Estimation and prediction in regression models with random explanatory variables

Nguyen Bac-Van

Displaying similar documents to “Estimation and prediction in regression models with random explanatory variables”

Statistical methods in physico-chemical characterization of newly synthesized compounds.

Djaković-Sekulić, Tatjana, Lozanov-Crvenković, Zagorka, Perišić-Janjić, Nada (2008)

Novi Sad Journal of Mathematics

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General $M$ -estimators in the presence of nuisance parameters. Skew projection technique.

Lazrieva, N., Toronjadze, T. (2003)

Georgian Mathematical Journal

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Robust median estimator for generalized linear models with binary responses

Tomáš Hobza, Leandro Pardo, Igor Vajda (2012)

Kybernetika

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The paper investigates generalized linear models (GLM's) with binary responses such as the logistic, probit, log-log, complementary log-log, scobit and power logit models. It introduces a median estimator of the underlying structural parameters of these models based on statistically smoothed binary responses. Consistency and asymptotic normality of this estimator are proved. Examples of derivation of the asymptotic covariance matrix under the above mentioned models are presented. Finally...

Reference points based transformation and approximation

Csaba Török (2013)

Kybernetika

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Interpolating and approximating polynomials have been living separately more than two centuries. Our aim is to propose a general parametric regression model that incorporates both interpolation and approximation. The paper introduces first a new $r$ -point transformation that yields a function with a simpler geometrical structure than the original function. It uses $r \geq 2$ reference points and decreases the polynomial degree by $r - 1$ . Then a general representation of polynomials is proposed based...

On ergodicity of some cylinder flows

Krzysztof Frączek (2000)

Fundamenta Mathematicae

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We study ergodicity of cylinder flows of the form $T_{f} : T \times ℝ \to T \times ℝ$ , $T_{f} (x, y) = (x + α, y + f (x))$ , where $f : T \to ℝ$ is a measurable cocycle with zero integral. We show a new class of smooth ergodic cocycles. Let k be a natural number and let f be a function such that $D^{k} f$ is piecewise absolutely continuous (but not continuous) with zero sum of jumps. We show that if the points of discontinuity of $D^{k} f$ have some good properties, then $T_{f}$ is ergodic. Moreover, there exists $ε_{f} > 0$ such that if $v : T \to ℝ$ is a function with zero integral such that $D^{k} v$ is of bounded...

Parametrized Cichoń's diagram and small sets

Janusz Pawlikowski, Ireneusz Recław (1995)

Fundamenta Mathematicae

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We parametrize Cichoń’s diagram and show how cardinals from Cichoń’s diagram yield classes of small sets of reals. For instance, we show that there exist subsets N and M of $w^{w} \times 2^{w}$ and continuous functions $e, f : w^{w} \to w^{w}$ such that • N is $G_{δ}$ and $N_{x} : x \in w^{w}$ , the collection of all vertical sections of N, is a basis for the ideal of measure zero subsets of $2^{w}$ ; • M is $F_{σ}$ and $M_{x} : x \in w^{w}$ is a basis for the ideal of meager subsets of $2^{w}$ ; • $\forall x, y N_{e (x)} \subseteq N_{y} \Rightarrow M_{x} \subseteq M_{f (y)}$ . From this we derive that for a separable metric space X, •if for all Borel (resp. $G_{δ}$ ) sets...

A statistical comparison of three goodness-of-fit criteria used in modelling distances.

Love, Robert F., Üster, Halit (2001)

Journal of Applied Mathematics and Decision Sciences

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Borel partitions of unity and lower Carathéodory multifunctions

S. Srivastava (1995)

Fundamenta Mathematicae

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We prove the existence of Carathéodory selections and representations of a closed convex valued, lower Carathéodory multifunction from a set A in $A (ℰ \otimes ℬ (X))$ into a separable Banach space Y, where ℰ is a sub-σ-field of the Borel σ-field ℬ(E) of a Polish space E, X is a Polish space and A is the Suslin operation. As applications we obtain random versions of results on extensions of continuous functions and fixed points of multifunctions. Such results are useful in the study of random differential...

Analytic determinacy and 0# A forcing-free proof of Harrington’s theorem

Ramez Sami (1999)

Fundamenta Mathematicae

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We prove the following theorem: Given a⊆ω and $1 \leq α < ω_{1}^{C K}$ , if for some $η < ℵ_{1}$ and all u ∈ WO of length η, a is $Σ_{α}^{0} (u)$ , then a is $Σ_{α}^{0}$ . We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: $Σ_{1}^{1}$ -Turing-determinacy implies the existence of $0$ .

A note on Tsirelson type ideals

Boban Veličković (1999)

Fundamenta Mathematicae

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Using Tsirelson’s well-known example of a Banach space which does not contain a copy of $c_{0}$ or $l_{p}$ , for p ≥ 1, we construct a simple Borel ideal $I_{T}$ such that the Borel cardinalities of the quotient spaces $P (ℕ) / I_{T}$ and $P (ℕ) / I_{0}$ are incomparable, where $I_{0}$ is the summable ideal of all sets A ⊆ ℕ such that $\sum_{n \in A} 1 / (n + 1) < \infty$ . This disproves a “trichotomy” conjecture for Borel ideals proposed by Kechris and Mazur.

Growth of the product $\prod_{j = 1}^{n} (1 - x^{a_{j}})$

J. P. Bell, P. B. Borwein, L. B. Richmond (1998)

Acta Arithmetica

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We estimate the maximum of $\prod_{j = 1}^{n} | 1 - x^{a_{j}} |$ on the unit circle where 1 ≤ a₁ ≤ a₂ ≤ ... is a sequence of integers. We show that when $a_{j}$ is $j^{k}$ or when $a_{j}$ is a quadratic in j that takes on positive integer values, the maximum grows as exp(cn), where c is a positive constant. This complements results of Sudler and Wright that show exponential growth when $a_{j}$ is j. In contrast we show, under fairly general conditions, that the maximum is less than $2^{n} / n^{r}$ , where r is an arbitrary positive number. One consequence...

On a discrete version of the antipodal theorem

Krzysztof Oleszkiewicz (1996)

Fundamenta Mathematicae

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The classical theorem of Borsuk and Ulam [2] says that for any continuous mapping $f : S^{k} \to ℝ^{k}$ there exists a point $x \in S^{k}$ such that f(-x) = f(x). In this note a discrete version of the antipodal theorem is proved in which $S^{k}$ is replaced by the set of vertices of a high-dimensional cube equipped with Hamming’s metric. In place of equality we obtain some optimal estimates of $i n f_{x} | | f (x) - f (- x) | |$ which were previously known (as far as the author knows) only for f linear (cf. [1]).

Ergodic averages and free $ℤ^{2}$ actions

Zoltán Buczolich (1999)

Fundamenta Mathematicae

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If the ergodic transformations S, T generate a free $ℤ^{2}$ action on a finite non-atomic measure space (X,S,µ) then for any $c_{1}, c_{2} \in ℝ$ there exists a measurable function f on X for which ${(N + 1)}^{- 1} \sum_{j = 0}^{N} f (S^{j} x) \to c_{1}$ and ${(N + 1)}^{- 1} \sum_{j = 0}^{N} f (T^{j} x) \to c_{2} µ$ -almost everywhere as N → ∞. In the special case when S, T are rationally independent rotations of the circle this result answers a question of M. Laczkovich.