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Strong law of large numbers for additive extremum estimators

João Tiago Mexia, Pedro Corte Real (2001)

Discussiones Mathematicae Probability and Statistics

Extremum estimators are obtained by maximizing or minimizing a function of the sample and of the parameters relatively to the parameters. When the function to maximize or minimize is the sum of subfunctions each depending on one observation, the extremum estimators are additive. Maximum likelihood estimators are extremum additive whenever the observations are independent. Another instance of additive extremum estimators are the least squares estimators for multiple regressions when the usual assumptions...

Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model

Amina Angelika Bouchentouf, Tayeb Djebbouri, Abbes Rabhi, Khadidja Sabri (2014)

Applicationes Mathematicae

The aim of this paper is to establish a nonparametric estimate of some characteristics of the conditional distribution. Kernel type estimators for the conditional cumulative distribution function and for the successive derivatives of the conditional density of a scalar response variable Y given a Hilbertian random variable X are introduced when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence...

Stručný průvodce statistickými intervaly

Martin Otava (2017)

Pokroky matematiky, fyziky a astronomie

Statistické intervaly představují rozšířenou metodu k popisu nejistoty, avšak jejich přesná interpretace může být pro laika obtížná. Následující článek se zabývá třemi typy intervalů - konfidenčními, predikčními a tolerančními intervaly. Každý z nich má jinou funkci a má smysl ho používat jen v jistém kontextu. Téma je představeno spíše neformálně a poskytuje čtenáři základní přehled jednotlivých typů intervalů. Důraz je kladen především na správnou interpretaci a pochopení nejčastějších chyb spojených...

Structural breaks in dependent, heteroscedastic, and extremal panel data

Matúš Maciak, Barbora Peštová, Michal Pešta (2018)

Kybernetika

New statistical procedures for a change in means problem within a very general panel data structure are proposed. Unlike classical inference tools used for the changepoint problem in the panel data framework, we allow for mutually dependent panels, unequal variances across the panels, and possibly an extremely short follow up period. Two competitive ratio type test statistics are introduced and their asymptotic properties are derived for a large number of available panels. The proposed tests are...

Study of Bootstrap Estimates in Cox Regression Model with Delayed Entry

Silvie Bělašková, Eva Fišerová, Sylvia Krupičková (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In most clinical studies, patients are observed for extended time periods to evaluate influences in treatment such as drug treatment, approaches to surgery, etc. The primary event in these studies is death, relapse, adverse drug reaction, or development of a new disease. The follow-up time may range from few weeks to many years. Although these studies are long term, the number of observed events is small. Longitudinal studies have increased the importance of statistical methods for time-to event...

Suavización no paramétrica en fiabilidad.

M.ª Angeles Fernández Sotelo, Wenceslao González Manteiga (1986)

Trabajos de Estadística

En este trabajo consideramos estimaciones no paramétricas de las funciones de razón de fallo y supervivencia en fiabilidad haciendo uso de suavizaciones no paramétricas de la función de distribución empírica (datos no censurados) y de la distribución de Kaplan-Meier (datos censurados). Se obtienen sesgos, varianzas y distribuciones asintóticas de los estimadores aquí propuestos probándose mediante técnicas de expansiones de segundo orden la eficiencia de éstos respecto de otras estimaciones introducidas...

Subset selection of the largest location parameter based on L -estimates

Jaroslav Hustý (1984)

Aplikace matematiky

The problem of selecting a subset of polulations containing the population with the largest location parameter is considered. As a generalization of selection rules based on sample means and on sample medians, a rule based on L -estimates of location is proposed. This rule is strongly monotone and minimax, the risk being the expected subset size, provided the underlying density has monotone likelihood ratio. The problem of fulfilling the P * -condition is solved explicitly only asymptotically, under...

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