<Para ID="Par1">From an observable <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(X,U)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>U</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mathbb R^p \times \mathbb R^k$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msup> <mi mathvariant="double-struck">R</mi> <mi>p</mi> </msup> <mo>×</mo> <msup> <mi mathvariant="double-struck">R</mi> <mi>k</mi> </msup> </mrow> </math> </EquationSource> </InlineEquation>, we consider estimation of an unknown location parameter <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\theta \in \mathbb R^p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">θ</mi> <mo>∈</mo> <msup> <mi mathvariant="double-struck">R</mi> <mi>p</mi> </msup> </mrow> </math> </EquationSource> </InlineEquation> under two distributional settings: the density of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$(X,U)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>U</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> is...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></para>

Strategies for comparison of alternative tests do not receive much attention in econometrics. The purpose of this paper is to introduce the concept of stringency and illustrate it in the context of a very simple hypothesis testing problem. Systematic use of this concept can be very helpful in...

This article deals with approximation of empirical distribution to standard normal distribution using Johnson transformation. This transformation enables us to approximate wide spectrum of continuous distributions with a normal distribution. The estimation of parameters of transformation...

Although the generalised autoregressive conditional heteroskedasticity (GARCH) model has been quite successful in capturing important empirical aspects of financial data, particularly for the symmetric effects of volatility, it has had far less success in capturing the effects of extreme...

We propose simple estimation of the location parameter for a density that is unbounded at the mode. The estimator maximizes a modified likelihood in which the singular term in the full likelihood is left out, whenever the parameter value approaches a neighborhood of the singularity location. The...

We study the test for location parameter of a random number from Cauchy density, focusing on point optimal tests. We develop analytical technique to compute critical values and power curve of a point optimal test. We study the power properties of various point optimal tests. The problem turned...

Economic, social, engineering, medical as well as financial activities lead very often (from the mathematical point of view) to deterministic optimization problems depending on an unknown probability measure. Evidently, an experience is then employed whenever it is possible. Mostly, it means...