistical Mathematics》1989,41(1):139-148
Analogous to Kingman's Poisson Counts, power law counts are defined. Further, these are used to obtain the maximum likelihood estimator of the scale parameter of a power law process. Comparison of this estimator is done with those obtained by using other sampling schemes. Also, cost comparisons are done under the assumption of equal asymptotic variances under different sampling schemes.Work done while the author was with the Department of Statistics, University of Poona. Current address: Dept. of Mathematics, CME, Pune. 相似文献
15.
V. Kanišauskas 《Lithuanian Mathematical Journal》2000,40(3):241-247
In this paper, we consider the problem of asymptotically minimax testing ofr≥2 simple hypotheses when a general stochastic process is observed. We establish general conditions for the exponential decrease
of maximal probability errors of minimax tests as the number of observations increases. At the present time, similar results
for testing several multinomial schemes were obtained by Salihov [8]. Similar results for testing two simple hypotheses were
obtained in [5]. In the proofs of the main results, we use the theory of large deviations ([3], [2]). In Sec. 1, the main
result is proved. In Secs. 2–4, we analyze the i.i.d. case, nonhomogeneous Poisson processes, and renewal processes as examples.
Published in Lietuvos Matematikos Rinkinys, Vol. 40, No. 3, pp. 313–320, July–September, 2000. 相似文献
16.
IG-OU processes are a subclass of the non-Gaussian processes of Ornstein–Uhlenbeck type, which are important models appearing
in financial mathematics and elsewhere. The simulation of these processes is of interest for its applications in statistical
inference. In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the sum of two independent
random variables—one has an inverse Gaussian distribution and the other has a compound Poisson distribution. And in distribution,
the compound Poisson random variable is equal to a sum of Poisson-distributed number positive random variables, which are
independent identically distributed and have a common specified density function. The exact simulation of the IG-OU processes,
proceeding from time 0 and going in steps of time interval Δ, is achieved via the representation of the stochastic integral.
Comparing to the approximate method, which is based on Rosinski’s infinite series representation of the same stochastic integral,
by the quantile–quantile plots, the advantage of the exact simulation method is obvious. In addition, as an application, we
provide an estimator of the intensity parameter of the IG-OU processes and validate its superiority to another estimator by
our exact simulation method.
相似文献
17.
Consider a Galton–Watson process with immigration. The limiting distributions of the nonsequential estimators of the offspring mean have been proved to be drastically different for the critical case and subcritical and supercritical cases. A sequential estimator, proposed by Sriram et al. (Ann. Statist. 19 (1991) 2232), was shown to be asymptotically normal for both the subcritical and critical cases. Based on a certain stopping rule, we construct a class of two-stage estimators for the offspring mean. These estimators are shown to be asymptotically normal for all the three cases. This gives, without assuming any prior knowledge, a unified estimation and inference procedure for the offspring mean. 相似文献
18.
We study the structure of solutions of Kesten’s equation (1.5), where a, b ⩾ 0 are the coefficients of the GARCH(1,1) process in (1.1). We prove that, for any b ∈ (0, 1) and any κ > 0 small enough, there exists a stationary GARCH(1,1) process with tail index κ.
The research was partially supported by the bilateral France-Lithuania scientific project Gilibert and the Lithuanian State
Science and Studies Foundation, grant no. T-15/07.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 196–210, April–June, 2007. 相似文献
19.
The problem of asymptotically efficient estimation of the density of invariant measure of a diffusion process is considered.
The efficient estimator is defined with the help of the minimax lower bound on the risk of all estimators. We show that the
local–time and kernel–type estimators are asymptotically efficient for the loss functions with polynomial majorants. The asymptotic
behavior of a wide class of unbiased estimators with the same limit variances is also discussed.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
We investigate the properties of maximum likelihood estimators in observation schemes of random variables that arrive at random time moments on a Poisson trajectory defined on some ergodic process.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 98–105, 1986. 相似文献