An efficient and fast algorithm for estimating the frequencies of superimposed exponential signals in zero-mean multiplicative and additive noise

In this paper, we consider the superimposed exponential signals in zero-mean multiplicative and additive noise when all the noise are independently and identically distributed. We use a three-step iterative procedure to estimate the frequencies of the considered model. It is observed that the estimators are consistent and work quite well in terms of biases and mean square errors. Moreover, the convergence rate of the estimators attains O _p (N ^?3/2), which is the best convergence rate in the case of only additive noise and constant amplitude.     

Accent on Teaching Materials

This department includes the two sections New Developments in Statistical Computing and Statistical Computing Software Reviews; suitable contents for each of these sections are described under the respective section heading. Articles submitted for the department, outside the two sections, should not be highly technical and should be relevant to the teaching or practice of statistical computing.

An unbiased estimator of e is used to motivate a simple simulation exercise that requires only observations from the distribution uniform on (0, 1). Antithetic variables are introduced and applied to the simulation problem to give a second unbiased estimator of e with reduced variance.     

Updating finite markov chains by using techniques of group matrix inversion

Several jackknife methods for the proportional hazards model are proposed. Instead of deleting observations in the calculation of the pseudovalues, we delete the conditional probabilities from the partial likelihood function. The parameter estimators and variance estimators for both the linear and weighted linear jackknife methods are strongly consistent. A limitted simulation study is conducted.     

Modified minimax estimation of regression coefficients

Working with the linear regression model (1.1) and having the extraneous information (1.2) about regression coefficients the problem exists how to build estimators (1.3) with the risk (1.4) which enable to utilize the known information in order to reduce their risk as compared with the risk (1.6) of the LSE (1.5). Solution of this problem is known for the positive definite matrix T, namely in form for estimators (1.8) and (1.10).First, it is shown that the proposed estimators (2.6),(2.9) and (2.16) based on psedoinversions of the matrix L represent the solution of the problem of the positive semidefinite matrix T=L'L.Further, the problem of interpretability of estimators in the sense of the inequality (3.1) exists; it is shown that all mentioned estimators are at least partially interpretable in the sense of requirements (3.2) or (3.10).     

Efficient Estimation of Parameters of the Negative Binomial Distribution

In this article we investigate a class of moment-based estimators, called power method estimators, which can be almost as efficient as maximum likelihood estimators and achieve a lower asymptotic variance than the standard zero term method and method of moments estimators. We investigate different methods of implementing the power method in practice and examine the robustness and efficiency of the power method estimators.     

Nonparametric regression estimation in a null recurrent time series

We derive an asymptotic theory of nonparametric estimation for a time series regression model Z_t=f(X_t)+W_t, where {X_t} and {Z_t} are observed nonstationary processes, and {W_t} is an unobserved stationary process. The class of nonstationary processes allowed for {X_t} is a subclass of the class of null recurrent Markov chains. This subclass contains the random walk, unit root processes and nonlinear processes. The process {W_t} is assumed to be linear and stationary.     

COMPARATIVE CALIBRATION WITH SUBGROUPS

The main object of this paper is to consider structural comparative calibration models under the assumption that the unknown quantity being measured is not identically distributed for all units. We consider the situation where the mean of the unknown quantity being measured is different within subgroups of the population. Method of moments and maximum likelihood estimators are considered for estimating the parameters in the model. Large sample inference is facilitated by the derivation of the asymptotic variances. An application to a data set which indeed motivated the consideration of such general model and was obtained by measuring the heights of a group of trees with five different instruments is considered.     

Exact likelihood inference for Laplace distribution based on Type-II censored samples

We develop exact inference for the location and scale parameters of the Laplace (double exponential) distribution based on their maximum likelihood estimators from a Type-II censored sample. Based on some pivotal quantities, exact confidence intervals and tests of hypotheses are constructed. Upon conditioning first on the number of observations that are below the population median, exact distributions of the pivotal quantities are expressed as mixtures of linear combinations and of ratios of linear combinations of standard exponential random variables, which facilitates the computation of quantiles of these pivotal quantities. Tables of quantiles are presented for the complete sample case.     

A class of high-breakdown scale estimators based on subranges

We consider a new class of scale estimators with 50% breakdown point. The estimators are defined as order statistics of certain subranges. They all have a finite-sample breakdown point of [n/2]/n, which is the best possible value. (Here, [...] denotes the integer part.) One estimator in this class has the same influence function as the median absolute deviation and the least median of squares (LMS) scale estimator (i.e., the length of the shortest half), but its finite-sample efficiency is higher. If we consider the standard deviation of a subsample instead of its range, we obtain a different class of 50% breakdown estimators. This class contains the least trimmed squares (LTS) scale estimator. Simulation shows that the LTS scale estimator is nearly unbiased, so it does not need a small-sample correction factor. Surprisingly, the efficiency of the LTS scale estimator is less than that of the LMS scale estimator.     

Mathematische aspekte zu einer methode zur numerischen bestimmung individueller thermodynamischer aktivitätskoeffizienten einzelner ionensorten in konzentrierten elektrolytlösungen

The mathematical problems of the – in an communication [3] described – principle for the calculation of individual thermodynamic activity coefficients of single ionic species in concentrated electrolyte solutions are specified. It is the Newtonian approximation method that makes possible the evaluation of the constants b ₁,…b ₄ in the concentration function (0.1) for the product of the activity coefficients.

The efficiency of the method is represented by the example of the activity coefficients of pure and of – with other electrolytes – mixed solutions of NaCIO₄. The individual activity coefficients of the single ionic species are evaluated for several electrolytes of the concentration range from m = 0 to m = 10 mole/kg and published at another place [3, 17, 18].