Simultaneous prediction of functionally dependent random variables by maximum likelihood estimation

2021 ◽  
Vol 16 (2) ◽  
pp. 143-150
Author(s):  
Nikita A. Moiseev
Keyword(s):  
Forecast Error ◽  
Random Variables ◽  
Likelihood Estimation ◽  
Random Variable ◽  
Parametric Approach ◽  
Functional Link ◽  
Dependent Random Variables ◽  
Steady Decrease ◽  
Simultaneous Prediction ◽  
The Mean

The paper presents a fundamental parametric approach to simultaneous forecasting of a vector of functionally dependent random variables. The motivation behind the proposed method is the following: each random variable at interest is forecasted by its own model and then adjusted in accordance with the functional link. The method incorporates the assumption that models’ errors are independent or weekly dependent. Proposed adjustment is explicit and extremely easy-to-use. Not only does it allow adjusting point forecasts, but also it is possible to adjust the expected variance of errors, that is useful for computation of confidence intervals. Conducted thorough simulation and empirical testing confirms, that proposed method allows to achieve a steady decrease in the mean-squared forecast error for each of predicted variables.

Uniform saddlepoint approximations

1988 ◽  
Vol 20 (3) ◽  
pp. 622-634 ◽  
Author(s):  
J. L. Jensen
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Tail Probability ◽  
Poisson Random Variable ◽  
Compound Poisson ◽  
Saddlepoint Approximations ◽  
The Mean ◽  
General Conditions

The validity of the saddlepoint expansion evaluated at the point y is considered in the limit y tending to ∞. This is done for the expansions of the density and of the tail probability of the mean of n i.i.d. random variables and also for the expansion of the tail probability of a compound Poisson sum , where N is a Poisson random variable. We consider both general conditions that ensure the validity of the expansions and study the four classes of densities for X1 introduced in Daniels (1954).

The Largest Missing Value in a Sample of Geometric Random Variables

2014 ◽  
Vol 23 (5) ◽  
pp. 670-685 ◽  
Author(s):  
MARGARET ARCHIBALD ◽  
ARNOLD KNOPFMACHER
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Missing Value ◽  
Asymptotic Expressions ◽  
Mean And Variance ◽  
The Mean ◽  
Special Case

We consider samples of n geometric random variables with parameter 0 < p < 1, and study the largest missing value, that is, the highest value of such a random variable, less than the maximum, that does not appear in the sample. Asymptotic expressions for the mean and variance for this quantity are presented. We also consider samples with the property that the largest missing value and the largest value which does appear differ by exactly one, and call this the LMV property. We find the probability that a sample of n variables has the LMV property, as well as the mean for the average largest value in samples with this property. The simpler special case of p = 1/2 has previously been studied, and verifying that the results of the present paper coincide with those previously found for p = 1/2 leads to some interesting identities.

Uniform saddlepoint approximations

1988 ◽  
Vol 20 (03) ◽  
pp. 622-634 ◽  
Author(s):  
J. L. Jensen
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Tail Probability ◽  
Poisson Random Variable ◽  
Compound Poisson ◽  
Saddlepoint Approximations ◽  
The Mean ◽  
General Conditions

The validity of the saddlepoint expansion evaluated at the point y is considered in the limit y tending to ∞. This is done for the expansions of the density and of the tail probability of the mean of n i.i.d. random variables and also for the expansion of the tail probability of a compound Poisson sum , where N is a Poisson random variable. We consider both general conditions that ensure the validity of the expansions and study the four classes of densities for X 1 introduced in Daniels (1954).

Analysis of the ratio of the mean square deviations of the kernel probability density estimation in the conditions of independent and dependent random variables

2021 ◽  
pp. 9-14
Author(s):  
Aleksandr V. Lapko ◽  
Vasiliy A. Lapko
Keyword(s):  
Probability Density ◽  
Statistical Data ◽  
Random Variables ◽  
Mean Square ◽  
Two Dimensional ◽  
Approximation Properties ◽  
Dependent Random Variables ◽  
Probability Densities ◽  
Distribution Laws ◽  
The Mean

The influence on the approximation properties of a nonparametric probability density estimate of Rosenblatt-Parzen type of the information on the dependence of random variables is determined. The ratio of the asymptotic expressions of the mean square deviations of independent and dependent random variables is obtained. This relation for a two-dimensional random variable is considered as a quantitative assessment of the influence of information about their dependence on the approximation properties of the kernel probability density estimate. The established ratio is determined by the kind of probability density and the volumes of the initial statistical data that are used in estimating the probability densities of dependent and independent random variables. The general results obtained are considered in detail for two-dimensional linearly dependent random variables with normal distribution laws. The functional dependence of the ratio of the mean square deviations of the independent and dependent two-dimensional random variables on the correlation coefficient is determined. The dependence of the considered ratio on the volume of statistical data is analyzed. A method for estimating the functional of the second derivatives of two-dimensional random variables with normal distribution laws is developed. The results obtained are the basis for the development of modifications of “fast” procedures for optimizing kernel estimates of probability densities in conditions of large samples.

