Conditional mode estimation for functional stationary ergodic data with responses missing at random

In this paper, we investigate the asymptotic properties of a non-parametric conditional mode estimation given a functional explanatory variable, when functional stationary ergodic data and missing at random responses are observed. First of all, we establish asymptotic properties for a conditional density estimator from which we derive almost sure convergence (with rate) and asymptotic normality of a conditional mode estimator. This new estimate take into account missing data, and a simulation study is performed to illustrate how this fact allows to get higher predictive performances than those obtained with standard estimates.     

Some statistical results on autoregressive conditionally heteroscedastic models

The aim of this paper is to present some statistical aspects of an order 1 autoregressive model with errors following a stationary and ergodic generalized threshold ARCH process. So, to analyse the precision of forecasts obtained with these models a probabilistic study will be done. Moreover, a consistent test for a general AR(1) model with errors following an ergodic white noise of null conditional median will be developed and adapted to our stochastic process.     

Conditional intensity: A powerful tool for modelling and analysing point process data

The conditional intensity function of a spatial point process describes how the probability that a point of the process occurs ‘at’ a particular point in its carrier space depends on the realisation of the process in the remainder of the carrier space. Provided that the point process is simple, the conditional intensity determines all of the properties of the process, in particular its likelihood function. In this paper, we review the use of the conditional intensity function in the formulation of point process models and in making inferences from point process data, giving separate consideration to temporal, spatial and spatiotemporal settings. We argue that the conditional intensity function should take centre-stage in spatiotemporal point process modelling and analysis.     

Characterization theorems for some discrete distributions based on conditional structure

The joint distribution of (X,Y) is determined if the conditional expectation E {g(X)|Y = y} is given and the conditional distribution of Y|(X = x) is a conditional power series distribution, where g(·) is a function satisfying some minor conditions.     

LAN property for an ergodic Ornstein–Uhlenbeck process with Poisson jumps

In this article, we consider an ergodic Ornstein–Uhlenbeck process with jumps driven by a Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients as well as its jump intensity depend on unknown parameters. Considering the process discretely observed at high frequency, we derive the local asymptotic normality property. To obtain this result, Malliavin calculus and Girsanov’s theorem are applied to write the log-likelihood ratio in terms of sums of conditional expectations, for which a central limit theorem for triangular arrays can be applied.     

Non-parametric estimation of the conditional mode

The problem of estimating the mode of a conditional probability density function is considered. It is shown that under some regularity conditions the estimate of the conditional mode obtained by maximizing a kernel estimate of the conditional probability density function is strongly consistent and asymptotically normally distributed.     

An autoregressive model based on the generalized hyperbolic distribution

We define a nonlinear autoregressive time series model based on the generalized hyperbolic distribution in an attempt to model time series with non-Gaussian features such as skewness and heavy tails. We show that the resulting process has a simple condition for stationarity and it is also ergodic. An empirical example with a forecasting experiment is presented to illustrate the features of the proposed model.     

Recursive kernel estimate of the conditional quantile for functional ergodic data

ABSTRACT

In this article, we study the recursive kernel estimator of the conditional quantile of a scalar response variable Y given a random variable (rv) X taking values in a semi-metric space. Two estimators are considered. While the first one is given by inverting the double-kernel estimate of the conditional distribution function, the second estimator is obtained by using the robust approach. We establish the almost complete consistency of these estimates when the observations are sampled from a functional ergodic process. Finally, a simulation study is carried out to illustrate the finite sample performance of these estimators.     

Uniform in bandwidth consistency for various kernel estimators involving functional data

The paper investigates various nonparametric models including regression, conditional distribution, conditional density and conditional hazard function, when the covariates are infinite dimensional. The main contribution is to prove uniform in bandwidth asymptotic results for kernel estimators of these functional operators. Then, the application issues, involving data-driven bandwidth selection, are discussed.     

Inequality Constraints in the Univariate GARCH Model

To keep the conditional variances generated by the GARCH (p, q) model nonnegative, Bollerslev imposed nonnegativity constraints on the parameters of the process. We show that these constraints can be substantially weakened and so should not be imposed in estimation. We also provide empirical examples illustrating the importance of relaxing these constraints.     

A Conditional Density Approach to the Order Determination of Time Series

The study focuses on the selection of the order of a general time series process via the conditional density of the latter, a characteristic of which is that it remains constant for every order beyond the true one. Using simulated time series from various nonlinear models we illustrate how this feature can be traced from conditional density estimation. We study whether two statistics derived from the likelihood function can serve as univariate statistics to determine the order of the process. It is found that a weighted version of the log likelihood function has desirable robust properties in detecting the order of the process.     

