Rate of strong consistency of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models

Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.

Strong Consistency of Estimators of a Semiparametric Regression Model under Fixed Design

In this paper, we consider the following semipaxametric regression model under fixed design： yi = xi′β＋g（xi）＋ei. The estimators of β, g（·） and σ^2 axe obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.

Strong Consistency of M Estimator in Linear Model for φ-mixing Samples

The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of M estimator under lower moment condition, which generalizes and improves the corresponding ones for independent sequences.

Strong Consistency of the Spline-Estimation of Probabilities Density in Uniform Metric

In the present paper as estimation of an unknown probability density of the spline-estimation is constructed, necessity and sufficiency conditions of strong consistency of the spline-estimation are given.

Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models

Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.

STRONG CONSISTENCY OF M ESTIMATOR IN LINEAR MODEL FOR NEGATIVELY ASSOCIATED SAMPLES

This paper discusses the strong consistency of M estimator of regression parameter in linear model for negatively associated samples. As a result, the author extends Theorem 1 and Theorem 2 of Shanchao YANG （2002） to the NA errors without necessarily imposing any extra condition.

FURTHER STUDY STRONG CONSISTENCY OF M ESTIMATOR IN LINEAR MODEL FOR ρ-MIXING RANDOM SAMPLES

The strong consistency of M estimators of the regression parameters in linear models for ρ-mixing random errors under some mild conditions is established, which is an essential improvement over the relevant results in the literature on the moment conditions and mixing errors. Especially, Theorem of Wu （2005） is improved essentially on the moment conditions.

Strong Consistency of Maximum Quasi-Likelihood Estimator in Quasi-Likelihood Nonlinear Models

This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models （QLNM）. Our results may be regarded as a further generalization of the relevant results in Ref. [4].

Strong Consistency and Convergence Rate of Modified Partitioning Estimate of Non.p.arametric Regression Function under α-Mixing Sample

In this paper, we study the strong consistency and convergence partitioning estimate of nonparametric regression function under the sample that is α sequence taking values in R^d × R^1 with identical distribution. rate of modified （（Xi,Yi）,i 〉 1} .

Strong Subgame Consistency of the Core in Stochastic Network Formation Games

We consider a model of network formation as a stochastic game with random duration proposed initially in Sun and Parilina(Autom Remote Control 82(6):1065–1082,2021).In the model,the leader first suggests a joint project to other players,i.e.,the network connecting them.Second,the players are allowed to form fresh links with each other updating the initially proposed network.The stage payoff of any player is defined depending on the network structure.There are two types of randomness in the network formation process:(i)links may fail to be formed with different probabilities although players intend to establish them,(ii)the game process may terminate at any stage or transit to the next stage with a certain probability distribution.Finally,a network is formed as a result of players’decisions and realization of random variables.The cooperative version of the stochastic game is investigated.In particular,we examine the properties of subgame consistency as well as strong subgame consistency of the core.We provide a payment mechanism or regularization of the core elements to sustain its subgame consistency and avoid the player’s deviations from the cooperative trajectory.In addition,the distribution procedure of the core elements is regularized in case there are negative payments to achieve only nonnegative payments to the players at any stage.The sufficient condition of a strongly subgame consistent core is also obtained.We illustrate our theoretical results with a numerical example.

EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.

ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.

KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA

Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.

PARAMETER ESTIMATION IN LINEAR REGRESSION MODELS FOR LONGITUDINAL CONTAMINATED DATA

The parameter estimation and the coefficient of contamination for the regression models with repeated measures are studied when its response variables are contaminated by another random variable sequence.Under the suitable conditions it is proved that the estimators which are established in the paper are strongly consistent estimators.

NON-PARAMETRIC ESTIMATION IN CONTAMINATED LINEAR MODEL

In this paper, the following contaminated linear model is considered:y i=(1-ε)x τ iβ+z i, 1≤i≤n,where r.v.'s ｛ y i ｝ are contaminated with errors ｛ z i ｝. To assume that the errors have the finite moment of order 2 only. The non parametric estimation of contaminated coefficient ε and regression parameter β are established, and the strong consistency and convergence rate almost surely of the estimators are obtained. A simulated example is also given to show the visual performance of the estimations.

SOME LARGE SAMPLE PROPERTIES OF AN ESTIMATOR OF THE HAZARD FUNCTION FROM RANDOMLY CENSORED DATA

In this paper, A nonparametric hazard estimator is introduced. Weak convergence and strong uniformly consistency of the proposed estimator lambda(n)(t) are investigated on a bounded interval, respectively. An asymptotic representation of lambda(n)(t) is also given, and the asymptotic representation is used to prove asymptotic normality of the hazard estimator.

PARAMETER ESTIMATION OF PATH-DEPENDENT MCKEAN-VLASOV STOCHASTIC DIFFERENTIAL EQUATIONS

This work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters.First,we prove the existence and uniqueness of these equations under non-Lipschitz conditions.Second,we construct maximum likelihood estimators of these parameters and then discuss their strong consistency.Third,a numerical simulation method for the class of path-dependent McKean-Vlasov stochastic differential equations is offered.Finally,we estimate the errors between solutions of these equations and that of their numerical equations.

SEMIPARAMETRIC REGRESSION MODELS WITH LOCALLY GENERALIZED GAUSSIAN ERROR'S STRUCTURE

This paper proposes parametric component and nonparametric component estimators in a semiparametric regression models based on least squares and weight function's method, their strong consistency and rib mean consistency are obtained under a locally generallied Gaussinan error's structure. Finally, the author showes that the usual weight functions based on nearest neighbor method satisfy the deigned assumptions imposed.

Nonparametric estimation for contamination distribution

In the paper, for the contamination distribution model F（x） = （1-α）F1（x）＋αF2（x）, the estimates of α and F1 （x） are studied using two different ways when F2 （x） is known and the strong consistency of the two estimates is proved. At the same time the consistency rate of estimate α is also given.

A KIND OF URN MODEL FOR ADAPTIVE SEQUENTIAL DESIGN

This paper proposes a new kind of generalized Friendman's urn model,which with adaptive nonhomogeneous generating matrix.This model may be applied in sequential medical experiment.In this model some limit theorems (strong consistency and asymptot- ical normality) have been obtained.