Journal of Statistical Planning and Inference最新文献

In this paper we treat statistical inference for a wavelet estimator of curves of symmetric positive definite (SPD) using the log-Euclidean distance. This estimator preserves positive-definiteness and enjoys permutation-equivariance, which is particularly relevant for covariance matrices. Our second-generation wavelet estimator is based on average-interpolation (AI) and allows the same powerful properties, including fast algorithms, known from nonparametric curve estimation with wavelets in standard Euclidean set-ups. The core of our work is the proposition of confidence sets for our AI wavelet estimator in a non-Euclidean geometry. We derive asymptotic normality of this estimator, including explicit expressions of its asymptotic variance. This opens the door for constructing asymptotic confidence regions which we compare with our proposed bootstrap scheme for inference. Detailed numerical simulations confirm the appropriateness of our suggested inference schemes.

A class of tests that are uniformly more powerful than the likelihood ratio test is derived for testing the hypothesis about the means of a subset of the components of a multivariate normal distribution with unknown covariance matrix, when the means of the other subset of the components are known.

In kernel-based learning, the random projection method, also called random sketching, has been successfully used in kernel ridge regression to reduce the computational burden in the big data setting, and at the same time retain the minimax convergence rate. In this work, we consider its use in sparse multiple kernel learning problems where a closed-form optimizer is not available, which poses significant technical challenges, for which the existing results do not carry over directly. Even when random projection is not used, our risk bound improves on the existing results in several aspects. We also illustrate the use of random projection via some numerical examples.

In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and negative binomial thinning operators. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares (CLS) and conditional maximum likelihood (CML) estimators are derived and the asymptotic properties of the estimators are established. The inference for the threshold parameter is obtained based on the CLS and CML score functions. Moreover, the Wald test is applied to detect the existence of the piecewise structure. Simulation studies are considered, along with an application: the number of criminal mischief incidents in the Pittsburgh dataset

In some experiments, the experimental units are all pairs of individuals who have to undertake a given task together. The set of such pairs forms a triangular association scheme. Appropriate randomization then gives two non-trivial strata. The design is said to have commutative orthogonal block structure (COBS) if the best linear unbiased estimators of treatment contrasts do not depend on the stratum variances. There are precisely three ways in which such a design can have COBS. We give a complete description of designs for which all treatment contrasts are in the same stratum. Then we give a very general construction for designs with COBS which have some treatment contrasts in each stratum.

The explosion of data volume and the expansion in data dimensionality have led to a critical challenge in analyzing high-dimensional matrix time series for big data-related applications. In this regard, factor models for matrix-valued high-dimensional time series provide a powerful tool, that reduces the dimensionality of the variables with low-rank structures. However, existing high-dimensional matrix factor models suffer from two limitations in complex scenarios. One is that it is difficult to make robust inferences for datasets with heavy-tailed distributions. The other is that existing models require additional parameters for fine-tuning to guarantee performance. We propose an adaptively robust high-dimensional matrix factor model based on a specified Huber loss function to tackle the challenges mentioned above. An efficient iterative algorithm is provided to consistently determine the additional parameters of our model for robust estimation. The robustness of the model estimation is greatly improved by incorporating the Huber loss. Furthermore, we theoretically investigate the proposed method and derive the convergence rates of the robust estimators to examine its performance. Simulations show that the proposed method outperforms previous models in the estimation of heavy-tailed data. A real-world data analysis on a financial portfolio dataset illustrates that the method can be used to extract useful knowledge from high-dimensional matrix time series.

We study the kernel estimators of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that these estimators are consistent and asymptotically normal. Next, in the numerical studies, we propose two data-driven methods to choose the bandwidth parameters. These methods, based on the so-called two bandwidths approach, are adaptation for bifurcating Markov chains of the least squares Cross-Validation and the rule of thumb method. Finally, we provide an example with real data.

Massive survival data has become common in survival analysis. In this study, a subsampling algorithm is proposed for Cox proportional hazards model with time-dependent covariates when the sample size is extraordinarily large but the computing resources are relatively limited. A subsample estimator is developed by maximizing a weighted partial likelihood, and shown to have consistency and asymptotic normality. By minimizing the asymptotic mean squared error of the subsample estimator, the optimal subsampling probabilities are formulated with explicit expression. Simulation studies show that the proposed method has satisfactory performances in approximating the full data estimator. The proposed method is applied to the corporate loan data and breast cancer data, with different censoring rates, and the outcome also confirms the practical advantages.

In linear models, omitting a covariate that is orthogonal to covariates in the model does not result in biased coefficient estimation. This generally does not hold for longitudinal data, where additional assumptions are needed to get an unbiased coefficient estimation in addition to the orthogonality between omitted longitudinal covariates and longitudinal covariates in the model. We propose methods to mitigate the omitted variable bias under weaker assumptions. A two-step estimation procedure is proposed to infer the asynchronous longitudinal covariates when such covariates are observed. For mixed synchronous and asynchronous longitudinal covariates, we get a parametric convergence rate for the coefficient estimation of the synchronous longitudinal covariates by the two-step method. Extensive simulation studies provide numerical support for the theoretical findings. We illustrate the performance of our method on a dataset from the Alzheimer’s Disease Neuroimaging Initiative study.