Adaptive estimators for parameters of the autoregression function of a Markov chain

Suppose we observe an ergodic Markov chain on the real line, with a parametric model for the autoregression function, i.e. the conditional mean of the transition distribution. If one specifies, in addition, a parametric model for the conditional variance, one can define a simple estimator for the parameter, the maximum quasi-likelihood estimator. It is robust against misspecification of the conditional variance, but not efficient. We construct an estimator which is adaptive in the sense that it is efficient if the conditional variance is misspecified, and asymptotically as good as the maximum quasi-likelihood estimator if the conditional variance is correctly specified. The adaptive estimator is a weighted nonlinear least-squares estimator, with weights given by predictors for the conditional variance.     

Parameter change test for zero-inflated generalized Poisson autoregressive models

In this paper, we consider the problem of testing for parameter change in zero-inflated generalized Poisson (ZIGP) autoregressive models. We verify that the ZIGP process is stationary and ergodic and that the conditional maximum likelihood estimator (CMLE) is strongly consistent and asymptotically normal. Based on these results, we construct CMLE- and residual-based cumulative sum tests and show that their limiting null distributions are a function of independent Brownian bridges. The simulation results are provided for illustration. A real data analysis is performed on some crime data of Australia.     

APPLICATIONS AND EXTENSIONS OF BASU'S RESULTS ON MAXIMAL ANCILLARITY

Maximality of ancillaries is important in both conditional inference without nuisance parameters and marginal inference with nuisance parameters. We extend results of Basu (1959) to the more classical former case and discuss the different nature of ancillaries in these two contexts. We apply the results to a general ancillary independent of a sufficient statistic. Finally, we discuss difficulties in finding necessary conditions for maximality.     

A new futility test approach in clinical interim data monitoring

Sequential monitoring of efficacy and safety data has become a vital component of modern clinical trials. It affords companies the opportunity to stop studies early in cases when it appears as if the primary objective will not be achieved or when there is clear evidence that the primary objective has already been met. This paper introduces a new concept of the backward conditional hypothesis test (BCHT) to evaluate clinical trial success. Unlike the regular conditional power approach that relies on the probability that the final study result will be statistically significant based on the current interim look, the BCHT was constructed based on the hypothesis test framework. The framework comprises a significant test level as opposed to the arbitrary fixed futility index utilized in the conditional power method. Additionally, the BCHT has proven to be a uniformly most powerful test. Noteworthy features of the BCHT method compared with the conditional power method will be presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Conditional mean residual life functions

In this paper a conditional mean residual life in the context of reliability theory is introduced. The properties of the conditional mean residual life are studied. Various characterizations by the conditional mean residual life are proposed.     

中国经济周期条件波动性特征的统计分析

在ARCH族模型动态地刻画了中国经济周期的条件波动性特征的基础上,分析了有关经济变量的波动机制、波动率对经济变量条件均值的影响程度与方向以及经济变量在扩张阶段和紧缩阶段波动力度差异等问题。得出以下主要结论：中国经济周期波动具有条件异方差性、持续性和非对称性的特征;经济的稳定有利于经济产出的持续增长;财政政策具有稳定经济、促进经济产出增长率提高的效应,而且这种效应具有一定的持续性与滞后性;国外需求受国内经济影响较小,具有其自身的发展规律。     

Conditional specifications of multivariate pareto and student distributions

A random vector has a multivariate Pareto distribution if one of its univariate conditional distribution is Pareto and some of its marginals are identically distributed.A general method developed in the course of the proof of this result is applied also to characterize the multivariate Student (Cauchy) measure by one univariate Student conditional distribution.     

On Testing Dependence between Time to Failure and Cause of Failure via Conditional Probabilities

Abstract.  Dependence structures between the failure time and the cause of failure are expressed in terms of the monotonicity properties of the conditional probabilities involving the cause of failure and the failure time. These properties of the conditional probabilities are used for testing four types of departures from the independence of the failure time and the cause of failure and tests based on U -statistics are proposed. In the process, a concept of concordance and discordance between a continuous and a binary variable is introduced to propose a statistical test. The proposed tests are applied to two illustrative applications.     

Weakly universally consistent static forecasting of stationary and ergodic time series via local averaging and least squares estimates

Given a stationary and ergodic time series the problem of estimating the conditional expectation of the dependent variable at time zero given the infinite past is considered. It is shown that the mean squared error of a combination of suitably defined local averaging or least squares estimates converges to zero for all distributions whenever the dependent variable is square integrable.