Numerous ratio-type estimators of the population variance are proposed in the existing literature based on different characteristics of the study as well as the auxiliary variable. However, mostly the existing estimators are based on the conventional measures of the population characteristics and their efficiency is dubious in the presence of outliers in the data. This study presents improved families of variance estimators under simple random sampling without replacement assuming that the information on some robust nonconventional location parameters of the auxiliary variable is known besides the usual conventional parameters. The bias and mean square error of the proposed families of estimators are obtained and the efficiency conditions are derived mathematically. The theoretical results are supplemented with the numerical illustrations by using real datasets which indicates the supremacy of the suggested families of estimators.

Chong (1995) and Bai (1997) proposed a sample splitting method to estimate a multiple-break model. However, their studies focused on stationary time series models, where the identification of the first break depends on the magnitude and the duration of the break, and a testing procedure is needed to assist the estimation of the remaining breaks in subsamples split by the break points found earlier. In this paper, we focus on nonstationary multiple-break autoregressive models. Unlike the stationary case, we show that the duration of a break does not affect if it will be identified first. Rather, it depends on the stochastic order of magnitude of signal strength of the break under the case of constant break magnitude and also the square of the magnitude of the break under the case of shrinking break magnitude. Since the subsamples usually have different stochastic orders in nonstationary autoregressive models with breaks, one can therefore determine which break will be identified first. We apply this finding to the models proposed in ) and Phillips et al. (2015a, 2015b. We provide an estimation procedure as well as the asymptotic theory for the model.

Let X, X 1 , X 2 , . . . be i.i.d. nondegenerate random variables with zero means, S n = n j =1 X j and V 2 n = n j =1 X 2 j . We investigate the precise asymptotics in the law of the iterated logarithm for self-normalized sums, S n /V n , also for the maximum of self-normalized sums, max 1 k n |S k |/V n , when X belongs to the domain of attraction of the normal law.

Abstract. This paper revisits the asymptotic inference for non-stationary AR(1) models of Phillips and Magdalinos (2007a) by incorporating a structural change in the AR parameter at an unknown time k 0 . Consider the model We derive the limiting distributions of the t-ratios of β 1 and β 2 and the least squares estimator of the change point for the cases above under some mild conditions. Monte Carlo simulations are conducted to examine the finite-sample properties of the estimators. Our theoretical findings are supported by the Monte Carlo simulations.

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In survey sampling, it is a well-established phenomenon that the e ciency of estimators increases with proper information on auxiliary variable(s). Keeping this fact in mind, the information on two auxiliary variables was utilized to propose a family of Hartley-Ross type unbiased estimators for estimating population mean under simple random sampling without replacement. Minimum variance of the new estimators was derived up to the rst degree of approximation. Three real datasets were used to verify the e cient performance of the new family in comparison to the usual unbiased, Hartley and Ross, and other competing estimators.

Domain of attraction of the normal law a b s t r a c t Let {X i , i ≥ 1} be a sequence of i.i.d. random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denotei . Then an almost sure central limit theorem for self-normalized partial sums S n /V n is studied under a mild condition in this paper.