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The problem of choosing the appropriate predictor is being considered. Generally, in this paper the analysis is focused on the problem of unbiasedness of the predictors. Several tests attempting to verify the unbiasedness of three predictors of the linear trend are proposed. They are based on some modifications of the well-known Janus quotient being a ratio of the variance of prediction errors and...
Estimation of the population average by means of a conditional strategy has been considered e.g. in [2–6,9] and [10]. Let us assume that the sampling design depends on a function of an auxiliary variable called an auxiliary statistic like: the sample mean or the sample variance. Under the conditional versions of these designs several estimators of the population mean are considered: the Horvitz-Thompson...
Testing the goodness of fit between a hypothetical trend function and its non-parametric variant will be considered. This problem was analysed e.g. by Domanski (1979, 1990), Wywiał (1990, 1995). Our result can be treated as a modification of the test proposed by Azzalini and Bowman (1993). The hypothetical trend function will be denoted by f(t, θ). It is estimated by an unbiased method. A trend function...
The problem of estimation of the mode of a continuous distribution
(unction is considered. The estimation of the mode based on estimators of the density
function is well known, see e.g. Härdle (1991) and Parzen (1962). New parameters
of the continuous distribution function will be defined: the quasi-mode and mean median.
They are parameters of the appropriately truncated random variable. Next,...
The quadratic form of the sample mean and sample variance was considered.
The sample is from normal distribution. The density function of the quadratic form has been
derived. The quadratic form can be applied as the test statistic for the hypothesis on expected
value and variance of normal distribution. The table with approximated critical values of the
test statistic has been derived.
Estimation of the population average in a finite population by means
of sampling strategy dependent on the sample quantile of an auxiliary variables is considered.
The sampling design is proportionate to the determinant of the matrix dependent
on some quantiles of an auxiliary variables. The sampling scheme implementing the
sampling design is proposed. The derived inclusion probabilities are applied...
Problem estymacji wartości przeciętnej w populacji na podstawie próby prostej losowanej
bezzwrotnie z populacji ustalonej i skończonej jest rozważany. Zakładamy, że wartości
zmiennej pomocniczej są obserwowane w całej populacji. Próba prosta, po jej wylosowaniu,
jest porządkowana zgodnie z rosnącymi wartościami zmiennej pomocniczej. Następnie próba
ta jest dzielona na H > 1 równolicznych podprób...
In the paper we present the examples of forecasts of time series with seasonal
fluctuations. Based on the jackknife method we estimate variances of seasonal factors and
the MSE of prediction. Jackknife method has been introduced by M. Quenouille (1949)
and then it has been developed among others by J. Tukey (1958) and J. Shao, D. Tu
(1995).
he problem of prediction of the total value in a domain based on simple regression superpopulation model (with one auxiliary variable and no intercept) is considered. The problem of robust estimation against outliers of regression function's parameter is shown. The presented robust estimator is median value of gradients of all straight lines each determined by the origin and one of n points (x, y),...
The trend of time series can change its direction. It is assumed that the
time interval is divided into subintervals where the trend is given as particular linear
function. The problem is how to divide the observation of time series into disjoint and
coherent groups where they have linear trend.
That is why the problem of the scatter of multivariable observation was first
considered. The degree...
The estimation of a vector of mean values is being considered. The vector
estimator consists of simple cluster sample means. It is assumod that a population of a fixed
size is divided into mutually disjoint clusters each of the same size. The variance-covariance
matrix of the vector estimator is derived. It is a function of a homogeneity matrix of
multidimensional variable which describes within-cluster...
The problem of estimation of the mode of a continuous distribution function of multidimensional
random variable is considered. The estimator of the mode is the vector of means
from appropriately truncated sample. The truncation sample is obtained th rough rejecting the
observation in such a way that the measure of skewnees of multidimensional variable takes
value as close zero as possible. We...
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