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Том 27, № 2 (2018)
- Год: 2018
- Статей: 4
- URL: https://journal-vniispk.ru/1066-5307/issue/view/13899
Article
Estimating the Index of Increase via Balancing Deterministic and Random Data
Аннотация
We introduce and explore an empirical index of increase that works in both deterministic and random environments, thus allowing to assess monotonicity of functions that are prone to random measurement errors. We prove consistency of the index and show how its rate of convergence is influenced by deterministic and random parts of the data. In particular, the obtained results suggest a frequency at which observations should be taken in order to reach any pre-specified level of estimation precision.We illustrate the index using data arising from purely deterministic and error-contaminated functions, which may or may not be monotonic.
83-102
Statistical Estimation of Parameters for Binary Conditionally Nonlinear Autoregressive Time Series
Аннотация
The problem of statistical parameter estimation is considered for binary GLM-based autoregression with the link function of general form and the base functions (regressors) nonlinear w.r.t. the lagged variables. A new consistent asymptotically normal frequencies-based estimator (FBE) is constructed and compared with the classical MLE. It is shown that the FBE has less restrictive sufficient conditions of uniqueness than the MLE (does not need log-concavity of the inverse link) and can be computed recursively under the model extension. The sparse version of the FBE is proposed and the optimal model-dependent weight matrices (parameterizing the FBE) are found for the FBE and for the sparse FBE. The proposed empirical choice of the subset of s-tuples for the sparse FBE is examined by numerical and analytical examples. Computer experiments for comparison of the FBE versus the MLE are performed on simulated and real (genetic) data.
103-118
A Test of Correlation in the Random Coefficients of an Autoregressive Process
Аннотация
A random coefficient autoregressive process in which the coefficients are correlated is investigated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the autocorrelation function of the process. Then we study some asymptotic properties of the empirical mean and the usual estimators of the process, such as convergence, asymptotic normality and rates of convergence, supplied with appropriate assumptions on the driving perturbations. Our objective is to get an overview of the influence of correlated coefficients in the estimation step through a simple model. In particular, the lack of consistency is shown for the estimation of the autoregressive parameter when the independence hypothesis in the random coefficients is violated. Finally, a consistent estimation is given together with a testing procedure for the existence of correlation in the coefficients. While convergence properties rely on ergodicity, we use a martingale approach to reach most of the results.
119-144
The Deficiency Introduced by Resampling
Аннотация
When the classical nonparametric bootstrap is implemented by a Monte-Carlo procedure one resamples values from a sequence of, typically, independent and identically distributed ones. But what happens when a decision has to be taken based on such resampled values? One way to quantify the loss of information due to this resampling step is to consider the deficiency distance, in the sense of Le Cam, between a statistical experiment of n independent and identically distributed observations and the one consisting of m observations taken from the original n by resampling with replacement. By comparing with an experiment where only subsamplingwith a random subsampling size has been performed one can bound the deficiency in terms of the amount of information contained in additional observations. It follows for certain experiments that the deficiency distance is proportional to the expected fraction of observations missed when resampling.
145-161