Annals of the Institute of Statistical Mathematics最新文献

In various applications of regression analysis, in addition to errors in the dependent observations also errors in the predictor variables play a substantial role and need to be incorporated in the statistical modeling process. In this paper we consider a nonparametric measurement error model of Berkson type with fixed design regressors and centered random errors, which is in contrast to much existing work in which the predictors are taken as random observations with random noise. Based on an estimator that takes the error in the predictor into account and on a suitable Gaussian approximation, we derive finite sample bounds on the coverage error of uniform confidence bands, where we circumvent the use of extreme-value theory and rather rely on recent results on anti-concentration of Gaussian processes. In a simulation study we investigate the performance of the uniform confidence sets for finite samples.

In this work, we propose nonparametric two-sample tests for population-averaged transition and state occupation probabilities for continuous-time and finite state space processes with clustered, right-censored, and/or left-truncated data. We consider settings where the two groups under comparison are independent or dependent, with or without complete cluster structure. The proposed tests do not impose assumptions regarding the structure of the within-cluster dependence and are applicable to settings with informative cluster size and/or non-Markov processes. The asymptotic properties of the tests are rigorously established using empirical process theory. Simulation studies show that the proposed tests work well even with a small number of clusters, and that they can be substantially more powerful compared to the only, to the best of our knowledge, previously proposed nonparametric test for this problem. The tests are illustrated using data from a multicenter randomized controlled trial on metastatic squamous-cell carcinoma of the head and neck.

We consider an integer-valued time series ((Y_t)_{tin {mathbb {Z}}}) where the model after a time (k^*) is Poisson autoregressive with the conditional mean that depends on a parameter (theta ^*in varTheta subset {mathbb {R}}^d). The structure of the process before (k^*) is unknown; it could be any other integer-valued process, that is, ((Y_t)_{tin {mathbb {Z}}}) could be nonstationary. It is established that the maximum likelihood estimator of (theta ^*) computed on the nonstationary observations is consistent and asymptotically normal. Subsequently, we carry out the sequential change-point detection in a large class of Poisson autoregressive models, and propose a monitoring scheme for detecting change. The procedure is based on an updated estimator, which is computed without the historical observations. The above results of inference in a nonstationary setting are applied to prove the consistency of the proposed procedure. A simulation study as well as a real data application are provided.

Some quasi-arithmetic means of random variables easily give unbiased strongly consistent closed-form estimators of the joint of the location and scale parameters of the Cauchy distribution. The one-step estimators of those quasi-arithmetic means of the Cauchy distribution are considered. We establish the Bahadur efficiency of the maximum likelihood estimator and the one-step estimators. We also show that the rate of the convergence of the mean-squared errors achieves the Cramér–Rao bound. Our results are also applicable to the circular Cauchy distribution .

Statistical analysis of large-scale dataset is challenging due to the limited memory constraint and computation source and calls for the efficient distributed methods. In this paper, we mainly study the distributed estimation and inference for composite quantile regression (CQR). For computational and statistical efficiency, we propose to apply a smoothing idea to the CQR loss function for the distributed data and then successively refine the estimator via multiple rounds of aggregations. Based on the Bahadur representation, we derive the asymptotic normality of the proposed multi-round smoothed CQR estimator and show that it also achieves the same efficiency of the ideal CQR estimator by analyzing the entire dataset simultaneously. Moreover, to improve the efficiency of the CQR, we propose a multi-round smoothed weighted CQR estimator. Extensive numerical experiments on both simulated and real data validate the superior performance of the proposed estimators.

The main purpose of the present work is to investigate kernel-type estimate of a class of function derivatives including parameters such as the density, the conditional cumulative distribution function and the regression function. The uniform strong convergence rate is obtained for the proposed estimates and the central limit theorem is established under mild conditions. Moreover, we study the asymptotic mean integrated square error of kernel derivative estimator which plays a fundamental role in the characterization of the optimal bandwidth. The obtained results in this paper are established under a general setting of discrete time stationary and ergodic processes. A simulation study is performed to assess the performance of the estimate of the derivatives of the density function as well as the regression function under the framework of a discretized stochastic processes. An application to financial asset prices is also considered for illustration.

Under minimal assumptions, we prove that an empirical estimator of the tail conditional allocation (TCA), also known as the marginal expected shortfall, is consistent. Examples are provided to confirm the minimality of the assumptions. A simulation study illustrates the performance of the estimator in the context of developing confidence intervals for the TCA. The philosophy adopted in the present paper relies on three principles: easiness of practical use, mathematical rigor, and practical justifiability and verifiability of assumptions.

For parameters in a threshold autoregressive process, the paper proposes a sequential modification of the least squares estimates with a specific stopping rule for collecting the data for each parameter. In the case of normal residuals, these estimates are exactly normally distributed in a wide range of unknown parameters. On the base of these estimates, a fixed-size confidence ellipsoid covering true values of parameters with prescribed probability is constructed. In the i.i.d. case with unspecified error distributions, the sequential estimates are asymptotically normally distributed uniformly in parameters belonging to any compact set in the ergodicity parametric region. Small-sample behavior of the estimates is studied via simulation data.

The segmentation of a time series into piecewise stationary segments is an important problem both in time series analysis and signal processing. In the presence of multiscale change points with both large jumps over short intervals and small jumps over long intervals, multiscale methods achieve good adaptivity but require a model selection step for removing false positives and duplicate estimators. We propose a localised application of the Schwarz criterion, which is applicable with any multiscale candidate generating procedure fulfilling mild assumptions, and establish its theoretical consistency in estimating the number and locations of multiple change points under general assumptions permitting heavy tails and dependence. In particular, combined with a MOSUM-based candidate generating procedure, it attains minimax rate optimality in both detection lower bound and localisation for i.i.d. sub-Gaussian errors. Overall competitiveness of the proposed methodology compared to existing methods is shown through its theoretical and numerical performance.