Strong convergence properties for arrays of rowwise negatively orthant dependent random variables

2017 ◽  
Vol 67 (1) ◽  
pp. 235-244
Author(s):  
Aiting Shen ◽  
Yu Zhang ◽  
Andrei Volodin
Keyword(s):  
Strong Convergence ◽  
Complete Convergence ◽  
Random Variables ◽  
Random Variable ◽  
Convergence Properties ◽  
Exponential Moment ◽  
Dependent Random Variables

Abstract Let {Xni , i ≥ 1, n ≥1} be an array of rowwise negatively orthant dependent random variables which is stochastically dominated by a random variable X. Wang et al. [15. Complete convergence for arrays of rowwise negatively orthant dependent random variables, RACSAM, 106 (2012), 235–245] studied the complete convergence for arrays of rowwise negatively orthant dependent random variables under the condition that X has an exponential moment, which seems too strong. We will further study the complete convergence for arrays of rowwise negatively orthant dependent random variables under the condition that X has a moment, which is weaker than exponential moment. Our results improve the corresponding ones of Wang et al. [15].

An extension of central limit theorem for randomly indexed m-dependent random variables

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4369-4377 ◽  
Author(s):  
Stefano Belloni
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Number ◽  
Random Variables ◽  
Random Variable ◽  
Positive Random Variable ◽  
Dependent Random Variables

In this note, we prove a conjecture of Shang about the sum of a random number Nn of m-dependent random variables. The random number Nn is supposed to converge in probability toward a positive random variable.

LIMITING BEHAVIOUR FOR ARRAYS OF UPPER EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES

2015 ◽  
Vol 92 (1) ◽  
pp. 159-167 ◽  
Author(s):  
JOÃO LITA DA SILVA
Keyword(s):  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Dependent Random Variables ◽  
Triangular Arrays ◽  
Negatively Dependent Random Variables ◽  
Limiting Behaviour

For triangular arrays $\{X_{n,k}:1\leqslant k\leqslant n,n\geqslant 1\}$ of upper extended negatively dependent random variables weakly mean dominated by a random variable $X$ and sequences $\{b_{n}\}$ of positive constants, conditions are given to guarantee an almost sure finite upper bound to $\sum _{k=1}^{n}(X_{n,k}-\mathbb{E}X_{n,k})/\!\sqrt{b_{n}\,\text{Log}\,n}$, where $\text{Log}\,n:=\max \{1,\log n\}$, thus getting control over the limiting rate in terms of the prescribed sequence $\{b_{n}\}$ and permitting us to weaken or strengthen the assumptions on the random variables.

scholarly journals On The Quotient of a Centralized and a Non-centralized Complex Gaussian Random Variable

2020 ◽  
Vol 125 ◽  
Author(s):  
Dazhen Gu
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Complex Signal ◽  
Tolerance Intervals ◽  
Practical Applications ◽  
Second Moments ◽  
Complex Gaussian Random Variable ◽  
The Mean ◽  
Theoretical Developments ◽  
Straightforward Extension

A detailed investigation of the quotient of two independent complex random variables is presented. The numerator has a zero mean, and the denominator has a non-zero mean. A normalization step is taken prior to the theoretical developments in order to simplify the formulation. Next, an indirect approach is taken to derive the statistics of the modulus and phase angle of the quotient. That in turn enables a straightforward extension of the statistical results to real and imaginary parts. After the normalization procedure, the probability density function of the quotient is found as a function of only the mean of the random variable that corresponds to the denominator term. Asymptotic analysis shows that the quotient closely resembles a normally-distributed complex random variable as the mean becomes large. In addition, the first and second moments, as well as the approximate of the second moment of the clipped random variable, are derived, which are closely related to practical applications in complex-signal processing such as microwave metrology of scattering-parameters. Tolerance intervals associated with the ratio of complex random variables are presented.

scholarly journals A Strong Law of Large Numbers for Set-Valued Negatively Dependent Random Variables

2016 ◽  
Vol 5 (3) ◽  
pp. 102
Author(s):  
Li Guan ◽  
Ying Wan
Keyword(s):  
Law Of Large Numbers ◽  
Hausdorff Metric ◽  
Random Variables ◽  
Random Variable ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Negatively Dependent Random Variables ◽  
Large Numbers

In this paper, we shall represent a strong law of large  numbers (SLLN) for weighted sums of negative dependent set-valued random variables  in the sense of the Hausdorff metric $d_{H}$, based  on the result of single-valued  random variable obtained by Taylor (Taylor, 1978).

Sign in / Sign up

Export Citation Format

Share Document